2010 Sound ﬁeld reproduction applied to ﬂight vehicles sound environments

8/11/2019 2010 Sound field reproduction applied to flight vehicles sound environments

1/10

Sound field reproduction applied to flightvehicles sound environments

Cedric Camier1, Philippe-Aubert Gauthier1, Yann Pasco1, and Alain Berry1

1Universit e de Sherbrooke, Sherbrooke, Quebec, J1K 2R1, Canada

Correspondence should be addressed to Cedric Camier ([email protected])

ABSTRACT

This paper proposes a preliminary theoretical study for sound field and sound environment reproduction inflight vehicles. A fully-coupled cavity, cylindrical shell and exterior radiation model approximates an aircraftcabin mock-up. Material and geometry charateristics are inspired by measurements perfomed on a cabinmock-up. The sound field reproduction is based on reproduction error minimization at a microphone arraypositionned in the cavity. Two reproduction systems, based on actuators or loudspeakers are simulated in

order to compare their feasability and performance. The model linking excitator strength with the soundpressure on the spatially extended array region is developped in a matricial form. The promising resultsobtained in terms of reproduced pressure in the array region in both cases presume the reliability of suchdedicated systems.

1. INTRODUCTIONSince the first spatial sound experiments [1], [2], interest

in spatial audio had continuously increased over the past

century [3]. Beside applications to music reproduction

and film presentation, spatial sound has recently gained

the attention from the transport industry for flight simula-

tors and as a potential sound quality evaluation or designtool. This paper presents a preliminary theoretical study

for sound field and sound environment reproduction in

mock-ups of aircraft cabins.

Since the 1970s, several works have been devoted to the

reproduction or synthesis of exterior and interior noises

of flight vehicles [4]-[7]. Most of these works are primar-

ily devoted to the evaluation of sound quality and annoy-

ance of vehicle noises without any in-depth consideration

of the spatial distribution of sound. However, it is known

that the spatial distribution of sound sources plays an im-

portant role in auditory stream segregation. Indeed, spa-

tial separation of sources reduces masking. Hence, thespatial distribution of sound should be addressed in cur-

rent work on sound environment reproduction for sound

quality testing or virtual rendering of flight scenarios in

flight vehicle mock-ups and flight simulators. Recent re-

search works go in that direction [8], [9].

1.1. Spatial audio and sound environment re-productionMost of the recent research works on spatial audio using

multichannel systems are based on few dominant tech-

nologies: stereophonic sound fundamentals extended to

Surround sound systems [2], Ambisonics [10] and

wave field synthesis (WFS) [11]. Each of which re-

lies on different perceptual and technological hypothe-

sis. Among these technologies, Ambisonics and WFS

are perhaps the twos that have the greatest potential forpsychophysically valid sound environment reproduction.

Ambisonics have already been use for soundscape re-

production [12]. Since these types of sound field repro-

duction systems are normally used in more or less well

controlled listening rooms, it has been argued that room

response may degrade the sound field reproduction sys-

tem ability to physically recreate and approach the tar-

get sound field [13], [14]. Several researchers have then

addressed the spatial room compensation problem [15]-

[22]. The great challenge behind these room compen-

sation methods stands in the requirement that the real

acoustic of the listening room must be replaced by a vir-

tual or target acoustic which have been computed or mea-sured in an acoustic space different from the listening

room.

1.2. Sound rendering of interior vehicle noisein vehicle mock-upsIn contrast with generic applications mentioned above,

sound environment or sound field reproduction in ve-

hicle mock-ups brings different challenges and some-

AES 40TH INTERNATIONAL CONFERENCE, Tokyo, Japan, October 810

1


2/10

Camier et al. Sound field reproduction in aircraft

how simplifies the room compensation issues. Firstly,

the highest quality vehicle sound environment reproduc-

tion system would not only involve a sound system, buta vehicle mock-up which is visually, mechanically and

