continuation of acoustic near fields this paper deals with the analytic continuation of a coherent pressure field specified on a finite sheet located close to and conformal to the surface of a vibrator this analytic continuation is an extension or extrapolation of the given measured field into a region outside and tangential to the original finite sheet and is based on the green s function the transfer function relating acoustic quantities on the two conformal surfaces the continuation of the measured pressure field is an inverse problem that requires the use or regularization theory especially when noise is present in the data an iteration algorithm is presented that is successful in continuing the pressure field into the tangential sheet the results are accurate close to the original boundary and taper decay toward zero with distance away from it the algorithm is tested on numerical and experimental data from a point driven rectangular plate results show the successful extrapolation continuation of this data into an area nearly double that of the original pressure field this algorithm is not limited to planar surfaces and can be applied to arbitrarily shaped surfaces

null controllability of a system of linear thermoelasticity we consider a linear system of thermoelasticity in a compact c infin n dimensional connected riemannian manifold this system consists of a wave equation coupled to a heat equation when the boundary of the manifold is non empty dirichlet boundary conditions are considered we study the controllability properties of this system when the control acts in the hyperbolic equation and not in the parabolic one and has its support restricted to an open subset of the manifold we show that if the control time and the support of the control satisfy the geometric control condition for the wave equation this system of thermoelasticity is null controllable more precisely any finite energy solution can be driven to zero at the control time an analogous result is proved when the control acts on the parabolic equation finally when the manifold has no boundary the null controllability of the linear system of three dimensional thermoelastic ity is proved

on the holographic reconstruction of vibroacoustic fields using equivalent sources and inverse boundary element method in using the near field acoustical holography based on the inverse boundary element method bem for the reconstruction of vibroacoustic source parameters an enormous number of measurements required in practice have limited the extended application of this method to obtain the sufficient field data with a small number of actual measured data the regeneration method of the radiated field using the multipoint equivalent sources is attempted in this paper in using the equivalent source method a vibrating source can be represented by distributed spherical sources inside the actual source surface in this paper the radiated field is expressed with a series of spherical hankel functions and spherical harmonics for suppressing the adverse effect of high order spherical functions spatial filtering of coefficients and wave vector components by a regularization scheme is adopted restored field data appended with actual measured data can be used as input for the inverse bem to reconstruct the source field

a computational acoustic field reconstruction process based on an indirect boundary element formulation the objective of the work presented in this paper is to develop a computational capability based on the indirect boundary element method ibem for evaluating appropriate velocity boundary conditions on an assembly of piston type sources in order to recreate a prescribed acoustic field information for the acoustic pressure of the original acoustic field at certain field points constitutes the input to the developed process the velocities on the piston type sources are computed from transfer functions evaluated between the field points where the acoustic pressure of the original field is prescribed and the velocity boundary condition on each element of the generic source the ibem is employed for computing the transfer functions in order to accommodate the presence of openings in the model and radiation from both sides of the piston type sources simulating the generic source as a thin surface that radiates from both sides eliminates the presence of irregular frequencies in the analysis a singular value decomposition svd solver is integrated with the ibem computations in order to evaluate the velocity boundary conditions from the transfer functions the number of field points where the acoustic pressure is defined can be considerably smaller than the number of elements where the velocity is computed the solution that demonstrates the smallest magnitude is selected from all possible solutions an algorithm is also developed for identifying the optimum field points where the acoustic pressure of the original field must be prescribed the optimum field points are selected from a set of prescribed candidate points the number of optimum points is considered smaller than the number of elements where the velocity is computed the properties of the transformation matrix and the quality of the reconstruction depend on the location of the field points thus the selection of the optimum points is based on achieving the highest possible orthogonality among the vectors that comprise the range of the transformation matrix several validation and application cases are presented

