A seminar report on

Measurement of Damping of Structures by the Power Input Method

By

Prashant.K.LIst sem M.Tech

CADSMCE Hassan

Introduction

Damping is an important model parameter for the design and analysis of vibrating structures. The damping in combined and complex structures is often dominated by losses at joints,supports etc. In addition, all engineering materials dissipate energy during cyclic deformation. Some of them, such as elastomers, plastics and rubber, dissipate much more energy per cycle of deformation than metallic materials under the same stress ratio.

Damping refers to the extraction of mechanical energy from a vibration system usually by conversion of this energy into heat. Damping serves to control the steady state resonant response and to attenuate traveling waves in the structure.

Nomenclature

Damping ration …………()

Log decrement…………….()

Loss factor…………………()

Loss angle…………………()

tan……………………..

Specific damping capacity………..()

Quality factor…………………(Q)

Damping Damping is a phenomenon and a material property that

can be described as mechanical energy dissipation under cyclic stress.

TYPES OF DAMPING

Damping is classified in many different ways but the three major mechanisms of damping are

material (internal) damping, structural damping and

fluid damping.

Material damping results from mechanical energy dissipation during cyclic deformation within almost all engineering materials.

Structural damping occurs when the mechanical energy dissipation is caused by rubbing friction resulting from relative motion between members in a structures that has common points of contacts or joints,supports etc..

Fluid damping can be described as if a member of the system moves in a fluid the mechanical energy caused by drag forces is dissipated.

Methods of damping test

a) Frequency- domain modal analysis curve fitting method,

b) Time domain decay-rate methods, and

c) Other method based on energy and wave propagation

(PIM).

Power Input Method (PIM) The power input method (PIM) from group (c) above,

is very powerful method for obtaining frequency – averaged loss factor of structures under steady state vibration.

The PIM is based on a comparison of the dissipated energy of a system to its maximum strain energy under steady state vibration. Some errors may be introduced through the measurement technique, but the PIM is fundamentally unbiased at the natural frequencies of well-defined modes or when the loss factors are frequency band averaged over many modes. These frequency-averaged damping values are widely used in the automotive industry in vehicle computer models based on Finite Element Method (FEM) and Statistical Energy Analysis (SEA).

The loss factors of a structural system can be defined as, (1)

where ESE is the strain energy, E is the energy dissipated from damping, and is the damping loss factor in the frequency band .

Assuming a stationary input energy at a fixed location, E can be replaced with Ein. And the value of Ein is determined by

(2) where

hff is the driving point mobility function and

Gff is the power spectral density of the input force

For obtaining the value of ESE it is necessary to make

some assumptions.

1. since the strain energy cannot be calculated directly from force and velocity measurements, it must be replaced with twice the kinetic energy - which holds true at the natural frequencies of the system.

2. the system being measured must be approximated by a summation as opposed to a volume integral when taking measurements. From this the kinetic energy is evaluated by.

(3)

Then finally assuming the system is linear,the transfer mobility function hif is calculated as

(4)

substituting the value of eqns 2,3 &4 in eq 1. We get the

loss factor as

Laser Vibrometer Laser vibrometers use optical interferometry to measure

surface velocities ranging from 0 to 125 mm/s/V and from 0 to 30 MHz depending on equipment arrangements. The shift beam frequency is given by

fs= 2v/ ,where fs is shift in beam frequency and v is vibrating

surface velocity ADVANTAGES OF LASER VIBROMETR

due to non-contact nature of the transducer, eliminates mass loading of the structure due to response measurement transducers

laser measurements can be taken more quickly than with accelerometers because of the reduction in setup time and time spent moving accelerometers between different measurement locations.

Experimental Setup and Procedure

For damping measurements of a commercial vehicle door glass assembly, a fully assembled door with the window installed and completely sealed in the weather stripping

was suspended with bungee cords as shown in Fiure1.

Reflective materials must be applied on the glass to

facilitate proper reflection of the laser beam. Reflective tape (3-M 510-10X) sections of 3mm square

were used to create a 4 cm grid across the approximately

50x70 cm visible portion of the vehicle side glass

A shaker was attached to the window on the opposite side as the reflective tape grid through a stinger-force

transducer combination as illustrated in Figure 2

For the estimation of the loss factors, the glass was excited using burst random excitation from 100 Hz to

8 kHz. Figure 3 shows an example of a typical measured

FRF at the driving point.

Result

Figure 4 shows the loss factor results. It can be seen that the laminated PVB glass has much higher damping than the regular tempered glass over the entire frequency range. The high loss factor values at the lower frequencies octave band are consistent with the driving point FRF figure. Dominant bending modes are more influenced by the internal system damping than less prominent modes. Also, the loss factors found through the PIM maintain the same trend found in most loss factor estimates, that is, decrease in damping with increasing frequency

Conclusion

An experimental technique for determining the internal loss factors (damping) of structures was investigated. The PIM coupled with the use of a laser vibrometer allows for quick, and accurate measurements of loss factors of flat panel type structures. The effectiveness of this method has been shown through a case study involving laminated and

tempered vehicle side glass windows.

Fig1: Hanging door assembly with reflective grid in place

Fig2:Experimental set up

fig3:Driving Point FRF measured with the tempered

glass

. fig4:Frequency-averaged loss factor comparison results

REFERENCES 1 Chu, F.H., and Wang, B.P., “Experimental Determination of

Damping in Materials and Structures” Damping Application

for Vibration Control, Torvik,P.J., editor, ASME Winter

Annual Meeing, Chicago, 1980, pp. 113-122.

2 Carfagni, M. and Pierini, M. “Determining the Loss Factor

by the Power Input Method (PIM), Part 1: Numerical

Investigation”. Journal of Vibration and Acoustics, 121 1997,

pp. 417-421.

3 Bies, D.A. and Hamid, S. In Situ Determination of Loss

and Coupling Loss Factors by the Power Injection Method,

Journal of Sound and Vibration, 70(2), 1980, pp. 187-204.

4 Polytec OFV-3000/OFV-302 Vibrometer Operators Manual,

1993, Waldbronn, Germany.

5 Silva, J.M.M., Maia, N.M.M. and Ribeiro, A.M.R.,

Cancellation of Mass-Loading Effects of Transducers and

Evaluation of Unmeasured Frequency Response Functions,

Journal of Sound and Vibration, 236(5), 2000, pp. 761-779.

6 Ashory, M.R.. “correction of Mass-Loading Effects of

Transducers and Suspension Effects in Modal Testing” 1998

Proceedings of the XVIth IMAC, CA, U.S.A, pp. 815-828.