geometrically very similar to the real vehicle. More-

over, reproduction sources (either acoustical or vibra-

tional) should be invisible to the listener. Accordingly,

it is expected that the original vehicle and corresponding

mock-up should have a similar, or at least a similar type

of, vibroacoustical behavior. Therefore, room compen-

sation could be more easily applied to that practical case

since the difference between the two systems are greatly

diminished. This have the potential to diminish residual

artifact. Secondly, since many transport applications of

spatial sound are concerned by the physically valid re-

construction of sound field, a closed-loop room compen-sation is mandatory to ensure and physically certify that

the reproduced sound field is a physical reconstruction

of the original sound field. Indeed, such spatial sound

systems could not rely on the illusory creation of an au-

ditory scene such as achieved in the audio industry since

it might have to be certified by various agencies, such as

for flight simulators or aircraft sales. Thirdly, most of the

major interior noises are stationary or nearly stationary

(turbulent boundary layer, engine, jet, etc. [23]) so that

any room compensation residual artifact such as pre- and

post-echoes should be inaudible. These three prelimi-

nary hypothesis motivate the interest of room compensa-tion for flight vehicles sound environment reproduction.

The purpose of this paper is to evaluate the feasibility

of sound field reproduction based on room compensa-

tion using a simplified theoretical model of an aircraft

cabin and mock-up. Several scenarios are compared on

the basis of different reproduction source types: vibra-

tional sources on the cabin structure or acoustical sources

located in the cabin cavity.

1.3. Paper outlineSection 1 introduces the general problem and formu-

lates the main research question addressed in this paper.

Section 2 describes the fully-coupled cavity, cylindri-

cal shell and exterior radiation model that approximates

an aircraft cabin and mock-up. The spatially-extended

sound field reproduction method based on reproduction

error minimization is presented in Sec. 3. Simulations

and numerical results are presented and discussed in

Sec. 4. Section 6 gathers the main concluding remarks

and presents future research avenues.

2. CAVITY, SHELL AND EXTERNAL SOUNDFIELD COUPLED MODEL

The vibroacoustic model developped in the followingwill be used both for simulating the image pressure field

and establishing the inverse model used in reproduction.

It considers a baffled closed cylindrical shell radiating to

interior and exterior spaces. The coupling between the

movement of the shell and the resulting external radia-

tion is taken into account as well as the internal coupling

with the closed acoustic cavity. For the sake of concise-

ness, key points of the model are presented in the sequel.

Full expressions of calculous will be detailed in a future

paper.

2.1. Geometry of the system

As shown in Fig. 1, the 3-component vector displace-mentu of the cylindrical shell at a given point Q of co-

ordinates (r= a,,z) is described by its longitudinal, cir-cumferential and radial displacements,u,vandwrespec-tively, along the surfaceSof the shell. At an other point

Bwhich could be situated in the internal volume Vi or in

the external volumeVe, both filled by air of density 0and characterized by the sound phase speed c, the acous-

tic pressure is noted p.

2.2. Vibroacoustic modelThe dynamic of the thin cylindrical shell closed by shear

diaphragms at both ends is governed by the Donnell-

Mushtari theory, referred in [24]. The shell displace-ment vector discretized onto its in vacuo natural modes

nwrites:

u(,z) =

n=1

Ann(,z) (1)

whereAn is the nth shell modal amplitude and n the set

of modal indexes which refers to nodes in the radial

and circumferential directions and to symmetry type.

Each shell mode shape is normalized with respect to the

modal mass mn and is associated to non-dimensional

natural pulsationnwhich is given by Leissa [24].

The vibrating shell, immersed into an air-filled open

space, creates an acoustical radiation which interacts

with its own movement. This coupling could be de-

scribed as an intermodal coupling impedance between

the shell modes [25]. Thanks to an assumption of

infinite-long cylinder, the radiation could be expressed

analytically and then the projection on the finite-long

surface leads to analytical coupling coefficients of the


Page 2 of 10


3/10


impedance. This useful approximation has been dis-

cussed and justified for similar configurations [26]-[28].

Expression of this impedance is not given here but thecoupling would be represented in matrix form in the fol-

lowing.

