Hand Out NVH Seminar IDIADA_SIAM_India

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Fundamentals of Noise, Vibration and Harshness

India Habitat Centre, New Delhi

1

Fundamentals of

Noise, Vibration and Harshness

(Hand out)

20th and 21st March 2007


INDIA

Organised by IDIADA Automotive Technology SA, Spain





2

PROLOGUE

The material presented in this handout is a selection of the most relevant ideas presented

by Applus+ IDIADA during the seminar held at India Habitat Centre, New Delhi, during the20th and 21th of March 2007.

The program covered during this two-day seminar is described below:

Monday, 20 th March 2007

Exterior noise measurements: ISO 362 and 1999/101 EC Exterior noise source ranking Case studies with applications

Fundamentals of body performanceStatic and dynamic aspects of body stiffness and performanceFundamentals of vehicle noise and vibration and its relationship with body stiffness

Tuesday, 21st March 2007

Interior noise measurements and characterisation of vehiclesSound level and sound quality: Are they correlated? Air-borne and structure-borne transmission paths

Experimental methods for analysis of air-borne and structure-borne noise contributions.Breaking down the signals.

Advanced experimental techniques for vehicle noise and vibration analysis

The material was originally designed for professional engineers in the automotive andtransportation industry involved in the analysis of noise, vibrations and durability of components who need a basic understanding of the methodology and modernexperimental techniques for the resolution of problems in these areas.

The material contained in this hand-out summarizes some of the most important ideaspresented during the seminar. The text has been organized so that it covers importantinformation presented in the program and has been rearranged to make it more readableand easy to follow.

The author would like to thank Mr Dilip Chenoy, Mr K K Gandhi and Mr Atanu Ganguli for their help and support in the organisation of the course.

It was the author’s good fortune to have the collaboration of Mr. Indranil Das Gupta whogave a great support in the logistics and many other details related to the seminar.

Juan J. García Ismael Fernández

L’Albornar, Tarragona, Spain

March 2007





3

CHAPTER I

FUNDAMENTALS OF

AUTOMOTIVE ACOUSTICS





4

FUNDAMENTALS OF

AUTOMOTIVE ACOUSTICS

1. INTRODUCTION

All vibrating bodies surrounded by a fluid, gas or liquid compress the layers of fluidadjacent to their surface. This compression is transmitted to the mass of surrounding fluid and is conveyed beyond the body. In these circumstances, thevibrating surface acts as a source of noise. Independently of whether the source of noise radiates in an open space (free field) or in an enclosed space (reverberatefield), the acoustic field at a particular point is determined by the fluctuatingpressure due to the wave propagation. The measurement of this acoustic pressureis of vital importance in any test to quantify the level of noise produced by acomponent or vehicle. Furthermore, the analysis of the variation of this pressure inthe time and frequency domain gives us fundamental information about the originof the noise studied.

2. SOUND AND NOISE

Sound is a disturbance in the balanced state of the air molecules, which vibratedue to the propagation of a compression wave created by a vibrating object. Thisdisturbance is associated with an alternative displacement of the layers of air and

a fluctuation of pressure (acoustic pressure) that, on reaching our ears, producesthe auditory sensation. Sound may generate pleasant or unpleasant sensationsdepending on the spectral and temporal characteristics of the fluctuating pressureaffecting our eardrums.

A clearly unpleasant or annoying sound is called noise. Nevertheless, the level of nuisance does not only depend on the type of sound, but also on our attitudetowards it, for example, a type of music that some people may like, may annoyothers, especially if it is very loud. Another example of the subjectivity of thepossible nuisance of a sound is the sensation that the exhaust system of a sportscar produces: it is pleasant for fans of this type of vehicles, but extremely annoyingfor others.

3. THE NATURE OF SOUND

Sound is defined as a pressure variation that the ears can detect, ranging fromvery low variations to levels that could cause damage. The study of sound is calledacoustics and covers all fields of generation, propagation and reception of sound.Noise is an unavoidable part of daily life and technological development, whichhas produced a notable increase in the noise level coming from machines,factories, traffic, etc.





5

Figure 1 consists of a piston mounted at the end of a cylindrical tube producing analternative forward and backward movement. When the piston moves forwards,the particles near to its surface accumulate creating a compression zone, when itmoves backwards, the particles separate creating a rarefaction zone or dilation. Incompression, the air pressure will be a little higher than its value of balance and indilation it will be a little lower. Therefore, a series of compressions and dilationswill be created along the tube. Thus, a sound wave will be generated in the tube,which can be heard at the other end. The speed of sound propagation along thetube is a function of the elasticity and air density, which depend on the staticpressure and temperature. At atmospheric pressure and at 20ºC the speed of sound in air is 344 m/s.

Figure 1. Vibrating piston at the end of the tube generates a compression wave that propagatesalong the tube, producing a compression and rarefaction (wave) which propagates at the speed of sound (345 m/s).

Figure 2 shows the variation of pressure around the static value Po (atmosphericpressure) as a function of time for a generic point inside the tube. The maximumfluctuation is called sound amplitude and the number of oscillations per secondthat coincide with the rhythm of vibration of the piston is called the sound frequency . We will call this sound a pure tone because it has been created by asound source that oscillates at a single frequency.

Very few man-made noises or natural sounds are pure tones. Even the sounds of a musical instrument, which seem to be made up of a clear single note, containmore than one frequency. Normally the sensation of frequency that we perceive(tonality) corresponds to the dominant frequency of the sound heard.

The range of audible frequencies, for a young and healthy person, goes fromapproximately 20 Hz up to 20,000 Hz. Frequencies below 20 Hz give rise toinfrasound and frequencies higher than 20 kHz to ultrasound. On the other hand,as we will see later on, not all audible frequencies are perceived equally by thehuman ear.

PistonCompression

Rarefactions

Fluctuating

speed Direction

ofpropagation





6

Figure 2. Variation of acoustic pressure with time at a particular point in the tube, which is inducedby the vibration of the piston. If that vibration is sinusoidal, pressure will follow the same trend.

4. THE HUMAN EAR

The ear is responsible for hearing and balance. It is divided into three zones:external, middle and internal. Acoustic perception is due to the excitation of theeardrum by the pressure fluctuation associated with the acoustic wave. Figures 3and 4 show a section of the human ear with its most important parts labelled.

4.1. Structure of the ear

The human ear is a sensor. It combines mechanical, fluid dynamic and electricalaspects, inducing a sensation of sound in the brain, which is then processed byelectrical information generated in the nerve cells. As a general rule, the ear canbe described as a membrane (eardrum) sensitive to the variations of acousticpressure which are linked to a system of levers formed by three tiny bones thatamplify the vibration. This vibration is then transmitted to a tube (cochlea)

containing a viscous fluid, producing pressure changes perceived by nerve fibreswhich generate electrical impulses proportional to the pressure perceived. Thebrain later processes these impulses in order to generate a specific soundsensation.

The outer ear includes the ear or external earlobe and the external ear canal,which is about three centimetres long. Figure 4 shows the internal structure of the human ear. The middle ear is located in the eardrum cavity, whose externalpart is formed by the eardrum, which separates it from the external ear. Itincludes the mechanism responsible for conducting sound waves to the internal

ear - a narrow canal that extends about fifteen millimetres vertically and another fifteen horizontally. The middle ear is connected to the nose and the throat

Piston

Fluctuating

SpeedDirection

of

propagation

Time (s)

P





7

through the Eustachian tube, permitting the entrance and exit of air from themiddle ear in order to balance the pressure differences with the exterior. There isa chain formed by three small, mobile bones crossing the middle ear. Thesethree bones are called the hammer , anvil and stirrup. They connect the eardrumacoustically to the inner ear, which contains a liquid. The function of the threebones is to mechanically amplify the vibration generated by the incident acousticwave in the eardrum.

The inner ear , or labyrinth, is inside the temporal bone containing the auditoryand balance organs, which are connected by the filaments to the auditory nerve.This is separated from the middle ear by the “fenestra ovalis”, or oval window.The internal ear consists of a series of membranous channels housed in a densepart of the temporal bone, which are divided into the cochlea (from Greek, snail

bone), the vestibule and three semicircular canals. These three channels arelinked together and contain a jelly-like fluid called endolymph.

4.2. Auditory capacity: considerations on the perception of sound

Sound waves are transmitted through the external auditory canal to the eardrum,where vibration is produced. These vibrations pass to the middle ear by means of the chain of small bones (hammer, anvil and stirrup) and, through the ovalwindow they reach the liquid in the internal ear. The movement of the endolymph

produced by the vibration of the cochlea stimulates the movement of a group of fine hairs, called hair cells. The group of hair cells constitutes the organ known asCorti, and they transmit signals directly to the auditory nerve, which takes theinformation to the brain. The response of the hair cells to the vibrations code theinformation about the sound to be understood by the brain.

Figure 3. Structure of the ear. The external parts are called the outer ear, which is the visiblearea of the ear, and the ear channel, closed at the end for trapping the dirt. This channel

transmits the changes in pressure to the air, and the sound waves to the eardrum, or eardrummembrane.

Acoustic

wave

Forced vibration

at the eardrum

Cochlear section

Auditory nerve

Eardrum canalCochlear canalVestibular canal

Vestibular canalCochlear canal

Hair cellsBasilar membrane

Nervous fibresEardrum canal





8

Figure 4. Structure of the ear. The eardrum is the start of the middle ear, which includes theEustachian tube and the three small vibrating bones: hammer, anvil and stirrup. The cochlea andthe semicircular canals make up the inner ear. The information goes through the inner ear to thebrain via the auditory nerve.

The audible range varies from one person to another. The maximum audible rangein man includes sound frequencies from 20 up to 20,000 cycles per second. The

smallest change in tone that can be detected by the ear varies according to thetone and volume. The most sensitive human ears are able to detect changes inthe frequency of vibration (tone) that corresponds to 0.03% of the originalfrequency, in the range between 500 and 8,000 Hz. The ear is less sensitive tochanges in frequency for sounds of low intensity or frequency. The sensitivity of the ear to the intensity of the sound (volume) also varies with frequency. From1000 to 3000 cycles the sensitivity of the ear is better and changes of 1 decibelcan be detected. This sensitivity is reduced when the sound pressure level is low.

The difference in the ear’s sensitivity to loud sounds causes several importantphenomena. Very high tones produce subjective effects of different tonality in theear that are not present in the original excitation. It is probable that thesesubjective tones are produced by imperfections in the natural function of themiddle ear. The discordance of the tonality that produces the increases in theintensity of sound is a consequence of the subjective tones that are produced inthe ear. This happens, for example, when the volume control of a radio isadjusted. The intensity of a pure tone also affects its intonation. High tones mayincrease with the intensity. Low tones tend to get lower as the intensity of thesound increases. This effect is only perceived in pure tones. Since most musicaltones are complex, in general, hearing is not appreciably affected by thisphenomenon. When sounds are masked, the production of harmonies of lower

tones in the ear could reduce the perception of the highest tones. That is why it isnecessary to raise our voice in order to be heard in noisy places.

Amplifying lever

system in the

eardrum cavity

External

earlobe

Auditory canal Temporal bone Anvil

Hammer

Semicircular canals

Auditory

nerve

Stirrup

Eardrum Eustachianube

Cochlea





9

5. SOUND PRESSURE: THE DECIBEL

As described above, sound is made up of a series of oscillations of pressure inrelation to atmospheric pressure. Therefore, it is logical to think that this pressureis the most obvious parameter to express the magnitude of the sound field. Strictlyspeaking, the amount to measure is the difference between the fluctuating value of pressure and its value of balance P o (atmospheric pressure). However, as thefrequency of the wave increases it is more difficult to measure these fluctuationssince they become faster. It is obvious that, even for the lowest vibration able toproduce audible sound, it is necessary to make a time average that serves as anindicator of the amplitude of the signal. The way this average is calculated is asfollows:

• Square all the values of pressure difference during any cycle. Hence,negative values become positive

• Average

• Calculate the square root

The final result is known as the effective value or r.m.s (root mean square) valuerepresented as prms. From now on we will refer to the value of acoustic pressurethat characterises an acoustic field at the measuring point as the r.m.s value of thepressure difference.

Mathematically, this is expressed by

( )∫ =T

rms dt t pT

p0

21(1)

The measurement unit of pressure is the newton/m2, called Pascal (Pa). Typicalacoustic pressures have values of fractions of a Pascal, whereas atmosphericpressure is approximately 100,000 Pa (=1 atmosphere). Therefore, sound wavesare associated with tiny variations in air pressure.