primal dual weak galerkin finite element methods for elliptic cauchy problems abstract the authors propose and analyze a well posed numerical scheme for a type of ill posed elliptic cauchy problem by using a constrained minimization approach combined with the weak galerkin finite element method the resulting euler lagrange formulation yields a system of equations involving the original equation for the primal variable and its adjoint for the dual variable and is thus an example of the primal dual weak galerkin finite element method this new primal dual weak galerkin algorithm is consistent in the sense that the system is symmetric well posed and is satisfied by the exact solution a certain stability and error estimates were derived in discrete sobolev norms including one in a weak l 2 topology some numerical results are reported to illustrate and validate the theory developed in the paper

the detection of the source of acoustical noise in two dimensions we consider the problem of detecting the source of acoustical noise inside the cabin of a midsize aircraft from measurements of the acoustical pressure field inside the cabin mathematically this field satisfies the helmholtz equation in this paper we consider the model two dimensional case we show that any regular solution of this equation admits a unique representation by a single layer potential so that the problem is reduced to the solution of a linear integral equation of the first kind we prove uniqueness of reconstruction and obtain a sharp stability estimate finally for two geometries and sources of noise simulating the cabin of the aircraft and two engines we give results of the numerical solution of this integral equation comparing regularization by the truncated singular value decomposition and the conjugate gradient method

combined helmholtz equation least squares method for reconstructing acoustic radiation from arbitrarily shaped objects a combined helmholtz equation least squares chels method is developed for reconstructing acoustic radiation from an arbitrary object this method combines the advantages of both the hels method and the helmholtz integral theory based near field acoustic holography nah as such it allows for reconstruction of the acoustic field radiated from an arbitrary object with relatively few measurements thus significantly enhancing the reconstruction efficiency the first step in the chels method is to establish the hels formulations based on a finite number of acoustic pressure measurements taken on or beyond a hypothetical spherical surface that encloses the object under consideration next enough field acoustic pressures are generated using the hels formulations and taken as the input to the helmholtz integral formulations implemented through the boundary element method bem the acoustic pressure and normal component of the velocity at the discretized nodes on the surface are then determined by solving two matrix equations using singular value decomposition svd and regularization techniques also presented are in depth analyses of the advantages and limitations of the chels method examples of reconstructing acoustic radiation from separable and nonseparable surfaces are demonstrated

measurement of structural intensity using boundary element method based nearfield acoustical holography the regularization method for measurement of structural intensity si using boundary element method bem based nearfield acoustical holography nah is proposed spatial derivatives of normal displacement are necessary to obtain the structural intensity the derivative operations amplify high wavenumber component of measurement noise and contaminate the measurement result of si to overcome this difficulty regularization method for measurement of si using fast fourier transform based nah has been introduced in this paper this regularization method is modified for the bem based nah the bem based nah avoids the aperture replication problem therefore measurement aperture for bem based nah can be set smaller than that for fft based nah the effectiveness of the proposed method is demonstrated by experiments

the use of partially measured source data in near field acoustical holography based on the bem in applying the conformal near field acoustical holography nah to actual source identification problems it is often possible to determine the velocity at certain points of the source surface in advance this partially known velocity data would reduce the problem size and permit better reconstruction accuracy in this paper the effectiveness of using partially measured source data in the conformal nah is investigated which uses the boundary element method a vibro acoustic transfer matrix and measured field pressure data which is involved with the boundary integral equation are reorganized in order to deal with the partially measured surface velocities for a baffled vibrating panel simulations were performed by varying the number of velocity known nodes in addition the effect of measurement error is investigated for two extreme positioning methods of velocity known nodes without regularization the reconstructed error can be reduced considerably by employing some of the source data and this err

identification of the number and locations of acoustic sources the identification of the number and locations of acoustic sources is a fundamental problem of engineering acoustics the method of multiple signal classification music has been widely used to solve this problem the main drawback of the music method is that the unavoidable measurement noise should be identical for all the channels of measurement system this requirement generally cannot be met in practical application in this work a method was proposed to identify the number and locations of multiple incoherent sources the proposed method was based on the traditional music method however without the basic assumption about the identity of the measurement noise besides a procedure was proposed to improve the calculation efficiency of identification the numerical and experimental results demonstrated that the identification accuracy of the proposed method was far better than that of the traditional music method the results also demonstrated that the proposed calculation procedure was very efficient only the data at a few frequencies should be used for identification