The shell internal volume Vi, also air-filled, is the seat

of an internal coupling between the shell and the closed

acoustical cavity. Besides, it is our region of interest

since the interior sound field would be the target of repro-

duction. Inside the internal volume, the complex sound

pressure field p(r,,z)is expressed as a linear combina-tion of real rigid-wall cavity modes m(r,,z)[27].

p(r,,z) =

m=1

Pmm(r,,z) (2)

wherePmis themth complex cavity modal amplitude and

m a set of modal indexes which refers to the 3 direc-

tions of space and to the symmetry type. The cavity

mode shapes are normalized with respect to the modal

volume Vm and associated to m which are analyticallyexpressed in [27]. The expressions of coupling coeffi-

cients between shell modes and cavity modes are also

analytically known [27]; nevertheless, as the previous

mentionned coupling, one will expressed them in matrix

form only.

Thus, the complete vibroacoustic model written for har-monic excitations in terms of modal co-ordinates is:

C(cav) D(cav,sh)

D(sh,cav) C(sh)

C

P(cav)

A(sh)

=

F(cav)

F(sh)

(3)

whereA(sh) andP(cav) are composed of the co-ordinates

Anand Pmof the truncated mode families {n}n[1,N]and

{m}m[1,M], respectively. The diagonal matrix C(cav)

is populated by the squared rigid-wall cavity natural

pulsations (where the imaginary part gives the modal

damping) substracted from the squared excitating pul-

sation2, D(sh,cav) andD(cav,sh) express the internal vi-broacoustic coupling described above whereas the non-

diagonal matrix C(sh) compiles the orthogonal movement

of the shell only plus the external intermodal coupling

via radiation. F(cav) and F(sh) are the generalized force

expanded onto the cavity mode shapes{m}m[1,M] andonto the shell mode shapes{n}n[1,N] respectively. For

the particular case of harmonic monopole sources char-

acterized by their source strength q(cav)i (,ri,i,zi), and

harmonic ponctual forces defined by surface force den-sityq

(sh)l (,l ,zl ), each elementn and m of the twofold

generalized force vector writes:

F(cav)

m =i

c2

Vij0q

(cav)i m(ri,i,zi) (4)

and

F(sh)

n =l

q(sh)l

(r)n (l ,zl )

mn(5)

with jthe imaginary number and (r)n the radial compo-

nent of

n.Considering a virtual array ofN(m) microphones measur-

ing the acoustic pressurep(rep) at thex(m) spatial points

in Vi produced by a serie q(rep) of N(ac) acoustic and

N(st) structural excitators such as described before, the

response of the complete system is resumed by the fol-

lowing equation:

p(rep) = 0

C1

P1 00 P2

Z(ma)

q(rep)

(6)where P1 and P2 denote the matricial expressions of

Eq. (4) and (5) respectively.

3. SOUND FIELD CONTROLThe sound field reproduction system is posed as an error

minimization task. The reproduction error at the micro-

phone array is given by

e(x(m),) =p(im)(x(m),)p(rep)(x(m),) (7)

wherep(im) components are the target or measured com-

plex sound pressures at the error microphones in x(m),

p(rep) components are the complex reproduced soundpressures at the microphones, these vectors are N(m) 1vectors for a reproduction system made of the N(m) er-

ror microphones. The reproduced sound field is resumed

from Eq. (6) in

p(rep) =Z(ma)(x(m),x(a),)N(m)(N(ac)+N(st))q

(rep) (8)

where the reproduction system frequency response func-

tions from reproduction sources (point forces on the shell


Page 3 of 10


4/10


Fig. 1: Geometrical convention for the cavity and thin

shell model.

and monopole inside the cylindrical cavity) to error mi-

crophones are stored in Z(ma)). This complex trans-

fer matrix includes the shell, the cavity, their coupling

and the external coupling dynamics. The reproduction

source amplitudes (force or acoustical source strength)

are stored in q(rep), a (N(ac) +N(st)) 1 vector. Sub-

scripts indicate matrix dimensions. A cost function withTikhonov regularization is introduced to summarize the

reproduction task for which the reproduction errorse(m)

(Eq. (7)) should be minimized [30], [31]

J=e(m)H

e(m) +2q(rep)H

q(rep) (9)

where H denotes Hermitian transposition, is the pe-nalization parameter. The optimal reproduction source

complex amplitudes q(rep) that will minimize J is given

by [31]

q(rep)opt =

Z(ma)H

p(im)

Z(ma)H

Z(ma) +2I (10)

whereI is the identity matrix. In the following section,

these equations are used for the simulation of stationary

and harmonic sound field reproduction in a specific cav-

ity and shell configuration which corresponds to a real

cabin mock-up at our laboratory.