Unfortunately, the measurement of sound pressure directly in Pascal gives rise toa series of difficulties, whose origin comes from the characteristics of the humanear, and which are explained below:

• The pressure range that the human ear can perceive is wide. The weakestsound pressure that can be perceived by a normal, healthy person is 2·10-5Pa at a frequency of 1000 Hz (auditory threshold), while the sound pressurethat begins to be painful is 100 Pa (pain threshold). That is, the scale of audible pressures covers a dynamic range of 1 to 5.000.000, which leads tothe use of unmanageable numbers.

• Our auditory system does not respond lineally to the stimuli that we receivebut rather has a logarithmic form. For example, if the pressure of a pure





10

tone of 1 kHz is doubled, the sensation produced by it will not be double.This is a clear demonstration of the non-linearity of hearing.

For these two reasons it seems reasonable to use a logarithmic scale in order toquantify the sound pressure. However, as the logarithm of a number lower than 1is negative, this would mean that any sound pressure whose value were a fractionof 1 Pascal would be expressed by a negative number. In order to avoid thisproblem a reference amount for which it will always be necessary to divide thecorresponding pressure before taking logarithms is introduced. This amount is infact the threshold of perception, that is, 2·10-5 Pa. Based on this, the level of soundpressure is defined by:

ref ref p

p

p

pSPL log20log10

2

2

⋅=⋅= (2)

This expression is called the sound pressure level and is measured in decibelsrelative to 2·10-5 Pa. The word level is added to indicate that the amount has acertain level above a pre-set reference value. The acronym SPL is used or thesymbol L p.

6. ACOUSTIC INTENSITY

Another parameter of interest in the definition of an acoustic field is the intensity.

The intensity of a sound wave is the amount of acoustic energy crossing the unit of area normal to the direction of propagation of the wave per unit of time. Therefore,it is expressed in units of power (energy per unit of time) per surface unit, that is, inwatt/m

2. In the case of a flat wave, as seen in the tube in Figure 1, the acoustic

intensity is given by:

c

p I

ρ

2

= (3)

Where p is the acoustic pressure (r.m.s), ρ is air density (kg/m2) and c denotes the

sound speed (m/s). Figure 5 illustrates the concepts associated with themeasurement of intensity. The vector crossing the plane that denotes the unit of area indicates acoustic power and has information about its associated direction.

As with the sound pressure, one can talk about the sound intensity level definedas

ref I

I SIL log10 ⋅= (4)

Where SIL is the sound intensity level, I is the intensity in W/m2 and I ref is the

intensity of reference that, in this case, is taken as 10 -12 watt/m2. The





11

measurement of sound intensity offers the opportunity to detect in situ the area of a vibrating surface that emits more noise. In this context, the expression emitsmore noise suggests that the surface injects acoustic energy into the environmentand acts like a loudspeaker. Intensimetry may also reveal those parts of a surfaceacting as energy drains and subsequently absorbing noise.

Figure 5. Acoustic field created by a source expands when going away from the vibrating surfacewhich generates it. The measure of acoustic intensity in a particular point of the acoustic field

indicates the power going through the perpendicular section into the direction of propagation.

It is of vital importance to keep in mind the vectorial nature of the measurement of intensity, i.e. all measurements of intensity have amplitude and direction.Therefore, it is very useful for the location of sources in acoustically complexspaces to be known.

7. ADDITION AND SUBTRACTION OF DECIBELS

7.1. Addition of decibels

When two sound sources radiate sound they both contribute to the existing soundpressure level at a point far from both sources. Let us assume that SPL1 and SPL2 are the sound pressure levels due to two sources that are radiatingsimultaneously. The acoustic pressure at a point in the space associated witheach source is given by

102

12

2

11

1

10log10

dB

ref

ref

p p p

pSPL ⋅=⇒⋅=

(5)

Acoustic

source

Pressure P

Unit area

perpendicular to

the direction of

propagation

Acoustic Power (Intensity vector)





12

102

22

2

22

2

10log10

dB

ref

ref

p p p

pSPL ⋅=⇒⋅=

In order to know what is the total sound pressure produced by the acousticsurfaces; we will refer to the concept of intensity established previously: intensity isthe energy per unit surface and per unit of time. Therefore, it seems logical to thinkthat the intensity due to both sources will be the sum of the intensities of eachsource. We have also seen that intensity is proportional to the r.m.s. pressuresquared (equation (3)). From this we can deduce that the r.m.s. pressure squareddue to the two sources will be the sum of the r.m.s. pressures squared for each of the sources; therefore, it will be

1021022

2

2

1

221

1010

dB

ref

dB

ref p p p p p ⋅+⋅=+= (6)

And the total sound pressure level will be

⎟⎟ ⎠

⎞⎜⎜⎝

⎛ +⋅=

⎟⎟ ⎠

⎞⎜⎜⎝

⎛ +

⋅=⋅=+ 10102

10102

2

2

21

21

21

1010log10

1010

log10log10

dBdB

ref

dBdB

ref

ref p

p

p

pdB (7)

This result could be extended to n sources, i.e.

⎟⎟ ⎠ ⎞⎜⎜

⎝ ⎛ ⋅= ∑=

n

i

dB

n

i

dB1

1010log10 (8)

According to equation (8), the sum of two equal levels of SPL produces anincrease of 3 dB. Therefore, two sources producing individually a sound level of 80dB at a certain point will generate a total pressure of 83 dB when actingsimultaneously.

7.2. Subtraction of decibels

In some cases it is necessary to subtract levels of noise. By means of amathematical development similar to that explained in the previous section it isdeduced that the difference of two levels of noise given by dB1 and dB2 is

⎟⎟ ⎠

⎞⎜⎜⎝

⎛ −⋅=⋅=− 1010

2

2

21

21

1010log10log10

dBdB

ref p

pdB (9)

The most usual case of the subtraction of decibels arises when we need tomeasure the noise of a component in the presence of background noise. In thesecases it is important to know if the measured noise is dominated by the noise of





13

the machine, the background noise or by a combination of both. The procedure isas follows

a) The total existing noise with the component in Ls+n operation is measured.b) The component is stopped or encapsulated and the background noise

measured Ln.c) The ∆L difference is calculated = LS+N - LN.

If ∆L is less than 3 dB the background noise is too high for an accuratemeasurement and, therefore, the level of noise produced by the component cannot be measured accurately as long as the background noise does not decrease.On the other hand, if the difference is above 10 dB, the background noise can beignored. If the difference is between 3 dB and 10 dB, the correct level of noise canbe found using equation (9).

8. FREQUENCY WEIGHTING SCALES

Section 4 demonstrated that the human ear is not consistent in its sensitivity todifferent frequencies. Therefore, the ear will perceive a sound at 1,000 Hz withgreater intensity than one of the same intensity at 200 Hz. In order to take intoaccount this phenomenon weighting scales of different frequencies have beenstandardised. These are shown as A, B, C and D in Figure 6. Initially, theseweighting scales were developed for different levels of noise: scale A was for lownoise level (40 dB), scale B for medium sounds (70 dB) and scale C for loudsounds (100 dB). However, in the end scale A has been applied universally to alllevels. Scale D is used exclusively for aircraft noise.

-60

-50

-40

-30

-20

-10

0

10

20

10 100 1000 10000 100000

Hz

d B

A

B

C

D

Figure 6. Weighing frequency scales A, B, C and D.

It is important to observe that scale A noticeably attenuates frequencies below 300Hz. This aspect should be borne in mind in the analysis of vehicle interior noise atlow speeds since this is dominated by the structural excitation that the engine

introduces into the passenger compartment, predominately at low frequencies (<200 Hz).





14

9. NOISE CONTROL

The term noise control refers to all those techniques that reduce the level of

acoustic pressure at a point in free space or inside a given enclosed space. Themethod used to get this noise reduction (or control) basically depends on the levelof understanding of the noise source and of the difficulty and cost associated withimplementing this method. The techniques of noise control most commonly usedat present are based on the following principles:

• Acoustic isolation

• Acoustic absorption

• Reduction of the excitation force that acts on the radiant surface

• Reduction of the level of vibration on the surface of the source

• Reduction of the transmissibility of the medium of propagation (air/structure)

• Cancellation of noise through destructive interference (active noise control)

Of the above techniques, the first two stand out for the simplicity of their application in a great number of situations. Acoustic isolation and absorption usethe idea of inserting an acoustic barrier combined with noise-absorbing materials.The combination of both principles could be used in those cases in which thenoise problem is found at high frequencies (> 1 kHz). However, these methods areineffective in reducing noise at low frequencies (< 400 Hz) since; in this case, thewavelength of the sound to be controlled is much greater than the thickness of the

materials and the absorbents used in the construction of the barriers (or encapsulation).

Noise does not always spread freely in space (propagation in free field). On manyoccasions the sound reaches obstacles such as roofs, walls and structural panelswhich cause reflections. Vehicle engine noise, for example, finds an obstacle inthe wall that separates the engine compartment from that of the passengers (thefirewall). A car with the bonnet open is noisier (external noise) than with bonnetclosed since the bonnet obstructs the noise escaping to the exterior. When anacoustic wave reaches a solid surface, such as the firewall of a vehicle, part of theacoustic energy is transmitted to the other side of the barrier, another part is

reflected and the barrier absorbs the rest. Figure 7 shows the distribution of theacoustic energy of a wave that hits a barrier of this type.

Isolation and absorption are the two characteristics that make a materialinteresting from an acoustic point of view. They are two different characteristics,but the combination of both is very desirable from the point of view of noisecontrol.





15

Transmitted sound

E t

Absorbed sound

by calorific

dissipation

Incident sound

E i

Reflected sound

Heat

Acoustic barrier

Figure 7. Sound reflected, absorbed and transmitted. The energy of the incident wave is notdestroyed, it is only reflected and transformed into heat. The rest of the energy generates atransmitted acoustic wave of lower amplitude than the incident wave.

10. ACOUSTIC ISOLATION

As mentioned previously, when a sound wave hits a barrier or panel, part of theincident energy is transmitted and part is reflected or absorbed by the panel. It issaid that a material is a good noise insulator when the sound energy transmitted is

small compared to the incident energy, i.e., when it does not allow the sound topass through it.

The coefficient that quantifies the isolation of a barrier or encapsulation is calledtransmission loss or TL and is defined as the relationship between the acousticenergy that hits the barrier and the acoustic energy that passes through it, i.e.,

t

i

E

E TL log10= (10)

Where TL is the transmission loss, E i the incident energy and E t is the transmittedenergy. This coefficient will be greater when the isolation capacity is higher. The

transmission coefficient τ is also defined as the relationship between thetransmitted energy and the incident energy. This coefficient can be expressed as

i

t

E

E =τ (11)





16

Where τ denotes the transmission coefficient, E i is the incident energy and E t isthe transmitted energy. Naturally, it can be verified that,

τ

1log10log10 ==

t

i

E

E TL (12)

10.1. Measurement of acoustic isolation

If we consider a barrier separating two cavities, as shown in Figure 8, isolation isdefined as the difference in the sound pressure level (in dB) between the two

cavities when one of them is acoustically excited, that is 21 L L D −=

Figure 8. Layout for the measurement of the transmissibility of acoustic barriers separating twocavities. Level L1 is the acoustic energy of the cavity that excites the wall and the level L2 is theproportion of the acoustic energy that has crossed it.

Normally the difference level D is corrected by the reverberation time of thereceiving cavity, since the isolation of the separating panel must be independent of the conditions of the cavity. If the receiving cavity has a very high reverberationtime, the sound level in a particular volume of air will increase in comparison to

another cavity that has a lower reverberation time. This leads to a lower isolation

L1 L2

Soundsource

L1

L2





17

value. In order to solve this problem some corrections, dependent on thereverberation time of the cavity, are used. The corrected level is equal to

⎟ ⎠ ⎞⎜⎝ ⎛ += 5.0log10

T D DnT (13)

And is known as the standardised level difference. In equation (13), T denotes thereverberation time of the receiving cavity. This time is defined as the time neededfor the sound pressure level in a cavity to fall 60 dB after eliminating its acousticexcitation. The reverberation time is due to the reflections that the waves undergoon colliding with the surfaces that make up the cavity. A high reverberation timeindicates that the acoustic energy in the passenger compartment dissipatesslowly.

The transmission of sound through a vehicle’s structural panels depends on:• The direct transmission through the separating panels between the noisy

zones and the passenger compartment

• The transmission of secondary paths

• The internal losses of the structure caused by friction and damping of thestructural materials

The transmission and attenuation of noise by means of panels is very common inthe automotive industry. In general, the passenger compartment is soundproofedfrom external noise by the isolating effect of certain panels that, as well as havinga structural purpose, lessen the airborne noise produced by the engine, rolling andair turbulence of the moving vehicle. Therefore, the study of the physical principlesthat control the transmissibility of panels is very important.