bayesian approach of nearfield acoustic reconstruction with particle filters this paper demonstrates that inverse source reconstruction can be performed using a methodology of particle filters that relies primarily on the bayesian approach of parameter estimation in particular the proposed approach is applied in the context of nearfield acoustic holography based on the equivalent source method esm a state space model is formulated in light of the esm the parameters to estimate are amplitudes and locations of the equivalent sources the parameters constitute the state vector which follows a first order markov process with the transition matrix being the identity for every frequency domain data frame filtered estimates of the state vector obtained are assigned weights adaptively the implementation of recursive bayesian filters involves a sequential monte carlo sampling procedure that treats the estimates as point masses with a discrete probability mass function pmf which evolves with iteration the weight update equation governs the evolution of this pmf and depends primarily on the likelihood function and the prior distribution it is evident from the simulation results that the inclusion of the appropriate prior distribution is crucial in the parameter estimation

identification of source velocities on 3d structures in non anechoic environments theoretical background and experimental validation of the inverse patch transfer functions method in noise control identification of the source velocity field remains a major problem open to investigation consequently methods such as nearfield acoustical holography nah principal source projection the inverse frequency response function and hybrid nah have been developed however these methods require free field conditions that are often difficult to achieve in practice this article presents an alternative method known as inverse patch transfer functions designed to identify source velocities and developed in the framework of the european silence project this method is based on the definition of a virtual cavity the double measurement of the pressure and particle velocity fields on the aperture surfaces of this volume divided into elementary areas called patches and the inversion of impedances matrices numerically computed from a modal basis obtained by fem theoretically the method is applicable to sources with complex 3d geometries and measurements can be carried out in a non anechoic environment even in the presence of other stationary sources outside the virtual cavity in the present paper the theoretical background of the iptf method is described and the results numerical and experimental for a source with simple geometry two baffled pistons driven in antiphase are presented and discussed

data extrapolation method for boundary element method based near field acoustical holography a new data extrapolation method for boundary element method bem based near field acoustical holography nah is proposed to reduce an error of the reconstructed result obtained from the pressure measured on an aperture small compared with the structure the finiteness of the measurement aperture is a serious impediment to actual large scale implementation of nah because nah requires the measurement of the pressure field over a complete surface of structure to eliminate the requirement the wave number space data extrapolation method for fast fourier transform fft based nah has been proposed in this paper the extension of this data extrapolation method to bem based nah is presented the effectiveness of this method is demonstrated by experiments the experiment results confirm that the reconstruction error is sufficiently suppressed by the proposed method

on the multiple microphone method for measuring in duct acoustic properties in the presence of mean flow nowadays the two microphone method is accepted as the standard as specified in astm e1050 90 for measuring in duct acoustic properties however research results on using the least square method with multiple measurement points and broadband excitation have been reported for enhancing the frequency response of the two microphone method in this paper the effects of varying the relative measurement positions on errors in the estimation of the acoustic quantities is studied for the multiple microphone method both the theoretical and experimental results show that among possible sensor positioning configurations the equidistant positioning of sensors yields the smallest error within the effective measurement frequency range in addition it is noted that the measurement accuracy can be increased and the effective frequency range can be widened by increasing the number of equidistant sensors measurement examples are shown and the results support the findings

analysis of r out of n systems with several repairmen exponential life times and phase type repair times an algorithmic approach abstract an r out of n repairable system consisting of n independent components is operating if at least r components are functioning the system fails whenever the number of good components decreases from r to r 1 a failed component is sent to a repair facility having several repairmen life times of working components are i i d random variables having an exponential distribution repair times are i i d random variables having a phase type distribution both cold and warm stand by systems are considered we present an algorithm deriving recursively in the number of repairmen the generator of the markov process that governs the process then we derive formulas for the point availability the limiting availability the distribution of the down time and the up time numerical examples are given for various repair time distributions the numerical examples show that the availability is not very sensitive to the repair time distribution while the mean up time and the mean down time might be very sensitive to the repair time distributions

