Applied Acoustics 67 (2006) 15–27

www.elsevier.com/locate/apacoust

Using a thin actuator as secondary sourcefor hybrid passive/active absorption in

an impedance tube

Marıa Cuesta *, Pedro Cobo, Alejandro Fernandez,Jaime Pfretzschner

Instituto de Acustica, CSIC, Serrano 144, 28006 Madrid, Spain

Received 5 November 2004; received in revised form 17 May 2005; accepted 17 May 2005

Available online 29 June 2005

Abstract

This paper describes the practical implementation of a piezoelectric actuator as secondary

source for hybrid passive/active broadband sound absorption in a standing-wave tube. This

actuator consists of a thin circular aluminium plate driven by a piezoelectric patch and glued

to a flexible rubber support. The resulting device has been mounted in a thin metallic ring that

fits perfectly to the tube diameter. Passive absorption is afforded by either a porous layer or a

microperforated panel, backed by an air gap. Active absorption is accomplished by releasing

the sound pressure at a microphone behind the material, using either a loudspeaker or the

actuator as secondary source. Results of broadband sound absorption reveal the feasibility

of the piezoactuator. Compared to the loudspeaker, this actuator allows to greatly reduce

the whole thickness of the hybrid absorber.

� 2005 Elsevier Ltd. All rights reserved.

Keywords: Broadband sound absorption; Thin piezoelectric actuator

0003-682X/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.apacoust.2005.05.001

* Corresponding author. Tel.: +34 91 5618806; fax: +34 91 4117651.

E-mail address: mcuesta@ia.cetef.csic.es (M. Cuesta).

16 M. Cuesta et al. / Applied Acoustics 67 (2006) 15–27

1. Introduction

The aim of this work has been the practical implementation of a hybrid passive/

active system to absorb the broadband sound field propagating in a standing-wave

tube. To reduce the whole thickness of the hybrid absorber, the active secondaryloudspeaker used for controlling the low frequency contents of the noise has been

replaced by a thin piezoelectric actuator.

Noise control can be achieved by either passive or active techniques. Passive noise

control affords suitable solutions to medium and high frequency problems, but be-

comes unpractical at low frequencies due to bulk and weight restrictions. High levels

of low frequency noise are nevertheless very common in urban environments (from

vibrations, engines, aircraft, industrial machinery, etc.) and their effects can be quite

harmful to health. Low frequency noise must be decreased by active techniques,which are based upon the destructive interference of the existing sound field (primary

noise) with an electronically introduced sound opposite in phase (secondary noise)

[1,2]. For broadband noise applications, hybrid solutions combining both passive

and active techniques are required [3,4].

In the last years, there has been an increasing interest in the development of

hybrid strategies for noise control based on the principle of the active sound absorp-

tion, firstly introduced by Olson and May [5]. Hybrid passive/active absorbers arise

as an interesting alternative in many noise control problems (inside vehicles, aircraft,buildings, etc.) where the traditional solution is too bulky and weighty. Passive

absorption has been usually achieved with a porous material backed by an air cavity

and a rigid wall. Such a system is suited for maximum absorption at frequencies for

which the air layer thickness is an odd integer of the quarter wavelength. Guicking

and Lorenz [6] proposed the active equivalent k/4 resonance absorber, driving a sec-

ondary loudspeaker at the back of this system so as to minimise the sound pressure

picked up by an error sensor just behind the passive layer. A second microphone in

front of the porous layer was needed to implement the analog control filter. Theyreported sound absorption coefficients between 0.6 and 0.7 in the low frequency

bandwidth 200–500 Hz. Furtoss et al. [7] proposed a hybrid strategy to control the

input impedance to the system in order to optimise the passive layer absorption at

low frequencies. This strategy allows defining an optimal impedance to be achieved

at the input of this hybrid system so as to maximise the broadband sound absorption