10.2. Panel Isolation. Simple panel

We shall consider a flat sound wave that hits an elastic panel at a given angle of incidence. Under the influence of the sound wave the panel will bend as shown inFigure 9. The displacement of the panel due to the sound pressure on one of itssides will generate sound pressure on the other side. Applying Newton’s law to themovement of the system, the reduction of noise through the panel will give us afunction that depends on: the panel mass M per unit surface, the frequency f of excitation and the incident angle of the wave θ . This reduction (in dB) is given by

⎟⎟ ⎠

⎞⎜⎜⎝

⎛ =

c

Mf R

ρ

θ π coslog20 (14)

Where M is the superficial mass of the panel in kg/ m2, f is the frequency of the

acoustic wave (Hz), θ denotes the incident angle of the sound wave, ρ is the air density (kg/m

3) and c is the speed of sound (m/s).





18

Figure 9. The spatial distribution of pressure produced by an incident wave on the panel generatesflexion waves that will radiate noise. This noise radiation of the panel causes the transmission of some incident acoustic energy by the panel.

From the previous equation we can obtain the first two laws of isolation of a simplepanel, which are the mass law and the frequency law. That is:

• The mass law states that every time we double the mass per unit area of the panel, the isolation increases by 6 dB

• The frequency law states that every time we double the frequency, theisolation increases by 6 dB

Until now, a specific value for the angle at which the sound wave hits the panelhas been considered, but in reality the incidence of the sound is totally randomand we cannot know all the incidence angles. A correction factor has been foundexperimentally which takes into account this effect, and it consists of subtracting 3dB from the above equation. It is known as random incidence, noise reduction andis given by

dBc

Mf

R 3log20 −⎟⎟ ⎠

⎞⎜⎜⎝

⎛ = ρ

π

(15)

Figure 10 shows the equation (15) for a variation of M between 5 and 15 kg/ m2 and a frequency range between 500 Hz and 2kHz. It can be seen that R increaseswith M and f .

θ θ

λ

θ θ

λ

λB

Incident

waveIncident

wave

Reflected

wave

Reflected

wave





19

The panel has an internal elasticity and a mass per surface unit that determines itscharacteristic resonance frequencies. These affect the isolation of the panelmainly at low frequencies since these resonances imply structural weaknesses.We can find the resonance frequencies for a simply supported panel from theexpression

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ ⎟⎟ ⎠

⎞⎜⎜⎝

⎛ +⎟ ⎠

⎞⎜⎝

⎛ ⋅−

=22

2 )1(122 y

m

x

n E h f res

υ ρ

π (16)

Where E is the Young’s modulus, I is the inertia moment, ρ denotes the surfacedensity of the panel (kg/m2), h is the thickness of the material, ( x , y ) represent thephysical dimensions of the panel and (m,n) are integer numbers.

Figure 10. Variability of transmissibility R with M and f (equation 15).

In equation (16), υ represents the Poisson’s ratio, which for steel is 0.3. The lowestresonance frequency corresponds to the pair of numbers (n= 1, m= 1). Figure 11shows the shape of this vibration mode for a panel where x= 1 m and y= 0.5 m. Inthis vibration mode the panel is displaced in phase when vibrating, so that thepanel will be very effective in compressing the air of the adjacent layers.Therefore, their transmissibility will be high at the resonance frequencycorresponding to the structural mode.

f (Hz) M (kg/m2)

R

Transmissibility R





20

Figure 11. Modal shape of a simply supported panel for (m,n)=(1,1).

10.3. Coincidence effect

The energy lost in resonance is small and depends on the damping of the materialor that of the panel supports. From the second frequency of lowest resonance, theisolation begins to follow the mass law (zone of control for mass). This continuesuntil it reaches the limit frequency called the coincidence frequency, in which the

length of the sound propagation wave is equal to the wavelength of the bendingwaves of the panel. This coincidence condition means that the panel would beparticularly ineffective for isolation.

Sound spreads in the air by longitudinal waves at the same speed for allfrequencies. Nevertheless, in solid structures sound can be spread by transverse,longitudinal or bending waves. The most important for noise generation are thebending waves. Unlike longitudinal airborne waves, bending waves travel atdifferent speeds depending on the frequency. This speed increases withfrequency. This means that for each frequency above the value of the criticalfrequency of the panel, there is an incidence angle for which the bending

wavelength is equal to the sound wavelength hitting the panel.

The condition of coincidence is fulfilled when

sinθ = Bλ

λ (17)

Where

λ = acoustic wavelength,

λB = bending wavelength of panel.

X (m)Y (m)

Mode (m,n) = (1,1)





21

This condition is very important since at the coincidence frequency the isolation isno longer controlled by the mass. In theory, at the coincidence frequency theisolation would be zero, but due to damping this can not be so.

We can calculate the coincidence frequency of a panel from the equation

B

M c f c

π 2= , where

)1(12 2

3

υ −=

h E B d (18)

Where

c = speed of sound in the air M = mass per unit area (kg/ m2)E d = elasticity modulus of the panel material

υ = Poisson’s modulush= thickness

The ideal isolation curves of a simple panel can be divided into four regionsnamed according to the mechanism that governs the value of the noise reductioncoefficient. These are:

• Control by stiffness

• Control by resonance

• Control by mass

• Control by coincidence

The idealised curves of isolation for a wall are shown in Figure 12. In the controlby resonance range the variations of the noise reduction value will be greater or smaller according to the damping characteristics of the panel. The control by massranges from the lowest resonance frequency to the coincidence frequency. Thesetwo frequencies fulfil the laws of mass and frequency described above. From thecoincidence frequency we obtain control by coincidence that will be dealt withlater. Note that the damping only acts at the resonance and frequency of coincidence. In general, for a given material, increasing the thickness reduces the

frequency of coincidence.





22

Figure 12. Ideal isolation curve of a simple panel.

10.4. Control by coincidence

From the frequency of coincidence, the equation expressing the isolation of asimple wall is:

dB f

f

c

Mf R

c

3log10log10log20 −+⎟⎟ ⎠ ⎞⎜⎜⎝ ⎛ +⎟⎟

⎠ ⎞

⎜⎜⎝ ⎛ = η ρ

π (19)

Where

M = mass per unit area of the wall (kg/ m2)f = frequency

ρ = air densityc = speed of sound in air f c = frequency of coincidence

η = damping coefficient

In this zone, every time we double the frequency the increase in isolation is 9 dB.If we double the mass the isolation increases by 6 dB, and if we double thedamping of the isolation the increase in isolation is 3 dB.

10.5. Double panel

Two simple panels separated by an elastic material, a damping material or air,basically form a double panel. In this case, the factors that affect sound reduction

are:

6 dB/octave

9 dB/octave

Control

by

stiffness

Control

by

resonance

Control

by

mass

Control

by

coincidence

R (dB)

f (Hz)

f c





23

• The individual behaviour of each panel

• The joining between the two panels

• The acoustic absorption of the elastic or damping material

A double panel can be described as two masses joined together by an elasticelement with a given stiffness, as shown in Figure 13.

Figure 13. Equivalent system to double panel

This tells us the system will have a resonance frequency f 0 that can be calculatedby:

⎟⎟ ⎠

⎞⎜⎜⎝

⎛ +=

21

11

2 M M d

c f o

ρ

π (20)

Where

c = sound speed propagation in the air,

ρ = density of the material placed between the two panels,

d = distance between the two panels,M1 and M2 = surface density of the panels.

If the material placed between the two walls were air, we would have:

⎜⎜⎝

⎛ ⎟⎟ ⎠

⎞+=

21

11160

M M d f o (21)

From these two expressions we can deduce that by increasing the masses or thedistance between the walls, we will decrease the resonance frequency of thedouble panel.

10.6. Curve of isolation of a double panel

Below the first resonance frequency of a double panel the curve of isolation has aslope of 6 dB/octave since it behaves as a simple wall of mass equal to the sum of the mass of each panel. In this case, the noise reduction can be calculated as

)(

⎜

⎜

⎝

⎛ −⎟⎟ ⎠

⎞+= dB

c

f M M R 3log20 21

ρ

π (22)

M1 M2

StiffnessForceOscillating

speed





24

where M 1 and M 2 are the superficial masses of each panel.

The location of the first resonance frequency of the double panel tells us thefrequency above which the isolation is controlled by the double panel effect. In thiszone R increases with a slope of +18 dB/octave. In practice, a curve of noiseisolation with a slope of +18dB/octave is rarely obtained since a double panel isnot a pure mass-spring-mass system.

On the other hand, since there is a separation between both panels, this mayproduce a resonant cavity phenomenon that is created by stationary wavesbetween the panels, which may generate a very irritating pure tone noise. Thisphenomenon occurs when half a wavelength fits inside the panels. From thisrelationship we can find the lowest frequency at which this phenomenon occurs

2

λ nd = (23)

f

cnd

f

c

2=⇒=λ (24)

,...3,2,1,1702

=≈= nd

n

d

nc f g (25)

At the frequency, f g , that this phenomenon occurs, the isolation decreases.Therefore, whenever a double panel is installed some kind of material should befitted between the two faces; mainly an absorbent, such as glass fibre, basaltwool, etc. This step will eliminate the formation of stationary waves.

From this we can determine the isolation curve of a double panel. As has beenmentioned previously, below the first resonance frequency the slope is +6dB/octave. Between this resonance frequency and the first frequency of coincidence or the frequency in which the resonant cavity effect takes place theslope is +18 dB/oct. If the resonant cavity effect is eliminated, then from the first

frequency of coincidence the total isolation of the double panel is equal to the sumof the isolation of the two individual panels. Figure 14 shows the slopes of thenoise reduction curve associated with a double barrier.





25

18 dB/octave

12 dB/octave

R (dB)

f (Hz)

fo min (fc, fg)

Figure 14. Ideal Isolation curve of a double panel

10.7. Secondary transmission paths

Not all sound transmitted from one cavity to another passes through the isolationpanel. In practice, there are other possible transmission paths (secondary paths)that often mean that the isolation is not as good as expected.

In all structures there are several transmission paths. All secondary transmissionpaths reduce the direct isolation calculated in the previous sections. In general, thegreater the attenuation introduced by a barrier, the greater is the percentage of energy transmitted by the secondary paths.

11. ABSORPTION

Materials are good noise absorbers when the sound energy dissipated inside thematerial is an important part of the incident energy. This absorbed energy isnormally transformed into heat by the material. Therefore, the material needs to beporous since the air inside the pores vibrates transforming the kinetic energy of thewave into heat through friction.

The parameter, which would characterise the absorption of these materials, iscalled the absorption coefficient, defined as the relationship between the acousticenergy absorbed by the material and the incident energy on their external surface.This coefficient depends on the frequency of the sound, on the angle of incidenceof the acoustic wave and on the disposition or assembly of the material.





26

11.1. Classification of absorbent materials

Absorbent materials can be classified according to their absorption mechanismand the frequency characteristics of their absorption coefficient. The mostimportant groups are (see Figure 15):

1) Porous materials: They transform acoustic energy into calorific energy as aconsequence of friction of air particles against the body of the material. Themagnitude of the absorption at each frequency depends on the speed of air vibration.

2) Resonators: in these materials the pressure of the acoustic perturbation

displaces a mass of air or solid which, through internal friction, transformsthe acoustic energy into heat. As is known, maximum displacements willoccur at the characteristic frequencies of the system and, subsequently, inthose frequencies the absorption is at a maximum.

Frequency

α

Porous

material

Frequency

α Resonator Resonance

requency

f r

Figure 15. Frequency characteristics of porous absorbent materials and resonators

11.2. Types of porous absorbent materials

Porous absorbent materials are generally found in the form of blankets, carpets,mats and composites. Some typical composites are:

• Textile fibres: cotton, wool, etc.

• Mineral fibres: basalt wool, asbestos, fibreglass, etc.

• Wood fibres: wooden wool, sawdust, etc.

• Vegetable fibres: jute, coconut, etc.

• Open-pore polymers derived from petroleum: polyurethane, PVC, etc.

• Metals: rustproof steel wool.

From these materials many forms of acoustic absorbent components aremanufactured, with higher or lower density and stiffness depending on the specific





27

application. In this type of absorbent material the vibrating air particles are slowedby the friction of the fibres of the material, losing part of their acoustic energy.

For each frequency, the absorption coefficient reaches its maximum value whenthe thickness of the material is such that it covers at least a maximum of acousticspeed. The first of these maximums is located a distance from the rigid wall equalto a quarter of the sound wavelength to be absorbed. Logically this means that, inorder to get high absorption at low frequencies, the thickness and the spaceoccupied by the porous material is important. Since the dissipation of acousticenergy is obtained mainly in the maximum speed zone, in order to save material,one can ignore the zone nearest to the wall where the speeds are lower. This isachieved by leaving an air chamber between the absorbent material and the wall.