4. SIMULATIONS AND RESULTSThe aim of the following simulations is to draw the out-

lines of the feasibility and the evalutation of reproduc-

20 40 60 80 1000

200

400

600

800

Naturalfrequency[Hz]

No

Fig. 2: Natural frequency [Hz] (), sorted in ascending

order, of the rigid-wall cavity and of the coupled system

(). Schroeder frequency [29] of the rigid-wall cavity isrepresented by a horizontal dash-dot line and excitation

frequencies of the two simulations presented (98 Hz and

300 Hz) are plotted in plain lines.

tion systems of a stationary external noise source includ-

ing structural actuators or acoustic excitators close to the

trim panel (here modeled by the shell). Typical simula-

tions will thus involve an exterior plane wave excitating

the dynamic model described in Sec. 2 and virtual mea-surements of the interior sound field by a microphone ar-

ray located in the listening plane of the simplified mock-

up. With the help of the control method presented in

Sec. 3 performed on the virtual measurements, complex

amplitudes of excitators are deduced to reproduce the tar-

get sound field. Then, the error between image sound

field (virtually defined in this paper) and reproduction er-

ror is evaluated.

One considers a unitary plane wave of pulsation im-pinging perpendicularly on the shell. The total sound

pressure results in the sum of the incident and the scat-

tered wave field [32]. Similarly to the case of ponctualstructural forces in Sec. 2, the total pressure on the shell

surface is projected onto the shell modes to be injected

asF(sh) in Eq. (3), then in Eq. (2), in order to obtain the

target image pressurep(im) at the microphone array.

Mechanical characteristics and geometrical dimensions

are inspired from measurements performed in a real

mock-up. Particularly, structural damping is computed

from the measured reverberation times. Configuration


Page 4 of 10


5/10


of the microphone array, actuator positions and speaker

positions have been choosen with respect to fabrication

considerations and in anticipation of the experimentalset-up constraints. Futhermore, one opts for the num-

ber of microphones to be equal to the number of repro-

duction sources in order to have a determined system.

Thus, the microphone array is a a/6 side-length squarecomposed of 88 regularly distributed microphones, the64-actuator systemwill denote 2 rows of 232 equally-spaced structural excitators placed on the intersection of

the cylinder with the mid-height plane or with the lis-

tening plane. The listening plane 64-speaker systemwill

denote 34 equally-spaced radiating monopoles on the lat-

eral edges of the plane combined with 30 equally spaced

monopoles at the ends, see Figs 4, 5, 7 and 8.

TypicalZ(ma) response is computed for one geometrical

and mechanical configuration of the mock-up. Following

results in terms of inside pressure field correspond to two

simulations computed for the same excitating plane wave

except from the selected pulsation. Three factors have

governed our choice of excitation frequency: truncations

of modal bases (to avoid prohibited computation cost),

eigen-frequencies of the coupled system (which guide

the response of the system in low frequency range) and

Schroeder frequency (which is an estimation of the tran-

sition from modal behavior to a diffuse behavior (more

than 3 excited modes for a single frequency)). As shown

in Fig. 2, the first excitation frequency is chosen to corre-spond to one of the first eigen-value of the coupled sys-

tem, below the Schroeder frequency. The second one is

situated just above the Schroeder frequency. In fact, to

choose a higher frequency imposes a higher truncation

order in modal bases to insure the convergence of the

solution and so a higher computational cost [31]. The

compromise is arbitrary made to be around 100 modes

forNas well as for M.

Fig. 3 and Fig. 6 show the image sound field produced

by an exterior harmonic scattering plane wave of fre-

quency f =98 Hz and f =300 Hz, respectively, im-

pinging on the shell in thex2 axis direction. The printedsound field is thus the complex interior acoustic response

of the vibro-acoustic system which consists in the trun-

cated summation of real modal shapes weighted by the

complex cavity modal amplitudes. As the whole sys-

tem is linear and the excitation is unitary, the visualized

sound field could be directly scaled with any excitation

amplitude.