[8]. Beyene and Burdisso [9] suggested the suppression of the reflected wave in the air

gap behind the material (impedance matching condition). Two closely spaced micro-

phones and a deconvolution circuit were required to separate the reflected compo-nent from the incident wave. A hybrid absorption coefficient between 0.8 and 1

was reported in the band 100–2000 Hz. Recently, a study has concluded that the

performance of both strategies (pressure release and impedance matching) strongly

depend on the flow resistance of the porous layer [10]. The pressure release condition

is suitable when the flow resistance of the passive layer is close to the acoustic imped-

ance of air (Z0). On the other hand, the impedance matching condition should be

implemented when the flow resistance of the porous layer is smaller than about

0.7Z0. Later on, Cobo et al. [11] have demonstrated the feasibility of designing

M. Cuesta et al. / Applied Acoustics 67 (2006) 15–27 17

thinner hybrid passive/active absorbers using microperforated panels instead of the

conventional porous materials. They reported an average absorption of 82% in the

frequency range from 100 to 1600 Hz, imposed by the tube dimensions. The main

benefits of such a proposal were the thickness reduction of the control system and

the use of materials cleaner than porous absorbers.The hybrid passive/active absorption technology is expected to be applied in the

automotive and aeronautic industries, and in building acoustics. The final solution,

including the passive material, the air cavity and the secondary source, must be suf-

ficiently reduced in size and weight for a practical implementation. In order to make

even thinner the hybrid passive/active absorber, the loudspeaker can be replaced by a

plate actuator. Nowadays, there is an increasing interest for the design of flat panel

actuators due to the great variety of applications, such as in multimedia and high

fidelity audio systems, or in active control prototypes.Heydt et al. [12] proposed a new type of loudspeaker which radiated sound

through the electrostrictive response of a thin polymer film. This electrostrictive

polymer film (EPF) loudspeaker was constructed with inexpensive and lightweight

materials, like silicone. They showed that such a very compact actuator was able

to provide large volumetric displacements as a consequence of large film thickness

strains, affording in this way high sound pressures. The authors suggested some

applications for EPF loudspeakers, including active noise control and general pur-

pose flat-panel loudspeakers. Zhu et al. [13] used a thin actuator based on theNXT technology (New Transducer Ltd.) to develop electronically controlled smart

thin panels, in an attempt to provide a surface with a predetermined reflection coef-

ficient (perfect reflector, absorber, or transmission blocker). The NXT technology is

operating with the principle of optimally distributed vibration modes. The frequency

response function (FRF) of such a panel, compared to that of a conventional cone

speaker, did not offer the kind of flat response that would be ideal for feedback con-

trol. However, the dynamic was found to be consistent and repeatable, and feed

forward control was successfully implemented. Lissek and Meynial [14] have devel-oped an isodynamic transducer as alternative to the conventional cone speaker for

use in active acoustic materials. Such active materials used locally reacting cells con-

taining the transducer and a feedback control loop. A finite element model for the

passive and active sound absorption coefficient of such a transducer under normal

incidence was derived. They showed an experimental absorption coefficient above

0.7 between 30 and 500 Hz, using a preliminary prototype of isodynamic transducer.

Bai and Liu [15] have built a large multi-exciter panel speaker. A numerical model

was first developed, where the electrical and mechanical systems, as well as theacoustical coupling in the panel speaker, were accounted for within a coupled frame-

work. Performance indexes including the frequency response, the sound power, and

the directional response were calculated. A genetic algorithm was utilized to search

for the optimal positions of the exciters and for the delays of input signals. Experi-

mental investigations were carried out in an anechoic room. The panel was assumed

to be simply supported and driven optimally by three exciters. This optimal design

produced an improved omni-directionality as compared to the non-optimal position

and higher acoustic output was radiated at all frequencies.