For random incidence, where the acoustic waves hit the absorbent material from

any direction, leaving a space between the absorbent and the wall lower than or equal to a third of the thickness of the porous material, the coefficient of theresulting absorption is similar to that which would be obtained with 33% moreporous padding material attached to the wall. The choice of fitting this air chamber or not would be made for economic reasons, taking into account not only the costof the material but also its installation.

11.3. Resonators

Resonators are acoustic elements with a mass of air contained in a cavity which isconnected to the surrounding environment and, therefore, to the acoustic wave to

be absorbed, through a small window. When an appropriate frequency wave hitsthe window of the resonator the interior air oscillates with great amplitude(resonance) and it behaves like an energy-dissipating element.

11.3.1. Helmholtz Resonator

A Helmholtz resonator is a volume of air, V , contained between rigid walls, with asmall opening of area S and length L (Figure 16). This cavity presents thepeculiarity that at a certain frequency, depending on the volume of the resonator and the dimensions of the opening, the sound pressure inside the resonator ismuch greater then that in the inlet section. At this resonance frequency, the air

near to the inlet section, S , oscillates with great amplitude and dissipates energy.





28

Figure 16. Basic geometry of a Helmholtz resonator

This phenomenon is known as resonance and is similar to that obtained with amechanical system made up of mass and spring. In this case, the mass of thesystem can be assimilated to the mass of air in the neck of the resonator and thespring would have the constant of stiffness equal to the compressibility of the air contained in V volume. The resonance frequency of the system in Figure 16 canbe calculated by the expression

LV

S c f

π 2= (26)

Where c is the speed of sound in air (m/s), S is the neck section of the resonator (m

2), V the volume of the resonator (m

3) and L is the apparent length of the neck

of the resonator (m). This length is given by

r L L f 6.1+= (27)

Where Lf denotes the physical length of the neck or window and r is its radius. If the area of the neck is not circular r can be considered as the radius of the circleequal to the real neck area.

11.3.2. Membrane resonator

A flexible membrane with a small air chamber behind behaves very much like aHelmholtz resonator. The resonance frequency of this type of resonator can becalculated by the expression:

mh

c f

ρ

π 2= (28)

Acoustic

wave

V

L

S





29

where f is the resonance frequency (Hz), c is the speed of sound in air (m/s),indicates the air density (kg/ m3), m is the surface density of the membrane (kg/m

2) and h is the distance between the membrane and the rigid wall.

11.3.3. Multiresonators

Perforated metal sheets with a space of air behind can be considered as multipleHelmholtz resonators with a volume equal to the total volume divided by thenumber of perforations. This type of resonator is widely used in the design of vehicle mufflers. As established above, the frequency of a Helmholtz resonator is

lV

S c f

π 2= (29)

n

hlS

S c f

v

π 2= (30)

Where n is the number of holes considered in the area S v . If porosity is given by

v

or S

Sn P = (31)

and the equivalent length of the holes is

r L L f 6.1+= (32)the resonance frequency of a metal sheet perforated with holes of radius r andseparated by a distance h from the rigid wall is

hr L

P c f

f

or

)6.1(2 +=

π (33)

By combining many different diameters of holes we can amplify the frequencyband of maximum absorption.

12. AUTOMOTIVE APPLICATIONS

12.1. Evaluation of ambient urban noise

12.1.1. Considerations regarding the effect of noise on people

The fact that ambient noise may produce negative effects on people’s health hasencouraged investigation into the field and motivated the fight against noisepollution. In general, the effects of noise on health (understood not as the absenceof illness, but in a much wider sense, as total physical, mental and social well-

being) are generally classified into six main groups:





30

• Effects on the auditory system

• Harmful effects due to stress

• Sleep disturbance

• Interference with oral communication• Effects on mental and psychomotor activity

• Subjective nuisance

The results obtained by numerous investigators confirm that noise is a veryimportant environmental problem with evident repercussions on the health andwell-being of a very high percentage of the population. Figure 17 summarisescurrently recognised effects of noise on people.

SONOROUS STIMULI

(Spectral-temporal energy)

EAR

BRAINSensations / perceptions

Memory / learning

Knowledge / Emotions

MIDDLEBRAIN

Auditory centre

(Warning reflex)

AUTONOMIC NEURAL – GLANDULAR

SYSTEMControlling homeostatic performance of

brain. Cardio - vascular, vegetative and

respiratory organs of the body

1. (A) Temporal & permanent auditory loss and ear injuries

AUDITORY EFFECT (A) AND NON AUDITORY (NA) OF NOISE

AND RESULTS OF THESE EFFECTS ON EMOTIONS AND

WELL-BEING

1. (A) Inherent sensations of nuisance received: sonority, duration,

impulsivity, tonality, complexity (‘Harshness’)

2. (A) Interferences in Behaviour; Audition of desired sounds;

disturbance in resting/dreaming; distraction in carrying out tasks

1. (NA) Nuisance emotions; bile; frustration, … due to the

interference behaviour

2. (NA) Bile emotions, fair to the source, anxiety, … due to worriesabout the noise effects on well-being, life quality, economic value of

houses and residential areas.

Abnormal temporal and persisting states of particular

homeostatic functions in the body, caused by emotions due

to the interference effects on noise behaviour and adverse

effects perceive associated as a consequence of noise

Figure 17. Diagram showing the relationship between physiological systems and non-auditoryones. The diagram also shows physiological and psychological effects due to the noise.

Solving this problem requires the urgent adoption of appropriate corrective

measures. By corrective action we refer to traffic restrictions at night-time (for example, by limiting access to certain urban zones to residents) and greater control of the sound sources that cause the most disturbance such as vehicles andmotorcycles.





31

12.1.2. Characterisation of the level of nuisance

Most of the investigations on acoustic pollution are based on the measurement of the levels of ambient noise produced by different sound sources and especially bytransport vehicles. It has been demonstrated that traffic is the most important andwidespread source of noise in industrial countries.

In order to express the existing relationship between exposure to noise and thesubjective responses of people affected by this environmental factor, all thestudies have used various noise indicators. However, in fact it has been shownthat all these indicators are closely related to each other. One of these is theequivalent continuous sound level measured during a 24-hour period, (Leq (24hr )).It can be used, with certain limitations, to predict the general response of a

community (subjective nuisance for the residents) in the face of the impactproduced by a wide variety of different sound sources. The Leq (24h) evaluates theaverage value of the noise level to which a predetermined zone is exposed duringa period of time. In general, the Leq measured in an interval of T time is calculatedby means of the expression:

⎟⎟ ⎠

⎞⎜⎜⎝

⎛ = ∫

T

eq dt p

t p

T T L

0

2

0

2 )(1log10)( (34)

That is to say, its value is the average constant amplitude of noise with the same

acoustic energy as that of the noise measured. Figure 18 illustrates the timevariation of an arbitrary acoustic signal during an interval of time T , its energy andthe value of Leq associated with this interval, that is, Leq (T). In general, urbannoise measurements show a frequency range between 125 Hz and 2 kHz, whichis typical of the noise generated by traffic. Above these frequencies the spectrallevel decays progressively. These bands of relative low frequency tend to beeasily transmitted through building structures (walls, windows, foundations, etc.)making the impact on the population still greater than expected.





32

Figure 18. Example of an acoustic time signal (a), its energy as a function of time (b) and theequivalent average level Leq (T) for T = 1 (c).

More recent investigations have shown that the characterisation of ambient noisein a given urban location with the Leq parameter alone could be incomplete. This isparticularly true for those environments that experience big variations in noiselevel during the time interval studied. In these circumstances, we also need todescribe the statistic and time variability of the noise level as a random variable.

12.2. Analysis of contribution of external noise sources in vehicles

For the measurement of the overall noise level emitted by a running vehicle (pass-by test), directive 96/ 20 defines the test set-up shown in Figure 19. In themeasurement of the noise level, the running vehicle approaches the test area(interval between the AA' and BB' lines) at a stabilised speed (the lowest between50 km/ h and 3/4 of maximum power). When reaching the AA' line the accelerator is fully depressed and then released when the rear part of the vehicle has passedthe BB' line. As the vehicle travels between lines AA' and BB' the vehicle noise isregistered by means of the microphone located in P (see Figure 19).

(a)

(b)

(c)





33

Figure 19. Pass-by test lay-out for exterior noise measurement according to European Directive96/20.

The pass-by test described does not give information about the structure or maincomponents of the total noise emitted by a vehicle. In order to understand thisstructure, we should bear in mind that the noise produced by vehicles is composedof the contribution of the following sources:

• Engine

• Intake system

• Exhaust system

• Rolling

• Aerodynamic

The contribution of each one of these sources to the overall noise level, changesin level and spectral content according to the vehicle speed and/or engine speed.The reduction of vehicle noise emissions achieved in the last 20 years are linkedto the increasing knowledge of the contribution associated with each noise sourcepresent in a vehicle. This section describes a method for analysing the contributionthat each acoustic source in a vehicle makes to the total noise. The resultsobtained in IDIADA for a group of vehicles that reflect the vanguard in acousticdevelopment, show that rolling noise is acquiring a notable importance as sourcethat contributes to the external measured noise both in the pass-by test and innormal driving conditions. In the case of the pass-by test described we canconsider that the contributing acoustic noise sources are:





34

• Engine

• Intake system

• Exhaust system

• Rolling

Depending on the type of vehicle and the problem we can consider others likegearbox, transmission system, radiation from the walls of the exhaust and intakemufflers, radiation of the catalytic converter, etc.

Obtaining a vehicle that complies with the levels marked in the directive obviouslyhappens by achieving partial reductions in the levels of noise radiated by some or all of the sources that contribute to the level of exterior noise of the vehicle. Inorder to get these partial reductions we need to know which sources radiate andtheir contribution to the global levels of emitted noise. To do this source

decomposition studies are carried out. These studies allow us to quantify thecontribution of each source to the global level of exterior noise and also to study itas a function of the position of the vehicle on the track, the vehicle side, and thevehicle speed and/or engine speed. The contribution could be expressed as apercentage of the total or as a contribution in dB(A). The source decompositionmethod consists of reducing as much as possible the different noise sources untila vehicle with minimum or residual noise has been obtained. The vehicle isequipped with additional intake and exhaust super-silencers and the engine isencapsulated as shown in the example in Figure 20.

Figure 20. Vehicle with minimum or residual noise by means of the use of intake and exhaustsupersilencers and engine encapsulation.

Next the source under study is uncovered and the levels of noise measured duringthe pass-by test in both states are compared. The difference between the level of this last test and that of minimum or residual noise is the contribution of that





35

source. The contribution of each source F i in dB(A) along the position of thevehicle on the track is given by:

( )10/10/

1010log10

NR NF

i

i

F −⋅= (35)

where F i : contribution of the n-th source.NF i : level of noise with the n-th source unshielded.NR : level of minimum or residual noise.

The percentage contribution of an acoustic source to the level of global noise iscalculated using the following equation:

( )10/10/1010100(%) NT NF

ii F ⋅= (36)

Where F i : contribution of the n-th source.NF i : level of noise with the n-th source unshielded.NT : level of total noise.

Figure 21 shows the result obtained for the contribution of the exhaust system of the vehicle in Figure 20 to the total noise of the vehicle (2nd gear).

Figure. 21. Contribution of the exhaust system to the global noise (2nd

gear, left side).

If this process is repeated for each source of interest, the contribution of each oneof these sources to the overall noise level is obtained. Figures 22, 23, 24 and 25show the noise contributions of the exhaust system, the intake system, the engineand the tyre rolling in 2nd and 3rd gear, all as a function of the position of thevehicle shown in Figure 20. Values are expressed as a percentage of the total

level in dB (A).

60

65

70

75

80

-15 -10 -5 0 5 10 15

POSITION(m )

L E V E L d B ( A )

EXHAUST

RESIDUAL NOISE





36

0.0

20.0

40.0

60.0

80.0

100.0

-15 -10 -5 0 5 10 15

POSICION (m)

C O N T R I B U C I O N ( % )

EXHAUST

ENGINE

INTAKE

BACKGROUND + ROLLING

Figure 22. Contribution of acoustic sources to the global noise level as a percentage of the totalnoise measured (2

ndgear).

0.0

20.0

40.0

60.0

80.0

100.0

-15 -10 -5 0 5 10 15

POSICION (m)

C O N T R I B U C I O N ( % )

EXHAUST

ENGINE

INTAKE


Figure 23. Contribution of acoustic sources to the global noise level as a percentage of the totalnoise measured (3

rdgear).