For each two cases of excitation, Figs. 4, 5, 7 and 8

present the results of the sound field reproduced by the

two excitator configurations. In order to evaluate the

quality of reproduction at microphone array location, rel-ative quadratic errors defined by

e(m)q =

e(m)H

e(m)

p(m)H

p(m), (11)

where p(m) =p(im)(x(m),), is computed. Similarly to

this expression, the quadratic errore(LP)q computed on the

whole listening plane will be given.

5. DISCUSSION OF THE RESULTSThe first general remark which has to be made is on the

dimension of the image pressure fields in the cavity. Due

to the unitary exterior acoustical excitation, the soundamplitude inside the system is very low. It shows the

large-scale relation between exterior and interior sound

for a model dimensionned on measurements on a real

mock-up. Nevertheless, as the complete system is linear,

the physical phenomena of reproduction are well repre-

sented. Secondly, the choice of parameter of regulariza-

tionis not motivated here, this study being not the pur-pose of this paper. One has just to note that for each case,

has been adjusted to reproducecorrectlyboth the pres-sure at the microphone array and the pressure field in the

listening plane. A future publication will provide a study

dedicated to this parameter.

For this particular study, one observes that the inverse

method is capable of global reproduction by minimiza-

tion of the error on a discrete local area. In spite of small

differences in the pressure field shapes, the two systems

of reproduction provide similar performances in terms of

relative quadratic errors. Nonetheless, the speaker con-

figuration produce generally rougher field shape (with

higher slopes) than the actuator configuration. Contrary

to structural excitations of whom the amplitudes result

in the projection on smoother mode shapes in this range

of frequencies, the acoustical excitations involve more

rough acoustic mode shapes because of the strong cou-

pling with rigid-wall cavity modes which are numerousin the considered frequency range. Because of the mode-

coupling involved in the inverse method, the global shape

of the contributions of the acoustical excitators and con-

sequently the global shape of the reproduced pressure

field will show more spatial variations compared to the

actuator configuration for a given truncation.

Preliminary, these first feasability results including the

two specific reproduction systems dedicated to simplified


Page 5 of 10


6/10


Fig. 3: Image sound field P(im) created inside the sys-

tem with a unitary scattering harmonic plane wave of

frequency 98 Hz. Grey surface plotted according to the

x1 axis in the cylinder represents the scaled pressure inthe listening plane. Pression at the microphone array ()

is also scaled. The pressure scaling factor is equal to

2.091013 Pa.

Fig. 4: Sound field P(rep) reproduced by the 64-actuator

system for an exterior harmonic plane wave of frequency

98 Hz. An acoustical response of actuators on the shell

is given by Eqs. (5) and (6). Origins of stems indicatethe 2-row locations of actuators. Their positive () ornegative () amplitudesq(rep) oriented towardsx1for thetop-row and towardsx1 for the bottom-row are scaledby 0.7035 N to fit in the graph. The scaling factor isthe same as the respective image field. Quadratic error

computations givee(m)q =0.067 ande

(LP)q =0.41.


Page 6 of 10


7/10


Fig. 5: Sound fieldP(rep) reproduced by the 64-speaker

system for an exterior harmonic plane wave of frequency

98 Hz. Radiation of speakers is modelized by acoustical

reproduction sources (see Eqs. (4) and (6)). Origins ofstems indicate locations of speakers. Their amplitudes

()q(rep) are scaled by 5.31791016 m.s1 to fit in thegraph. The pressure scaling factor is the same as the re-

spective image field plot. Quadratic error computations

givee(m)q =0.044 ande

(LP)q =0.54.

Fig. 6: Image sound field P(im) created inside the sys-

tem with a unitary scattering harmonic plane wave of fre-

quency 300 Hz. Grey surface plotted according to thex1

axis in the cylinder represents the scaled pressure in thelistening plane. Pression at the microphone array () is

also scaled. The sound pressure scaling factor is equal to

1.9061014 Pa.


Page 7 of 10


8/10


9/10


aircraft space are encouraging. Without any optimization

work, they provide good local reproduction results for

the two examplified excitation frequencies: 1) below theSchroeder frequency where the cavity response is dom-

inated by a modal behavior and 2) above the Schroeder

frequency.