18 M. Cuesta et al. / Applied Acoustics 67 (2006) 15–27

This paper deals with the design of a 0.5-mm thick actuator made with a thin alu-

minium plate driven by a piezoelectric patch, for an application of broadband noise

absorption in a circular impedance tube. Rather than presenting theoretical results

for the plate vibration and radiation, special attention has been paid to practical

aspects and experimental results. This paper completes the previous theoreticaland experimental studies carried out by the authors in the field of broadband sound

absorption [10,11]. The actuator characteristics are analysed in Section 2. The exper-

imental setup as well as the results on hybrid passive/active absorption are reported

in Section 3. Comparisons of the results obtained with such a piezoactuator to those

with a loudspeaker show the feasibility of this practical design.

2. Actuator design

The secondary source has been designed according to the features of the actu-

ators used for active structural acoustic control (ASAC) of low frequency noise

radiated by vibrating structures [2]. These actuators are mounted on the vibrating

surface and are commonly implemented by piezoceramic patches. Therefore, the

higher is the bending moment provided by these piezopatches to the structure,

the higher is the control authority of such secondary sources. The vibration of

either rectangular or circular plates, driven by piezoelectric patches, has been al-ready studied [16,17]. Many parameters, describing both the plate (density, flexural

rigidity, Poisson ratio, damping, dimensions, etc.) and the piezoelectric elements

(dimensions, piezoelectric constants, voltage, etc.), should be taken into account

for modelling the overall plate motion. However, in a first attempt to maximise

the induced plate vibration under a constant applied electric field, without any fre-

quency analysis, most care should be taken on the thickness of the piezoelectric

elements. This parameter should be optimised in relation to the mechanical prop-

erties and thickness of the plate [16,17]. In this research, the thickness for the pie-zoelectric patch has been estimated according to [16]. The main purpose was to

compare the capabilities of such a piezoactuator to those of the ideal secondary

source for hybrid passive/active absorption in normal incidence [10,11]. The prac-

tical procedure proposed for designing the piezoactuator could be applied to other

setups.

Fig. 1(a) shows three views of the designed piezoelectric actuator, which is com-

posed of three assembled elements:

� A thin aluminium circular plate with a piezoelectric patch pasted in its centre.

This patch is made of two piezoelectric ceramics, bonded each one to a plate face.

In order to provide highest vibration, the plate material has been selected with low

flexional stiffness and small thickness.

� A thin flexible rubber support. It consists on a ring of commercial rubber 2-cm

wide and 1-mm thick.

� A thin aluminium ring whose internal diameter perfectly fits to the external tube

diameter (Fig. 1(a), right).

Fig. 1. Pictures of the designed actuator: (a) rear, front and profile views. (b) Electrical connections of the

piezoactuator. The dots inside the piezoelectrics denote polarity.

M. Cuesta et al. / Applied Acoustics 67 (2006) 15–27 19

The characteristics of the plate/piezoelectric combination have been summarized

in Table 1. Note that the plate diameter is slightly smaller than the tube diameter so

that the diaphragm together with the flexible support can vibrate freely. Then, this

resulting device has been fixed to the metallic ring. The piezoelectric patch(PKG21 from Stelco) has been chosen from the commercially available stock, with

a thickness slightly higher than 0.19 mm, which is the optimal one for the considered

plate. In general, if the optimal thickness is not available, it is recommended to

choose somewhat thicker piezoceramics, since the decrease in the effective moment

is less severe than with thinner piezoceramics [16]. Furthermore, as suggested by