37

50

60

70

80

-15 -10 -5 0 5 10 15

POSITION (m)

L E V E L d B ( A )

EXHAUST

ENGINE

INTAKE

BACKGROUND +ROLLING

SERIE

Figure 24. Contribution of acoustic sources to the global noise level in dB(A) (2nd

gear)

50

60

70

80

-15 -10 -5 0 5 10 15

POSICION (m)

N I V E L d B ( A )

EXHAUST

ENGINE

INTAKE

BACKGROUND +ROLLING

SERIE

Figure 25. Contribution of acoustic sources to the global noise level in dB(A) (3rd

gear)

We can see that the most important noise contributions come from the engine andthe tyres both in 2

ndand in 3

rdgear. This result is general for current passenger

cars, which is illustrated by the comparative graphs (Figures 26 and 27) obtainedin IDIADA between 6 vehicles, 4 diesel (vehicles A, B, D, E) and 2 petrol (vehicles

C and F) of the same category and currently on the market. Figures 26 and 27show the measured contribution of the different noise sources of the above





38

vehicles for the position in which the maximum noise level is obtained during thepass-by test.

1 0 . 7

1 4 . 4

8 . 2

1 4 . 5

1 . 5

3 . 0

5 6 . 9

5 5 . 6

4 0 . 4 4

9 . 0

7 6 . 3

4 3 . 4

4 . 2

0 . 0 4

. 5

4 . 0

1 . 5

1 2 . 0

2 8 . 2

3 0 . 0

4 6 . 9

3 2

. 5

2 0 . 7

4 1 . 6

0.0

10.0

20.0

30.040.0

50.0

60.0

70.0

80.0

90.0

100.0

A B C D E F

VEHICLE

C O N T R I B U T I O N %

EXHASUT

ENGINE

INTAKE

BACKGROUND +

ROLLING

Figure 26. Comparison of noise sources for diesel vehicles (A, B, D, E) and petrol (C y F); (2nd

gear).

7 , 9

1 , 4

8 , 7

1 , 5

0 , 0

1 0 , 8

3 3

, 3

6 4 , 2

2 0 , 4

3

4 , 4

3 3

, 4

1 2 , 8

5 , 2

3 , 7

0 , 0

1 , 5

1 , 5

3 , 4

5 3 , 6

3 0 , 7

7 0 , 9

6 2 , 7

6 5 , 1 7

3 , 0

0,0

10,0

20,0

30,040,0

50,0

60,0

70,0

80,0

90,0

100,0

A B C D E F

VEHICLE

C O N T R

I B U T I O N %

EXHAUST

ENGINE

INTAKE


Figure 27. Comparison of noise sources for diesel vehicles (A, B, D, E) and petrol (C y F); (3rdgear).





39

Figures 26 and 27 demonstrate the small contribution that intake and exhaustsystems have on the global noise emitted by current vehicles and that the greatestcontribution is from the engine and tires. This, together with the fact that at higher speeds (between 70 and 100 km/h) the predominant noise comes from rolling, hasmotivated the ECE to study a proposal for controlling the noise levels produced bythe tires.

12.3. Interior noise of vehicles

Figure 28 shows the main sources of noise and vibration in a vehicle. The maincomponents exciting vehicle structure are the engine, the gearbox, the clutch, theexhaust system and the forces on the suspension induced by the road.

Figure 28. Definition of the main excitation sources in a vehicle. The vibration transmissionelements represent the mechanical link between the sources and the passenger compartment of

the vehicle (structural excitation). The acoustic waves generated by these sources also excite thepassenger compartment inducing part of the interior noise (airborne excitation).

It is important to observe that all the excitation paths indicated in Figure 28respond to the structure indicated in Figure 29, where each block represents a partof the structure or the air of the passenger compartment with its influence on thetransmissibility of vibrations or noise. Figure 30 is an enlargement of Figure 29 inwhich the system labelled passenger compartment in Figure 28 has been brokendown into its structural and air components. This breakdown is fundamental inunderstanding the structural and acoustic aspects that define the noise and

vibration perceptions inside the passenger compartment.

Engine

supportsBody supportTransmission

supports Suspension

VEHICLE CABIN

Sources

Sound waves

(Air excitation)

Vibration transmission elements

Engine

Gear box and

clutch

Road excitation

Tyre resonances

Suspension

Exhaust

system





40

Figure 29. Basic structure of a vibration transmission path from the source to the passenger compartment where it becomes noise.

Figure 30. The global response of the vehicle passenger compartment breaks down into itsstructural response (movement of the “skin” of the passenger compartment-structural resonance)and into the response of the air contained in the cavity (acoustic resonance)

The perception of noise and vibration by the passengers depends on thecharacteristics of each one of the blocks in Figure 30.

Technically, any response associated with the blocks shown can be modified inorder to obtain a reduction of the noise and vibration level in the passenger compartment. However, the difficulty and cost in implementing modifications in any

of these blocks can be very different. In general, the efficiency of any action toreduce vibration or the noise level is greater when it acts closer to the source of the problem. This is one of the reasons why it is so important to choose correctlythe supports of the elements that act as vibration sources. Once the vibrationalenergy is transmitted to the structural components with a large surface area(panels, firewall, vehicle floor, etc.), the problem of controlling the noise andvibrations that affect the passengers become more complicated. This is because,in this case, the whole “skin” of the passenger compartment becomes a globalsource that radiates noise into the interior. In these cases, the correct definition of the vibration modes of the structure and the air of the passenger compartment isnecessary. This information will allow us to define at what frequencies the “skin” of

the cavity is more susceptible to vibration and the mode of vibration. In the sameway, the acoustic modes of the air contained in the passenger compartment

Source Mechanical joint

Structure cavityresponse

Passengercompartment

Mountings

Vibration

Noise

SourceMechanical

joint

Structural

transmission path

Air

cavity

response

Effect on

passengers

Acoustic

perception

Vibrational

perception

Structure

cavity

response





41

indicate the frequencies at which it tends to enlarge the acoustic pressure and theinterior zones where it happens. Figures 31 and 32 show, respectively, a structuralmode and an acoustic mode of the air contained in the passenger compartment of a vehicle.

Figure 31. Deformation in a structural mode (experimental) of a body at 44.31 Hz. These resultswere obtained by processing the structural response of the body measured at 800 triaxial points.

Because the structure and the air of the cavity interact, it is important to investigatethe possible frequency and spatial coincidence of the structural and acousticmodes. This situation of coincidence is undesirable since it implies that, at the

frequencies where this happens, the structure is especially weak and the interior air is very reactive (resonate). This situation will bear high levels of interior noisenormally called booming. Booming appears at those values of engine r.p.m. thatexcite structural or acoustic modes or both simultaneously.





42

The control of booming is done through the identification of which mode(s) cause itand the possible structural or acoustic modifications for reducing their effect.Booming problems happen at low frequencies (< 200 Hz). The solution isdependent on reducing the excitation force transmitted by the engine mountings(or the causal element), modifying the chassis or body structure (modification of the vibration modes), modifying the fixing points between the chassis and theactive element or modifying the resonances of the air of the passenger compartment.

Figure 32. Distribution of the pressure in an acoustic mode (experimental) of the body shown inFigure 31 at 71.5 Hz. These results were obtained by processing the acoustic response of the air of the passenger compartment measured at 200 points.

At higher frequencies (> 1 kHz), vehicle noise problems can be solved usingabsorption and isolation techniques like the one described previously. In thesecases, once the noise source has been located, it can be isolated or encapsulatedwith an acoustic barrier that in addition to mass also contributes acousticabsorption through the use of porous materials. The correct positioning of thesebarriers can be achieved with the use of intensimetry techniques that help todefine the zones of the source surface that radiate noise most efficiently. The iso-intensity maps obtained can be applied directly as geometric definitions of thezones to be covered for encapsulating. Figures 33 and 34 show the iso-intensitymap obtained in a vertical plane within the acoustic field produced by the engine,the crankcase and the gearbox of a truck in neutral at 2700 r.p.m.. The level of the





43

contour plot indicates that the crankcase is contributing notably to the noiseradiation in the measured plane.

Figure 33. Vertical Grid of iso-intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

1

2

3

4

5

6

7

8

9

10

11

OVERALL

108-111

105-108

102-105

99-102

96-99

93-96

90-93

87-90

Figure 34. Intensimetry obtained in the plane shown in Figure 33 with a truck in neutral at 2.700r.p.m. The values shown correspond to dB (ref. 10

-12W/m

2)





44

CHAPTER II

EFFECTS OF ROAD SURFACE ACOUSTIC IMPEDANCE ON

INTERIOR AND EXTERIOR VEHICLE NOISE





45

EFFECTS OF ROAD SURFACE ACOUSTIC IMPEDANCE ONINTERIOR AND EXTERIOR VEHICLE NOISE

1. INTRODUCTION

Tyre noise is an important component of the total noise produced by a vehicle.This noise component has a strong contribution to the overall quality associatedwith interior and exterior vehicle noise. It is also recognised that road acousticimpedance is of paramount importance in understanding and quantifying the noiseproduced by the interaction between the tyres and the road surface.In this paper the authors present a novel non-destructive method for themeasurement of the frequency dependence of the acoustic impedance of road

surfaces. The effect of this impedance on the total radiated tyre noise is assessedand its implications on interior and exterior vehicle noise quality are explored. It isalso shown that by a suitable selection of building materials, road surfaces can beacoustically tuned to improve their effectiveness.

The high level of noise that exists in our cities is a major concern for the citizensand institutions responsible for maintaining this noise below the legal levels. Theapplication of road surfaces with absorbent acoustic characteristics is a methodwidely used to obtain a reduction in the level of vehicle rolling noise. Thesesurfaces can absorb an important part of the noise generated by the vehicles andespecially the contribution caused by tyre noise. Additionally, these surfaces affect

not only the exterior noise generated by the vehicles, but also the interior noiseperceived by the passengers while driving. This double effect of low-noise roadsurfaces is very helpful in improving both the acoustic quality of the environmentalnoise perceived by pedestrians and by the acoustic comfort felt by vehiclepassengers.

Making a correct assessment of the acoustic impact of low-noise road surfacesrequires the quantification of not only the overall noise level reduction, but alsotheir effect on the sound quality perceived. This aspect is frequently forgotten,which makes the global quantification of the acoustic impact of low-noise roadsurfaces incomplete.

In this work, we show that low-noise road surfaces bring an improvement to theacoustic comfort perceived by pedestrians and by vehicle passengers. Thisimprovement of the perceived acoustic quality is not only reflected by a reductionof the overall noise level but also by a desirable variation of psycho-acousticparameters that quantify subjective perceptions associated with the level and thesmoothness of the sound, such as the loudness and the sharpness. The combinedconsideration of the variation in noise level, dB(A), and the changes in the relevantpsycho-acoustic parameters allows a more accurate quantification of the globalimpact on the acoustic comfort associated to the use of low-noise road surfaces.





46

2. INSTRUMENTATION

In this section we describe the instrumentation used for the measurementsdescribed in this paper. This instrumentation is necessary if we want tocharacterise not only the objective but also the subjective aspects of urban noise,and if an accurate description of the acoustic properties of the road surface isrequired.

• Precision Sound Level Meter Brüel & Kjaer Type 2236 A-006

• Artificial head (Head Acoustics®)

• Acoustic impedance tube adapted for the in situ non-destructivemeasurement of the absorption coefficient of road surfaces.

3. MEASUREMENTS OF INTERIOR AND EXTERIOR VEHICLE NOISE

One of the objectives of this work was to quantify the order of magnitude of theeffect that absorbent road surfaces can produce on urban noise and on the interior noise of vehicles. The measurements carried out to assess this effect aredescribed below:

3.1. Exterior noise measurement with sound level meter

Measurements of equivalent levels (duration of 10 minutes) were carried out using

an integrator sound level meter. The measurements were made on two streets inthe city of Barcelona before and after the application of a new low-noise roadsurface. For these measurements, the ISO-R1996 standard was considered. In allthe measurements the level meter was located 1.2 m from the ground and adistance greater than 3.5 m. from any wall.

3.2. Exterior noise measurement with Binaural Acoustic Head

An acoustic head was also used to produce binaural recordings of the urban noiseas measured at the same point where the sound level meter was used. Theduration of these recordings was 15 minutes each. In these measurements, the

ISO-R1996 standard recommendations were also taken into account.

3.3. Interior noise measurement with Acoustic Head

In addition to the exterior noise measurements, the binaural system was also usedto measure the interior noise perceived by a passenger seated on the front seat of a Ford Focus Wagon 2.0i (reference vehicle). The measurement was made withthe vehicle passing along the two studied streets before and after the applicationof the new low-noise surface. During the measurements, the vehicle was driven inthird gear and at a constant speed of 50 km/h.