6. CONCLUSIONConsidering the recent gain of interest of transport in-

dustry for spatial sound, the present paper has proposed

a theoretical formulation of a dedicated sound field re-

produced system applied to a simplified model of flight

aircraft space dimensionned on basis of measurements

in a real mock-up. A complete vibroacoustic model in-

cluding external and internal coupling expanded on the

shell and the rigid-wall cavity modes is used in the in-verse problem. The spatially-extended sound field re-

production method using Tikhonov regularization mini-

mizes the-dependent cost function. Two specific repro-duction systems have been simulated in order to evaluate

their efficiency. The first represented lateral trim-panel

actuator system and the second represented enclosing

loudspeaker system. Both of which show good perfor-

mance for the local reproduction and are capable of quite

good global reproduction by ajusting the regularization

parameter.

Recasting these results within the framework of the

project, they provide good expectations for the pratical

method we will use for the reproduction of external-noise

induced sound field in the cabin. Indeed, the Z(ma) ma-

trix characterizing the vibroacoustic model will be later

computed from measurements in the real system submit-

ted to reproduction excitation and obtained with a mi-

crophone array (presently under construction at GAUS

laboratory). The microphone array would then be re-

moved and the image pressure field would be reproduced

by the method described in Sec. 3 for a chosen reproduc-

tion source set-up . The approach using inverse method

is in our case justified by the type of source signals we

want to reproduce. In fact, for nearly stationary soundssuch as most of the flying aircraft noises, room compen-

sation and equalization residual artifact such as pre- or

post-echoes should be inaudible.

This preliminary study raises some expectations which

will be questionned in a near future. As a first prospec-

tive, effect ofon reproduction error at the microphonearray and in the listening plane should be the object of a

parametric study. More generally, an optimization of the

excitator positions, a more refined vibroacoustic model

computed on a broadband fitting responses of real cabin

mock-up should be the main lines of future work.

7. ACKNOWLEDGMENTThe authors would like to aknowledge Eric Chambatte

for the measurement of mock-up reverberation times.

This work is part of a project involving: Consortium for

Research and Innovation in Aerospace in Quebec, Bom-

bardier Aeronautique, CAE, Universite de Sherbrooke

and McGill University, supported by a Natural Sciences

and Engineering Research Council of Canada grant.

8. REFERENCES

[1] W.B. Snow, Basic principles of stereophonic

sound, Journal of the SMPTE61(1953), 567589.

[2] F. Rumsey,Spatial audio, Focal Press, 2001.

[3] B. Blesser and L.R. Salter,Spaces speak Are you

listening?, MIT Press, 2007.

[4] D.A. McCurdy and R.E. Grandle, Aircraft Noise

Synthesis System, NASA technical memorandum

89040 (1987).

[5] D. Berckmans, K. Janssens, H. Van der Auwer-

aer, P. Sas and W. Desmet, Model-based synthe-sis of aircraft noise to quantify human perception

of sound quality and annoyance, Journal of Sound

and Vibration311 (2008), 11751195.

[6] K. Janssens, A. Vecchio, H. Van der Auweraer,

Synthesis and sound quality evaluation of exterior

and interior aircraft noise, Aerospace Science and

Technology12 (2008), 114124.

[7] S.A. Rizzi and B.M. Sullivan, Synthesis of virtual

environments for aircraft community noise impact

studies, 11th AIAA/CEAS Aeroacoustics Confer-

ence4 (2005), 22912306.

[8] N. Epain, E. Friot, G. Rabau, Indoor sonic boom

reproduction using ANC, Proceedings of Active

2004.

[9] M. Keller, A. Roure, F. Marrot, Acoustic field re-

production for psychoacoustic experiments: appli-

cation to aircraft interior noise, Proceedings of Ac-

tive 2006.


Page 9 of 10


10/10


[10] J. Daniel, R. Nicol and S. Moreau, Further Inves-

tigations of High Order Ambisonics and Wavefield

Synthesis for Holophonic Sound Imaging, Con-vention paper 5788, presented at the AES 114th

convention, Amsterdam, The Netherlands, 2003

March 2225.