Table 1

Parameters describing the designed piezoelectric actuator

Actuator characteristics

Plate diameter (m) 95 · 10�3

Plate thickness (m) 5 · 10�4

Piezoceramic thickness (m) 24 · 10�5

Piezoceramic diameter (m) 20 · 10�3

Piezoelectric charge coefficient d31 (m/V) 250 · 10�12

Dielectric constant k33 2800

Loss factor tand 22 · 10�3

20 M. Cuesta et al. / Applied Acoustics 67 (2006) 15–27

Banks et al. [17], the radius of the circular piezoelectric has to remain smaller than

the plate radius. Other important features are the specific electromechanical param-

eters. For high structural bending, a large piezoelectric charge coefficient (d31) is re-

quired. For low frequency applications, it is also recommended to employ ceramics

with high dielectric constants (k33) and high loss factors (tand).To strengthen the low frequency bending of the structure, as it is usual in ASAC

control, both ceramics have to be driven 180� out-of phase [2]. In this manner, the

expansion of one piezoelectric coincides with the contraction of the other and an

overall bending movement is excited in the plate. Fig. 1(b) illustrates the electrical

connections between the plate and the patch. Note that the plate is connected to

ground so that the device is protected from any electrical discharge. The final proto-

type is very lightweight and thin, and can be perfectly matched at the end of the

impedance tube (Fig. 2), avoiding any sound leak or unwanted vibration. This pic-ture displays the experimental setup built up to perform absorption measurements

with the actuator as active termination. The primary broadband noise is generated

by the loudspeaker located at the opposite side.

Before carrying out hybrid passive/active control tests, the control authority of this

actuator has been checked and compared to that of a loudspeaker in the impedance

tube. This assessment has been accomplished measuring the transfer function between

either control source (the loudspeaker or the actuator) and a microphone in prede-

fined locations of the tube. The MLS technique was used for this purpose. As anexample, Fig. 3 shows the FRFs measured at the microphone located 35-cm away

from the secondary actuator (microphone m2 in Fig. 4). Fig. 3(a) overlays the mea-

sured FRFs when the plate is driven in three ways: with each ceramic alone and with

the whole patch. Therefore, it is verified that both piezoceramics perform evenly in

practice and that sound radiation is effectively reinforced using the patch configura-

tion. These results are presented in the range 100–1600 Hz, which is the frequency

band considered for the passive and active absorption experiments, as described in

Fig. 2. Final implementation of the actuator at the end of the impedance tube.

200 400 600 800 1000 1200 1400 1600-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

Patch External ceramic Internal ceramic

200 400 600 800 1000 1200 1400 1600-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

Frequency (Hz)

FR

F (

dB

)

Frequency (Hz)

FR

F (

dB

)

PatchLoudspeaker

a

b

Fig. 3. (a) FRFs between the actuator and the microphone m2 (see Fig. 4) when the plate is driven in

different ways. Note that the curves for the external and internal ceramics are undistinguishable for the

resolution of the Figure. (b) Comparison of the FRFs of the actuator and loudspeaker.

M. Cuesta et al. / Applied Acoustics 67 (2006) 15–27 21

the next section. Fig. 3(b) compares the actuator and loudspeaker FRFs, measuredboth with the same amplification level (an audio amplifier was used). To match the

high impedance of the piezopatch to the low impedance of the audio amplifier, a

transformer was employed for measurements with the actuator. In the frequency

Fig. 4. Experimental setup for measuring hybrid absorption.

22 M. Cuesta et al. / Applied Acoustics 67 (2006) 15–27

range of interest for active experiments (<700 Hz), both transducers perform simi-

larly. However, between 400 and 650 Hz, the actuator response is slightly higher.Note that the resonances that appear in these FRFs are mainly produced by the

standing wave field in the tube.

3. Experimental setup and results

Both passive and active absorption measurements have been carried out in a

standing wave tube of 10 cm of diameter and 1 m of length. Two experiments havebeen conducted: one with a porous material as passive layer and another with a thin-

ner microperforated panel (MPP). High broadband sound absorption coefficients

have been reported previously by each absorber and a loudspeaker as secondary

source [10,11,18]. In this paper, these results are compared to those obtained when

the above described piezoactuator replaces the secondary loudspeaker. Preliminary

tests carried out with this actuator already showed encouraging potentiality [19].