47

3.4. Acoustic characterisation of road surfaces

In order to make an assessment of the acoustic properties of the road surfaces inthe streets, the acoustic absorption coefficient of the roads was measured beforean after the application of the new asphalt. The measurements were carried outwith the acoustic impedance tube mentioned in section 2. This tool allows us tomake in situ non-destructive measurements of the absorption coefficient of anysurface.

4. DATA ANALYSIS

4.1. Psychoacoustic parameters versus traditional metrics

Sound contains information that is not registered by conventional measuringmethods. A sound can transmit pleasant or unpleasant information and conveyinformation on the functionality and quality of the source. “Noise” is a sound whosequality is perceived as unpleasant or annoying. Therefore, noise is an undesirableand annoying sound. The human ear is a complex receiver whose process islargely unknown. This processing of the electro-acoustic signals in the human ear is very quick and intelligent and differs considerably from the conventional analysistechniques used in acoustics.The sound level in dB(A) is obtained by measuring the sound pressure andevaluating the modified frequency spectrum with the A weighting curve, which is

practically the opposite of the frequency sensitivity curve of the ear. The frequencysensitivity of the human ear to sound pressure depends on the level of the soundpressure, and the A weighting curve is valid for noise levels below 65 dB.However, in practice this weighting curve is used for pressure levels above 65 dBas well. As a general rule, the sound pressure levels in dB(A) only permit theevaluation of sounds that have particularly negative effects. For example, a longexposure to a weighted sound level of 85 dB(A) affects negatively the hearingability of people. However, sound levels below 85 dB(A) may harm the hearingsystem and have indirect psychological effects if the sound is judged as annoying.On the other hand, the analysis of sound in 1/ 3 octave does not give us completeinformation regarding the sound quality.

Concerning the fundamental differences between human hearing and theconventional measuring techniques we can point out the following importantaspects:

1) The external ear is a directional filter that weights the sound level in a rangefrom +15dB to -30dB, depending on the frequency and direction of incidence.However, a conventional microphone shows a flat frequency response for incident waves from any direction (diffused-field microphone).

2) The human hearing system has two channels that permit binauralprocessing, spatial hearing, frequency selection and suppression of binauralnoise.





48

3) The impression produced by a sound is not only given by the sound level, butalso by the psycho-acoustic parameters of sonority and sharpness, which willbe described later on.

4) The human hearing system has a high resolution in frequency and timecombined with a large dynamic range. Consequently, the ear is able todifferentiate simultaneously the small and quick frequency, and timevariations of an acoustic signal.

Another important aspect that justifies the use of an artificial head for understanding noise annoyance is the directionality of the head-upper body unitand the external ear. The head and the external ear is a directional filter.Diffraction and reflection of the incident sound waves in the ear and the head

cause this filtering action as well as resonance in the ear canal. As an example of the complexity of this wave interaction, Figure 1 shows the calculated diffractionpattern produced by a spherical body with a diameter of 0.18m on an incidentplane wave at 1kHz and 2kHz respectively. These pictures show that the presenceof a head introduces an important complexity of the diffracted and reflectedacoustic field which will have a noticeable effect on the perceived noise. Thisresult shows one of the reasons why artificial heads are useful when we want toquantify the noise characteristics as perceived by people.

Figure 1: Example of the calculated diffraction pattern suffered by an incident plane wave (yellowarrow) when it impinges on a rigid spherical body with a diameter of 0.18 m. The unit of thehorizontal and vertical axes are meters. Left: 1000 Hz; Right: 2000 Hz. Contour lines: Continuousline, 2dB; dashed line, 1dB; dash dot line, 0dB and dotted line, -1dB.

It is important to point out that the effects of reflection and diffraction of the incidentsound waves depend on the direction. The amplifying effect produced by the

geometric characteristics of the external ear, the head and the upper-body cannotbe generated if the acoustic measurement is carried out with a conventional





49

microphone or a sound pressure level meter. The additional fact that humanhearing is based on the analysis of the information in two channels (ears) enablesus to recognise time structures in noise, detect the direction of incidence and applyfrequency selectivity and binaural noise suppression. These capabilities would notbe possible if the human hearing system worked like a conventional single-channel system.Taking into account the above considerations, in this work we have considered thefollowing acoustic parameters to assess the effect produced by low noise asphaltson the acoustic comfort perceived by pedestrians and vehicle passengers:

Equivalent continuous sound level: Leq This parameter is defined as

( )

( )

⎟⎟ ⎠

⎞

⎜⎜⎝

⎛ =

∫

T

eqdt

p

t p

T T L

0 0

21

log10 (1)

We observe that the definition of Leq (dB(A)) indicates that this parameter is a timeaverage of the acoustic energy at the measurement point. Thus, one of the mainlimitations of this parameter is the fact that it is quite insensitive to transients andshort events that can dictate the urban noise annoyance.

Loudness It is defined as the sound pressure level of a pure tone of 1 kHz that gives thelistener the same sensation of sound level as the sound studied. Its unit is the

phon. The calculation of the sonority takes into account the distribution of thecritical bands in the human ear. Therefore, the masking effects and the tonalcomponents of the noise are considered in the calculation of this parameter.Sonority not only depends on the level of sound pressure but also on the spectralcomposition of the noise analysed. This parameter is one of the most important inquantifying the subjective perception of the noise.

Sharpness Sounds with a high spectral content at high frequency are established as sharp. Itsunit is the acum. Depending on the spectral structure, sounds with the samesonority may present values of very different sharpness. In general, the sounds

with greater sharpness are judged as more unpleasant and annoying that thosewith a small value for this parameter.

Articulation index It is defined as the percentage of words that will be heard perfectly during aconversation in the sonorous ambience studied. It is wished this value to be highin any acoustic environment. Its unit is %.

The parameters of Loudness, Sharpness and Articulation Index are part of thegroup of the psycho-acoustic parameters accepted by the international community.The information provided by these parameters allows us to assess the aspects of

the quality of the analysed noise that cannot be quantified by measuring the







51

Figure 2. Preparation of the set-up for the measurements with the artificial head (Paseo Bonanova- Barcelona)

Table II. Global results of Leq and Loudness of the normalised measurement of exterior noise withthe binaural acoustic head (AH). We observe that the effect of the porous asphalt on the noise inPaseo Bonanova is mainly a quite uniform reduction of the overall level of the frequency bandabove 500 Hz

Balmes street Exterior noise with AH Leq (dB(A)) Loudness(aver.)[sone] Existent asphalt 76,1 40,45 Low-noise asphalt 72,3 33,25

Reduction= 3,8dBA 7,2soneGF

P. Bonanova Exterior noise with AH Leq (dB(A)) Loudness(aver.)[sone] Existent asphalt 77,4 36,1 Low-noise asphalt 71,4 27,8

Reduction= 6dBA 8,3soneGF





52

Figure 3. The spectrum of the exterior vehicle noise (environmental noise) in Paseo Bonanova(Barcelona). The plots show the difference in noise level before and after the implementation of thelow noise road surface.

4.4. Results of Interior vehicle Noise with artificial Head

The measurement of the interior noise of the reference vehicle (Ford FocusWagon 2.0i) was carried out under controlled driving conditions (3

rdgear, 50

km/h.) using the artificial head (see Figure 4). In this driving condition, the enginenoise inside the vehicle was relatively low. In this case the measured data wasprocessed in a way that the presented results correspond to time histories in whichthe vehicle was completely stabilised and the recordings were free from anyexterior noise source. The results of the psycho-acoustical parameters of Sharpness, Loudness and Articulation Index are presented because they arerelevant parameters in relation with the sound quality inside the vehicle. Figure 5shows the change in the noise spectrum of the interior noise of the car when it was

driven along Paseo Bonanova before and after the resurfacing of the road.

Table III shows the values of de Leq, Loudness, Sharpness and Articulation Index associated with the interior noise of the reference vehicle for the two streetsstudied before and after the implementation of the porous asphalt. This resultproves that porous asphalt has a very important impact on the level and quality of the noise inside the vehicle. The attenuation of the high frequency componentsreduces the value of the loudness and the sharpness of the interior noise, makingit more comfortable. This also improves the value of the Articulation Index which isclosely related to comfort perception.

77,4 dB(A) Old road surface

71,4 dB(A) Low-noise surface





53

Figure 4. Position of the binaural acoustic head in the reference vehicle for the measurement of interior noise (passenger position).

Figure 5. Interior noise spectrum of the reference car driven (3rd

gear, 50 km/h) on PaseoBonanova in Barcelona.

Balmes street Interior noise with AH Leq (dB(A)) Loudness(aver.)(sone) Sharpness(aver.)(acum) A.I.(aver.)(%) Existent asphalt 64,1 15,9 0,813 90,2 Low-noise asphalt 63,3 14,7 0,809 91,3

Reduction= 0,8dBA 1,2soneGF 0,004acum 1,10%

P. Bonanova Interior noise with AH Leq (dB(A)) Loudness(aver.)(sone) Sharpness(aver.)(acum) A.I.(aver.)(%) Existent asphalt 64,9 16,3 0,89 90,1 Low-noise asphalt 61,9 13,5 0,717 93,2

Reduction= 3dBA 2,8soneGF 0,173acum 3,10%

Table III. Result of the measurements of interior noise in the reference vehicle (Ford Focus Wagon2.0i) with a binaural acoustic head

64,9 dB(A) Old road surface

61,9 dB(A) Low noise surface





54

4.5 absorption coefficient of road surfaces

The equipment used to measure the absorption coefficient of the road surfaces isan impedance tube based on the two-microphone technique and adapted byApplus+ IDIADA to characterise acoustically the rolling surface. The two-microphone method uses the measurement of the acoustic pressure at two pointson the duct to distinguish the incident and the reflected component of the soundfield produced by a sample of material. This allows the measurement of theabsorption coefficient on the surface located at the end of the duct. Figure 6depicts the results of the measurement of the absorption coefficient carried outwith the acoustic impedance tube in Paseo Bonanova before and after theimplementation of the porous surface. We observe that the new porous asphaltexhibits a dramatic change in the absorption coefficient which explains the big

influence that this type of road surface has on both the interior and the exterior vehicle noise.

Acoustic absorption coefficient - P. Bonanova

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 f(Hz)

Figure 6. The measured absorption coefficient of the road surface in Paseo Bonanova before (blue

line) and after (red line) the implementation of a low-noise road surface. The data has beenobtained using the impedance tube shown in section 2.

5. TUNING OF ACOUSTIC PROPERTIES OF ROAD SURFACES

The main characteristics determining noisiness of road surfaces are geometricalfeatures, acoustical and mechanical properties of the pavement. Previousresearch has shown that two independent tyre noise generation processes can beidentified; one in the low frequency range below 1kHz which is roughness induced;the other in the high frequency range is identified as air-pumping. It has been

shown that the noise level increases with increasing texture depth. However, at a





55

certain point this increase ceases due to the tyre being unable to form a seal downto the base of the aggregate, hence reducing air-pumping.In addition to the reduced levels of noise being produced by road surfaces withoptimised textures some surfaces, notably porous asphalts actually attenuatenoise levels by an absorptive mechanism. In order to achieve the greatest possiblenoise reduction, the sound absorption of the road must be optimal which meansthat the sound absorption of the road must be as high as possible in the frequencyrange which is most significant for road noise.

5.1 Influence of construction parameters on the acoustic absorption of roadsurfaces

The absorption coefficient of road surfaces can be expressed as a function of physical parameters that interact to define the capability of the material to

dissipate acoustic energy [1] [2]. These parameters are the porosity, Ω , the air flow resistivity, s R , the tortuosity, K , and the thickness of the road layers, d . In

general, the absorption coefficient of a porous material can be expressed as

oo

oo

c Z

c Z

ρ

ρ α +−−=1 (2)

where Z is the surface impedance and ooc ρ is the specific impedance of air ( o ρ is

the air density ando

c is the speed of sound). The value of Z can be calculated by

)coth( jkd W Z ⋅= (3)

where k is the wave-number of the medium, d is the thickness and 1−= j . The

value of k and W in equation (3) can be expressed respectively as

⎟⎟ ⎠

⎞

⎜⎜⎝

⎛ −⎟⎟ ⎠

⎞

⎜⎜⎝

⎛ −−−=

f

f j

f

f j K

c

f k u

o

θ

γ γ

π 11

1111

2(4)

⎟⎟ ⎠

⎞⎜⎜⎝

⎛

−⎟⎟ ⎠

⎞⎜⎜⎝

⎛ −−

−

Ω=

f jf

f jf K cW uoo

/1

1111

1

θ γ

γ

ρ (5)

In equations (4) and (5), γ is the ratio of the specific heats of air and the terms u f

and θ f represent the characteristic frequencies associated to viscous and thermal

effects. These are given by





56

K

R f

o

su

Ω=

ρ π 2

1(6)

pr o

s

N

R f

Ω=

ρ π θ

2

1(7)

where pr N is the Prandtl number of air.