[11] A.J. Berkhout, D. de vries and P. Vogel, Acous-

tic control by wave field synthesis, Journal of the

Acoustical Society of America 93 (1993), no. 5,

27642778.

[12] C. Guastavino, B.F.G. Katz, Perceptual evaluation

of multi-dimensional spatial audio reproduction,

Journal of the Acoustical Society of America,116

(2004), no. 2, 11051115.

[13] B. Klehs and T. Sporer, Wave field synthesis in the

real world: Part 1 In the living room, Conven-

tion paper 5727, presented at the AES 114th Con-

vention, Amsterdam, The Netherlands, 2003 March

2225.

[14] P.-A. Gauthier and A. Berry, Objective evalua-

tion of room effects on wave field synthesis, Acta

Acustica united with Acustica 93 (2007), no. 5,

824-836.

[15] A.O. Santillan, Spatially extended sound equaliza-

tion in rectangular rooms, Journal of the Acousti-cal Society of America 110, (2001), no. 4, 1989

1997.

[16] F. Asano and D.C. Swanson, Sound equalization

in enclosures using modal reconstruction, Journal

of the Acoustical Society of America 98 (1995),

no. 4, 20622069.

[17] L.D. Fielder, Practical Limits for Room Equaliza-

tion, Convention paper 5481, presented at the AES

111th Convention, New York, USA, 2001 Novem-

ber 30-December 3.

[18] M. Miyoshi and Y. Kaneda, Inverse Filtering ofRoom Acoustics, IEEE Transactions on Acoustics,

Speech, and Signal Processing 36 (1988), no. 2,

145152.

[19] P.-A. Gauthier, A. Berry and W. Woszczyk,

Sound-field reproduction in-room using optimal

controle techniques: Simulations in the frequency

domain, Journal of the Acoustical Society of

America117 (2005), no. 2, 662678.

[20] P.-A. Gauthier and A. Berry, Adaptive wave field

synthesis with independent radiation mode con-

trol for active sound field reproduction: Theory,Journal of the Acoustical Society of America 119

(2006), no. 5, 27212737.

[21] S. Spors, A. Kuntz and R. Rabenstein, An ap-

proach to listening room commpensation with wave

field synthesis, presented at the AES 24th Interna-

tional Conference, Banff, Canada, 2003 June 26-

28.

[22] S. Spors, H. Buchnera and R. Rabenstein, Effi-

cient active listening room compensation for wave

field synthesis, Convention paper 6119, presented

at the AES 116th Convention, Berlin, Germany,

2004 May 8-11.

[23] J.F. Wilby, Aircraft interior noise, Journal of

Sound and Vibration190 (1996), no. 3, 545564.

[24] A. W. Leissa,Vibration of Shells, Acoustical Soci-

ety of America, Woodbury, 1993.

[25] C. Lesueur, Rayonnement acoustique des struc-

tures, Eyrolles, Paris, 1988.

[26] M.C. Junger and D. Feit, Sound, structures, and

their interactions, Acoustical Society of America,

Woodbury, 1993.

[27] D. Li and J. S. Vipperman, Mathematical model

for characterizing noise transmission into finite

cylindrical structures, Journal of Acoustical Soci-

ety of America117 (2005), 679689.

[28] C. Wang and J.C.S. Lai, The sound radiation ef-

ficiency of finite length circular cylindrical shells

under mechanical excitation II: Limitations of the

infinite length model, Journal of Sound and Vibra-

tion241 (2001), 825838.

[29] H. Kuttruff, Room acoustics (fourth ed.), Spon

Press, London, 2000.

[30] P.C. Hansen,Rank-Deficient and Discrete Ill-Posed

Problems, SIAM, 1998.

[31] S. Elliott, Signal Processing for Active Control,

Academic Press, 2001.

[32] H. Teutsch, Modal array signal processing: princi-

ples and applications of acoustic wavefield decom-

position, Springer, Berlin, 2007.


Page 10 of 10

2010 Sound ﬁeld reproduction applied to ﬂight vehicles sound environments

Documents

Transcript of 2010 Sound ﬁeld reproduction applied to ﬂight vehicles sound environments