A sketch of the impedance tube for measuring hybrid passive/active absorption is

presented in Fig. 4. The primary broadband noise was generated by a loudspeakerlocated at one end. The passive system, consisting on a layer of either porous mate-

rial or MPP, backed by a 4.5-cm thick air cavity, was placed at the opposite side of

the tube. The porous material was a 4-cm thick melamine foam with air flow resis-

tivity of 14000 N s/m4 [10,18]. The MPP is made with a 0.13-mm thick rigidified

metallic sheet with a perforation ratio of 0.5% and an orifice diameter of 0.13 mm

[11]. The active control system consisted of a secondary source (either the designed

actuator or a flat diaphragm loudspeaker), a 1/4 in. microphone at the rear face of

the material as error sensor, and a digital controller. The absorption coefficient

M. Cuesta et al. / Applied Acoustics 67 (2006) 15–27 23

was measured according to the transfer function method (ISO 10534-2) using two

microphones (m1 and m2) separated either 9 or 18 cm. Both, the tube dimensions

and the distance between the measuring positions, set the valid frequency range from

95 to 1715 Hz. Complementary information about the experimental setup is avail-

able in [11,18].In a first step, the passive absorption coefficient of the two-layer system was mea-

sured. The material, either the porous layer or the MPP, was placed in a custom

holder ensuring that was plane parallel and backed by a 4.5-cm thick air cavity. After

that, active control was implemented replacing the rigid end cap by the secondary

source. For experiments with active control, the same air cavity thickness was set

from the back face of the material to the surface of either the secondary actuator

or the loudspeaker diaphragm. An adaptive controller based on a C40 DSP from

TI, and implementing both the FXLMS and FULMS algorithms, was configured.A feedforward strategy was performed, using as reference signal the same white noise

which drives the primary source. Maximum cancellation of the error signal for each

configuration was achieved with FIR filters of 50 taps for both the control and sec-

ondary path filters.

Fig. 5 compares the passive, active (using either the actuator or the loudspeaker),

and hybrid passive/active (with the loudspeaker) absorption coefficients from 100 to

1600 Hz, measured with the porous layer as the passive absorber. The highest passive

absorption was achieved around 950 Hz. When the error signal is directly minimizedby the secondary loudspeaker, the active absorption coefficient is higher than the pas-

sive one at frequencies below720 Hz. Thus, a hybrid configuration can be implemented

200 400 600 800 1000 1200 1400 16000

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ab

sorp

tio

n C

oef

fici

ent

PassiveActive with loudspeakerActive withthin actuatorHybrid passive/active with loudspeaker

Fig. 5. Absorption coefficients of a two layer system consisting of a 4-cm thick melamine foam and a 4-cm

thick air gap for several control conditions.

24 M. Cuesta et al. / Applied Acoustics 67 (2006) 15–27

just low-pass filtering the error signal. Therefore, the control system operates in fact

passively and actively, respectively, above and below this cut-off frequency. In this

case, the error signal was low-pass filtered with a 14th-order Butterworth filter. An

average absorption coefficient of 0.97 and 0.9, in the range from 100 to 1600 Hz,

was achieved with the loudspeaker performing in hybrid passive/active and purely ac-tive configurations, respectively [18]. However, when the actuator is used as secondary

source, purely active control provides an average absorption of 0.96, comparable to

that with the loudspeaker in hybrid performance. Therefore, when using the designed

actuator the controller needs less computational power, since it does not require low-

pass filtering the error signal. Furthermore, in the low frequency range between and

700 Hz, the absorption with the actuator is slightly higher than that obtained with

the loudspeaker. In fact, as observed in Fig. 3(b), in this frequency range the actuator

response is faintly higher than the loudspeaker response.Results with the MPP as passive material are given in Fig. 6. As compared to the

porous absorber, slightly lower absorption is obtained with half of the total thick-

ness. Passive control is maximum around 850 Hz. The absorption curves show the

same trend that those measured in Fig. 5. The average absorption coefficient with

the loudspeaker was 0.82 and 0.76, for the hybrid and purely active configuration,

respectively [11,18]. Very similar purely active absorption coefficient is obtained in

average (0.81) with the actuator. It should be emphasised that the total thickness

of the hybrid absorber is either 4.63 or 10 cm, when the actuator or the loudspeaker,respectively, are used as secondary source. Table 2 summarises the average absorp-

tion coefficients, for each absorber and control condition.