The model described above allows the prediction of the acoustic absorption of aroad surface from the knowledge of the porosity, the resistivity, the tortuosity andthe thickness of the layer.

Woodside et al [3] have investigated the relationship between these parameters

and the size and shape of the type of aggregates used to build road surfaces. If these relationships are used to express the acoustic parameters Ω , s R and K as

a function of the aggregate size [4], s , and shape (flake versus cubic geometry),equations (2) to (7) can be used to explore the combination of aggregate size andshape that will exhibit a higher absorption coefficient at a desired frequency.Figure 7 shows the calculated effect that the aggregate size and geometry canhave on the absorption coefficient at 1 kHz and 2 kHz respectively. To help theinterpretation of the curves, the two surfaces depict the same information but fromdifferent view points.

0.005

0.01

0.015

0.02

0.025

0

0.5

10

0.1

0.2

0.3

0.4

0.5

Aggregate size (m)Shape factor

A b s o r p t i o n c o e f f i c i e n t

1 kHz

2 kHz







58

0.008 0.01 0.012 0.014 0.016 0.018 0.02 0.0220

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Absorption coefficient for f = 2000 Hz

Aggregate size (m)

S h a p e

f a c t o r

0.20.3

0.4

0.45

Figure 8: The contour plots corresponding to the surfaces depicted in figure 7

6. CONCLUSIONS

In this paper the authors have presented an advanced way of assessing the effectof porous asphalts on the exterior and the interior vehicle noise. This approach isbased not only on the measurement of the time average sound pressure level butalso on binaural measurements with an artificial head and an impedance tube that

allows the in situ non-destructive assessment of the absorption coefficientpresented by a road surface. This integral assessment methodology provides allthe information needed to quantify the impact of low-noise road surfaces on theacoustic comfort of pedestrians and vehicle passengers. Futhermore, theinformation obtained from the combined use of these measurement tools allows amore precise definition of the type of acoustic characteristics expected from a roadsurface to maximise the acoustic comfort.

This investigation of the effect of porous asphalts on the acoustic comfort can alsobe used in combination with a mathematical model of the acoustic absorption of road surfaces. The availability of a model to predict the acoustic absorption allows

the definition of the geometric characteristics of the road surface components toachieve the desired absorption coefficient in the frequency band of interest.

REFERENCES

(1) Meier, A. , “A poro-elastic road surface for traffic noise reduction”, Internoise ‘85, 1985, pp.287 – 290.

(2) Hamet, J.F., Berengier, M., “Acoustical characteristics of porous pavements: Anew phenomenological model”, Internoise ’93, 1993, pp 641 – 646.





59

(3) Woodside, A. R., Hetherington, J.O. and Anderson, G.A., “The optimisation of porous asphalt road surfaces to maximise sound absorption”, Internoise ‘99,1999.

(4) British Standards Institution BS 812 Section 105.1:1989 Testing Aggregates –Methods for determination of particle shape. British Standards Institution,London





60

CHAPTER III

FUNDAMENTALS OF

AUTOMOTIVE VIBRATION





61

FUNDAMENTALS OFAUTOMOTIVE VIBRATION

1. INTRODUCTION

Vibration refers to a mechanical oscillation in relation to a reference position. Notonly is a phenomenon of nuisance, it can also cause machines or structures tobreak.

2. VIBRATION WAVES

A mechanical wave can be defined as a phenomenon in which a physicalmagnitude (pressure, stress, deformation, energy, etc.) propagates in a medium,without transporting matter. There are basically two types of vibration waves:longitudinal waves and transversal waves.

2.1. Longitudinal waves

Longitudinal waves are those in which the particles are displaced in the samedirection as the wave. They are the only ones that occur in gases. They also occur in solids but from an acoustic point of view they are not interesting since they donot produce sound radiation (Figure 1).

Figure 1. Longitudinal wave.

2.2. Transversal waves

Transversal waves are those in which the particles move perpendicular to thedirection of propagation of the wave. These waves do not occur in fluids since theycannot transmit tangential forces. In solids they permit the transmission of

movement to the surrounding fluid (air) and therefore constitute a source of noise(Figure 2).





62

Figure 2. Transverse wave.

3. TYPES OF VIBRATIONS

Vibrational movement can be repeated in regular intervals, as in the case of apendulum or the vibrations in coming from the engine of a vehicle ( periodic vibration). Alternatively they can exhibit a complete lack of periodicity as in thecase of the vibrations produced in the vehicle by irregularities of the road surface(random vibration). Figure 3-(a) shows a periodic vibration signal and Figure 3-(b)

shows random vibration signal.

An important parameter to define when talking about periodic vibrations is theperiod. It is defined as a period of a periodic vibration (T ) the duration of theinterval in which the signal is repeated. Its inverse is known as frequency (f ) and isthe number of times per second that the vibration is repeated. The period ismeasured in seconds and frequency in cycles per second or Hertz (Hz). Hence

T f

1= (1)

Sometimes frequency is expressed in radians per second (ω ). Thus

f π ω 2= (2)

The simplest periodic vibration is the harmonic vibration in which the position of the vibrating point describes a cosine curve (or sine curve) (Figure 4-(a)) and isexpressed as





63

Figure 3. a) Periodic vibration. b) Random vibration.

( ) ( )( )00 2cos t t f X t x −= π (3)

Where x(t) is the position of the vibrating point, X 0 is the amplitude or maximum displacement in relation to theposition of equilibrium,f is the frequency of movement,t is time,t 0 is the phase angle, which depends on the position of the point atthe initial instant.

Defining ϕ 0=2π ft 0, we can write

( ) ( )00 2cos π −= ft X t x (4)

(a)

(b)

L e v e l

Time (t)

Time (t)

L e v e l





64

Considering (2) we can write

( ) ( )00

cos −= t X t x (5)

A useful way of describing a harmonic vibration is through a vector or a complexturning number (complex representation) whose real part (projection on X-axis) isthe true position of the vibrating point (Figure 4-(b)). Therefore the vibrating pointwill be the real part of

t je X x ω

0= (6)

(a)

(b)ω t

Figure 4. Harmonic vibration a) Time representation b) Representation through turning vector.

4.- FOURIER’S THEOREM

All vibration measurements can be analysed from the point of view of how thesignal evolves in time or how the signal decomposes in a given frequency range.In the time domain, the most frequently used parameter to characterise a vibrationis its rms (root mean square) value. This value gives an average of the energy of the signal and is defined as

( )∫ =T

rms dt t xT

x0

21(7)

Where, in this case, T is the interval of integration.





65

If we want to find out the distribution of vibration in a given interval of frequencies,we will need to use the Fourier´s Theorem which establishes that any periodicvibration can be broken down into a sum of harmonic vibrations.

( ) ( )∑∞

=

−=1

cosi

ii t i X t x ϕ ω (8)

where x (t ) is the position of the vibrating point, X i is the amplitude or maximum displacement in relation to theequilibrium position of the n-th component,

ω is the frequency of the vibration in radians per second,t is time,

ϕ i is the phase angle which depends on the position of the point atthe initial instant

This result will allow any periodic vibration to be treated as the sum of harmonicvibrations (sine or cosine) and the theory of harmonic vibrations presented belowwill allow any periodic vibration to be studied.

5. CONCEPT OF DEGREE OF FREEDOM

The number of degrees of freedom of a structure or vibrating system is the number of parameters we must know in order to fully define its position when it vibrates.

The system in Figure 5-(a) has one degree of freedom given that it is enough toknow the position of a single point, x, in order to define its position. The system inFigure 5-(b) has two degrees of freedom and therefore it is necessary to know theposition of two points, x 1 and x 2 , to fully determine its position. Finally the systemin Figure 5-(c) has infinite degrees of freedom therefore it is necessary to know theposition of all points to fully determine its position.

The vibrating systems found in practice, show, on many occasions, infinitedegrees of freedom. However, from an engineering point of view, they are madediscreet to simplify the calculation. This process involves the assumption of a finitenumber of degrees of freedom, which are chosen with the objective of describingthe possible movements of a structure in the functional range of a system.





66

x

(a)

x1

x2

(b)

(c)

Figure 5. Vibrating systems: a) Single degree of freedom, b) 2 degrees of freedom, c) infinite

degrees of freedom.

6. ONE DEGREE OF FREEDOM SYSTEMS

A simple vibrating system can be modelled as a mass which can only move in onedirection and is joined to a single fixed point through a spring and a damper (Figure 6-(a)). This type of idealisation is very useful in engineering since it can beapplied to elements such as silent-blocks, suspension systems, tyres, etc. Thefundamental limitation of this model is that it does not take into account other possible movements that the structure can make when vibrating.

The fundamental elements of single degree of freedom systems are the spring andthe damper. By spring we mean a mechanical device that when deformed reactsproducing a force proportional to the deformation in the opposite direction. Therelationship between the force and the deformation is called stiffness (k). Bydamper we understand a mechanical device that when deformed reacts producinga force proportional to the velocity with which it is deformed and in the oppositedirection to the said velocity. The relationship between force and velocity is calleddamping (c).

All vibrating systems can vibrate in a free or natural way, without external forces

applied, or in a forced way, under the effects of external forces.





67

6.1. Undamped free system

An undamped free system is shown in Figure 6-(a). It is made up of a mass joinedto a fixed point via a spring. If the mass moves, thereby deforming the spring, andthen is released, the system will vibrate according to a harmonic movementdefined by the equation (Figure 6-(b))

( ) ( )000 cos −= t X t x (9)

k m

Time (t)

x(t)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1

-0.5

0

0.5

1

x(t)

(a)

(b)

Figure 6. Single Degree of freedom system without damping. a) Diagram of system. b) Timeevolution of movement.

where x (t ) is the position of the vibrating point, X 0 is the amplitude or maximum displacement in relation to theposition of equilibrium,

ω 0 is the frequency in radians per second,t is time,

ϕ 0 is a phase angle that depends on the position of the point in theinitial instant.

The frequency with which the mass moves is called resonance or naturalfrequency and is given by the formula

m

k =0ω (10)

Where k is the stiffness constant of the spring,





68

m is the vibrating mass.

6.1.1. Example: natural frequency in an anechoic chamber

A floating anechoic chamber is mounted on 162 springs whose constant stiffnessis k = 4.36 x 105 N/m, and its mass is about 146 tonnes. Applying formula (10) and(2) the resonance frequency in Hertz will be

Hz m

k f 5.3

146000

1036.4162

2

1

2

1 5

=⋅⋅

==π π

(11)

Figure 7. Floating anechoic chamber.

A similar, but rather different case to that of the anechoic chamber is that of avehicle on its suspension system (Figure 8). Here, as will be shown later, thepresence of dampers will stop the vehicle from oscillating uncontrollably.

6.2. Damped free system

This is the system shown in Figure 9-(a). It is made up of a mass joined to a fixedpoint through a spring and a damper. If the mass moves, deforming the spring andthe damper, and after that the system is released, the system will vibrateaccording to a movement defined by the equation (Figure 9-(b))





69

Figure 8. Detail of a vehicle’s rear suspension system.

( ) ( )00 cos

0

ϕ ω

ζω

−=

−

t e X t x (12)

where x is the position of the vibrating point, X 0 is the amplitude or maximum displacement in relation to theposition of equilibrium,

ζ is the reduced damping of the system defined later,

ω 0 is the frequency of vibration for a system with equal mass m andstiffness k , but without damping, in radians per second.

ω is the frequency in radians per second,t is time,

ϕ 0 is a phase angle that depends on the position of the vibrating point

at the initial instant.

Reduced damping is given by

km

c

2=ζ (13)

where c is the damping constant,k is the spring stiffness constant,m is the vibrating mass.

The frequency is given by the formula





70

m

k 21 ζ ω −= (14)

where k is the stiffness constant of the spring,m is the vibrating mass,

ζ is the reduced damping of the system defined earlier in (13).

k

m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1

-0.5

0

0.5

1

x(t)

Time (t)

c

(a)

(b)

Figure 9. Damped single degree of freedom system. a) Diagram of the system. b) Time evolution of movement for different damping values.

The time history of a free damped system for different damping values isshown in Figure 9b. This system has the following differences compared to thesystem mentioned above:

- The movement progressively dies out and it does this more quickly when the

damping is greater - The natural frequency of an undamped system is given by

m

k =0ω (15)

Whereas that of a damped system is

m

k 21 ζ ω −= (16)

Therefore, damping lowers the natural frequency.





71

We can see that systems found in practice have an internal damping that, from thepoint of view of vibration control, is highly desirable.

6.3. Forced system

The structures used vibrate because they are forced to do so by some type of excitation (engine forces, forces transmitted to the vehicle by its suspensionsystem, etc.) The study of forced systems is, therefore, very important for understanding the behaviour of a mechanical system when it is excited by a forceat a given frequency.