200 400 600 800 1000 1200 1400 16000

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ab

sorp

tio

n C

oef

fici

ent

PassiveActive with loudspeakerActive with thin actuatorHybrid passive/active with loudspeaker

Fig. 6. Absorption coefficients of a two layer system consisting of a 0.13-mm thick MPP and a 4.5-cm

thick air gap for several control conditions.

Table 2

Average absorption coefficients ðaÞ obtained with each absorber and control condition

Absorber a (100–1600) Hz

Porous layer (4 cm) + air cavity (4.5 cm)

Passive control 0.79

Active control with loudspeaker 0.90

Active control with thin actuator 0.96

Hybrid control with loudspeaker 0.97

MPP (0.13 mm) + air cavity (4.5 cm)

Passive control 0.68

Active control with loudspeaker 0.76

Active control with thin actuator 0.81

Hybrid control with loudspeaker 0.82

M. Cuesta et al. / Applied Acoustics 67 (2006) 15–27 25

The main advantage of the proposed prototype, as compared to the traditional

system using a loudspeaker, is to provide high broadband absorption with a reduced

volume and a simple manufacture. Besides, from the previous results, it seems that

the active absorption curves obtained with the actuator slowly fall at frequencies

higher than with the loudspeaker. In fact, from 700 to 1200 Hz, these active absorp-

tion curves are similar to the passive ones. This could be due to the fact that the actu-

ator does not radiate sufficiently in this frequency range, as can be seen in Fig. 3(b).

This behaviour suggests that a piezoactuator could be theoretically designed havinga frequency response which implements the expected band-pass filter for each con-

trol application.

4. Summary and conclusions

This paper has reported the practical implementation of a piezoelectric actuator

as secondary source for hybrid passive/active broadband sound absorption in a cir-cular standing-wave tube. This research completes the theoretical and experimental

results on hybrid absorption in the tube, previously reported by the authors. The

proposed actuator consists of a 0.5-mm thick aluminium plate driven by a piezoelec-

tric patch. Special attention has been paid to practical aspects and experimental re-

sults. The piezoelectric ceramics have been selected with a thickness as close as

possible to the optimal value defined in [16]. Both the thickness and the radius of

the circular piezoelectric remain small in relation to the dimensions of the plate.

The designed actuator has been checked in active experiments for broadband noiseabsorption in normal incidence. Both passive and active absorption coefficient mea-

surements have been carried out in an impedance tube with two absorbers: one with

a porous layer (4-cm thick) as passive material, and other with an MPP (0.13-mm

thick). For both cases, a 4.5-cm thick air cavity between the passive layer and the

rigid wall is set. The low frequency absorption has been improved with active control

inside the air cavity. Active absorption was accomplished by releasing the pressure at

26 M. Cuesta et al. / Applied Acoustics 67 (2006) 15–27

the error sensor behind the material, using either a traditional loudspeaker or the

actuator as secondary source.

Experimental results have demonstrated that is possible to obtain high broadband

absorption, including low frequencies, with very thin absorbers. For instance, a hy-

brid absorber made up with an MPP as the passive system and a plate actuator assecondary source provides an average absorption of 81% in the frequency range

from 100 to 1600 Hz. This passive/active absorber has a total thickness of

4.63 cm, as compared with 10 cm when using a loudspeaker as secondary source.

These results reveal the feasibility of the described piezoactuator for hybrid pas-

sive/active sound absorption with reduced size and easy manufacture.

Acknowledgement

This work has been supported by the Ministry of Education and Science through

Grant DPI2001-1613-C02-01.

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