The system in Figure 9-(a) is submitted to a harmonic excitation of the followingtype

( ) ( )t F t f Ω= cos0 (17)

where f(t) is the force at each instant,F 0 is the amplitude or maximum force,

Ω is the frequency of the force in radians per second,t is time.

It will have a displacement whose value will be (Figure 10-(b))

( ) ( )00 cos −Ω= t X t x (18)

where

2

0

2

22

0

00

41 ⎟⎟ ⎠

⎞⎜⎜⎝

⎛ Ω+⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ ⎟⎟ ⎠

⎞⎜⎜⎝

⎛ Ω−

=

ω ζ

ω k

F X (19)

2

0

0

0

1

2

tg

⎟⎟ ⎠

⎞⎜⎜⎝

⎛ Ω−

⎟⎟

⎠

⎞⎜⎜

⎝

⎛ Ω

=

ω

ω

ζ

ϕ (20)





72

k

m

c

F 0 cos( Ω t)(a)

0

0.001

0.002

0.003

0.004

0.005

0.006

0 1 2 3 4

Frecuencia reducida

R e l a c i ó n e n t r e d e s p

l a z a m i e n t o y f u e r z a

( m

/ N )

0 0,1 0,25 0,5 0,7 1 2

(b)

ζ

Figure 10. Forced system. a) Diagram of system. b) Displacement-force relationship againstfrequency.

where X 0 is the maximum displacement (amplitude of displacement).F 0 is the maximum force (amplitude of force).k is the stiffness constant of the spring.

Ω is the frequency of the excitation force.

ω 0 is the natural frequency defined below.

ζ is the reduced damping defined below.

The natural frequency mentioned above is exactly the frequency at which thesystem vibrates freely, and is defined in the expression (10)

m

k =0ω (21)

where: k is the stiffness constant of the springm is the mass of the system

The reduced damping is defined in the expression (13)

D i s p l a c e m e n t - f o r c e r e l a t i o n s h i p

( m / N )

Reduced frequency





73

km

c

2=ζ (22)

where c is the damping,k is the stiffness of the spring,m is the system mass.

The graph of equation (19) is shown in Figure 10-(b) for different values of the

damping coefficient ζ .

Equation (19) and equation (20) show two very important concepts. The first is that

an increase of damping, ζ , produces a reduction of the displacement X for a given

force. The second is that when the excitation frequency Ω coincides with thenatural frequency of the system ω 0 , the denominator of equation (19) is very smalland its value depends on the damping, which means that the displacement X willbe great. Therefore from the point of view of vibration control it is important thatthe natural and excitation frequencies do not coincide.

6.3.1.- Example. Calculation of the vibration of a single-cylinder engine

This section studies the case of a single-cylinder engine (Figure 11) as anexample of a forced system. The engine mass is M and its reciprocating mass

(piston + gudgeon pin + connecting rod) is m. If the engine rotates at a speed of Ω radians/second, the engine will be excited by a force of inertia equal to

( ) ( ) ( ) ( )t l

r mt mr t

l

r t mr F Ω

Ω−ΩΩ−=⎥⎦

⎤⎢⎣

⎡ Ω+ΩΩ−= 2coscos2coscos2

22(23)

where m is the reciprocating mass (piston + gudgeon pin + connecting rod)

Ω is the rotating speed or frequency in radians per secondr is the eccentricity of the crankshaft,l is the length of the connecting rod.

There is a periodic excitation that is the sum of the two harmonic excitations. One,

known as primary excitation ( )t m ΩΩ− cos2 , has a frequency equal to the rotation

frequency of the engine, and the secondary excitation ( )t l

r mΩ

Ω− 2cos

2

, has a

frequency which is twice that of the rotating frequency of the engine.





74

Figure 11. Single-cylinder engine.

The displacement in the engine will be:

( ) ( )

( ) ( )⎥⎦⎤

⎢⎣

⎡ Ω+Ω

⎟⎟ ⎠

⎞⎜⎜⎝

⎛ Ω+⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟ ⎠

⎞⎜⎜⎝

⎛ Ω−

−=

=

⎟⎟ ⎠

⎞⎜⎜⎝

⎛ Ω+⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟ ⎠

⎞⎜⎜⎝

⎛ Ω−

ΩΩ−+

⎟⎟ ⎠

⎞⎜⎜⎝

⎛ Ω+⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟ ⎠

⎞⎜⎜⎝

⎛ Ω−

ΩΩ−=

t l

r t

k

m

k

t l

r m

k

t m X

2coscos

41

41

2cos

41

cos

2

0

2

22

0

2

2

0

2

22

0

2

2

0

2

22

0

2

ω ς

ω

ω

ω ς

ω ω ς

ω (24)

Where m is the reciprocating mass (piston + gudgeon pin + connecting rod),

Ω is the rotating speed or frequency in radians per second,r is the eccentricity of the crankshaft,l is the length of the connecting rod.

ω 0 is the natural frequency of the system whose value is

m

k =0ω (25)

Where m is the reciprocating mass (piston + gudgeon pin + connecting rod),k is the stiffness of the engine springs





75

7. CONCEPT OF RESONANCE IN A VIBRATING SYSTEM

From equation (19) shown in the graph of Figure 10-(b) we can observe:

a) When the excitation frequency of the system coincides with the natural

frequency (Ω /ω 0 =1) the displacement is maximum.

b) The value of this maximum displacement will increase when the dampingdecreases. If the damping is zero this displacement becomes infinite. In reality,although it will be small, there will always be some damping.

When the excitation frequency coincides with the natural frequency, it is said that

the system is in resonance. For this reason the ω0 frequency is also calledresonance frequency . Resonance, which is a structural “weakness” with respect toexcitation, is responsible for many noise and vibration problems as well as fatigue-induced failure.

Systems try to be designed in a way that the natural frequencies are moved awayfrom the excitation frequencies. When this is not possible (for example, becausethe excitation frequency is variable, as is the case with vehicles) damping must beused. This is what is being done when viscous or damping materials are stuck tobodies (deadening materials).

8.- Several degrees of freedom systems

The systems seen above, as established in part 5, are single degree of freedomsystems. From now, we will look at systems with several degrees of freedom.These systems can have a finite number (2, 3, … , 20, … , 200, … , 2000, etc.) or an infinite number of degrees of freedom. Systems with a finite number of degreesof freedom (however large they are) are called discrete systems, whereas systemswith infinite degrees of freedom are called continuos systems. As can be seen inthe chapter on modal analysis, continuous systems normally approximate throughdiscrete systems.

8.1. Principal modes

It has been observed that when a single degree of freedom system vibrates it doesso following a cosine or sinusoidal relationship (harmonic vibration). This meansthat all single degree of freedom systems can only vibrate freely in one way andwith a determined frequency.

A system with two degrees of freedom, when vibrating freely, can do so in twodifferent ways. These natural vibrating modes are called mode shapes.Furthermore, when the system vibrates in each of these mode shapes it will do so





76

with a given frequency, which is different for each mode shape, and called thenatural frequency corresponding to this mode shape.The set composed by a mode shape and its corresponding natural frequency is

called eigenmodeA system has as many eigenmodes or ways of freely vibrating as it has degrees of freedom.

The system in Figure 12 is a system with two degrees of freedom, since two co-ordinates are needed to fully define its position.

k k k

m m

Figure 12. System with two degrees of freedom.

This system has, therefore, two eigenmodes, each of which has its own naturalfrequency and mode shape

Mode 1: X 11 = 1 X 12=1m

k =1ω (26)

Mode 2: X 21 = 1 X 22=-1m

k 32 =ω (27)

This shows that in eigenmode 1 when the left-side mass displaces 1 cm to theright so does the right-side mass, that is to say that both masses move in phasesimultaneously and the middle spring does not work. In eigenmode 2 when theleft-side mass displaces 1 cm to the right, the right-side mass displaces 1 cm tothe left, that is both masses move in antiphase.

In general mode shapes are more complicated, but they always exist and eachone has its own frequency. The knowledge of modes and their structure is theobject of the modal analysis technique.





77

8.2. Example. Bidimensional model of a vehicle suspension

Another example of a two degree of freedom system is the bidimensional model of

vehicle suspension shown in Figure 13. This model allows us to calculate the pitchand bounce frequencies given by the following expressions:

( )2

22

142 r

β γ α γ α ω +

−−+

= (28)

( )2

22

242 r

β γ α γ α ω +

−++

= (29)

Figure 13. Bidimensional model of vehicle suspension.

Being

M

k k r f +=α (30)

M

bk ckK f r −= β (31)

y

r f

I

ck bk 22 +

=γ (32)

M

I r

y= (33)

Wherek f is the stiffness of the front suspension,k r is the stiffness of the rear suspension,M is the vehicle mass,b is the horizontal distance between the front axle and the centre of gravity,c is the horizontal distance between the rear axle and the centre of gravity,

I y is the pitch inertia moment.





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9. WAYS OF DESCRIBING A VIBRATION: DISPLACEMENT, SPEED ANDACCELERATION

The vibration of a point can be described by means of three parameters:acceleration, speed and displacement. The most frequently used parameter isacceleration, since the vibration transducers most commonly used areaccelerometers. However, it is possible to obtain the speed or displacement, bothin the time and the frequency domain from acceleration.

In the time domain speed is obtained by the integration of the acceleration:

∫ = adt v (34)

and the displacement by the integration of the speed

∫ = vdt x (35)

In the frequency domain speed is calculated by the expression

jav = (36)

and displacement by the expression2

ω ω a jv x −== (37)

where 1−= j ,

ω is the frequency in radians per second.

From these expressions it is important to point out:

• The speed amplitude is ω times the displacement amplitude.

• The acceleration amplitude is

ω

2times displacement amplitude.

• The speed is 90º out of phase in relation to the displacement.

• The acceleration is in antiphase in relation to the displacement.

As a consequence of the above it can be deduced that the high frequencyvibration displacements are very small.





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10. THE ISOLATION OF VIBRATIONS

A vibrating system with one degree of freedom excited by a sine force is

expressed by:

( ) ( )00 cos −Ω⋅= t F t f (38)

The relationship between the force applied to the mass and the force that thesystem transmits through the spring and the damper is called the transmissionfactor of a vibrating system. The transmission factor is given by the expression

( )2222

22

0 41

41

ρ ζ ρ

ρ ζ ξ

+−

+==

F

F T F (39)

where F T is the amplitude of the transmitted force,F 0 is the amplitude of the excitation force.

ζ is the reduced damping as defined in the expression (13),

ρ is the relationship between the excitation frequency and theundamped natural frequency

0ω ρ Ω= (40)

where Ω is the excitation frequency,

ω 0 is the undamped natural frequency as defined in expression (10).

The relationship between the force transmitted and its deformation is called thedynamic stiffness of an isolating element (mounting).

X

F k T

D ∆= (41)

This dynamic stiffness should not be mistaken with the static stiffness we havestudied up till now. The relationship between both parameters is given by theexpression

222 ck k D Ω+= (42)

This concept enables us to measure the force transmitted through a mounting.Dynamic stiffness is a value supplied by the manufacturer and deformation can becalculated in the following way:

• The accelerations on both sides of the mounting are measured.





80

• Both signals are integrated twice in order to obtain the displacement asexplained in the previous point.

• Both signals are subtracted to obtain the deformation of the mounting.

11. THE ACOUSTIC RADIATION OF VIBRATING SURFACES

11.1. Monopole sources

The simplest source for generating acoustic waves is the monopole source. Amonopole source is a small sphere (its dimensions are small compared to thewavelength) whose radius varies sinusoidally in time. This sphere producessinusoidal, spherical waves which travel through the medium which is infinite andhomogenous (Figure 14). The acoustic pressure of such waves will be

r

p(r,t)

Figure 14. Monopole source.

( )

( )kr t jer

At r p −= ω , (43)






The structure, i.e., the vehicle and its components, has frequencies called naturalfrequencies that, even under small excitations, show high levels of vibration.Therefore, a control strategy is to decouple the excitation frequencies from thenatural frequencies. When this is not possible other strategies can be used suchas structural internal damping.

As a summary, the presence of vibration in a vehicle may be due to a high level of excitation or to the presence of resonances.

When the cause of vibration is a high level of excitation, the excitation should bereduced, or, if this is not possible, the transmission path should be interrupted. For example, if it is found that the vehicle vibration is due to excessive enginevibration, the engine balance should be improved, and if this is not possible (for

technical or feasibility reasons), the silentblocks should be improved.

When the cause of the vibration is structural resonance, first we should try toisolate it as much as possible from any excitation frequencies or, if this is notpossible or is insufficient, we should try to increase the structural damping.

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