effect of sensor proximity over the non conformal hologram plane in the near field acoustical holography based on the inverse boundary element method near field acoustical holography nah is a useful tool for the identification and visualization of vibro acoustic sources in particular nah can be applied to many practical sources having irregular shape if the inverse boundary element method bem is employed once the relation between the source and the radiated field is defined in the transfer matrix modeled by the bem the reconstruction of acoustic parameters on the source surface can be conducted by the multiplication of the inverse transfer matrix and the field data measured over the hologram surface the usual practical way to measure the field data radiated from an irregular shaped source is to adopt a regular hologram surface which can be a flat cylindrical or spherical shape for the measurement ease then the hologram surface is not conformal to the source surface and the resulting transfer matrix becomes further ill posed than the conformal case to investigate the effect of sensor proximity and distance variability on the reconstruction error simulation and measurement were conducted for an interior problem comprised of a parallelepiped rigid box with a vibrating end plate flat tilted and randomized hologram surfaces were adopted in the test it was shown that the reconstruction error is greatly affected by the conditioning of transfer matrix which is related to the positioning of sensor to improve the reconstruction accuracy an investigation was conducted to find proper field points among a large number of overdetermined field points the number of field data was reduced gradually under various reduction schemes using condition number effective independence value and sensor distance it was demonstrated that the quality of reconstruction result given by the non conformal measurement can be improved by removing some field points that contribute to the ill conditioning of the inverse problem a small improvement of the reconstruction accuracy was observed by reducing the field points in the overdetermined situation however further reduction of the field points becoming an underdetermined situation yielded a drastic improvement of the reconstruction accuracy

reconstruction of vibro acoustic fields using hybrid nearfield acoustic holography hybrid nearfield acoustical holography is utilized to reconstruct the vibro acoustic fields generated by an arbitrary structure vibrating in an unbounded fluid medium this hybrid nah is based on the modified helmholtz equation least squares method that expresses the field acoustic pressure in terms of expansions of outgoing and incoming waves the expansion coefficients are determined by solving an over determined linear system of equations obtained by matching the assumed form solution to a finite number of acoustic pressures measured in the field via least squares the measurements are taken over a conformal surface around the source at close range so that the evanescent waves can be captured once the expansion coefficients are specified enough field acoustic pressures are regenerated on a conformal surface around the source and are taken as input to the helmholtz integral formulation implemented numerically by the boundary element method the acoustic pressure and normal velocity on the source surface are reconstructed using singular value decomposition modified tikhonov regularization and generalized cross validation method this hybrid nah enables one to obtain a satisfactory reconstruction cost effectively because the majority of the input data are calculated but not measured numerical examples of reconstructing the vibro acoustic quantities on the surfaces of an engine block and a highly elongated cylinder are demonstrated

asymptotic behavior of the stationary distributions in the gi ph c queue with heterogeneous servers this paper deals with the stablec server queue with renewal input the service time distributions may be different for the various servers they are however all probability distributions of phase type it is shown that the stationary distribution of the queue length at arrivals has an exact geometric tail of rate 0 0 the quantities and may be evaluated together by an elementary algorithm for both distributions the multiplicative constants which arise in the asymptotic forms may be fully characterized these constants are however difficult to compute in general

a herglotz wavefunction method for solving the inverse cauchy problem connected with the helmholtz equation this paper is concerned with the cauchy problem connected with the helmholtz equation on the basis of the denseness of herglotz wavefunctions we propose a numerical method for obtaining an approximate solution to the problem we analyze the convergence and stability with a suitable choice of regularization method numerical experiments are also presented to show the effectiveness of our method

on the traveling wave solutions for a parabolic hyperbolic system in linear thermoelasticity in this paper the parabolic hyperbolic system of linear thermoelasticity with variable coefficients is transformed into a system of two coupled equations we discuss first the conditions which govern this separation in the case of a system of two coupled equations for which a general result on the separability is formulated it is then shown that the explicit traveling wave solutions are obtained in the exact form

sound source identification in a noisy environment based on inverse patch transfer functions with evanescent green s functions abstract a modified inverse patch transfer function iptf method is used to reconstruct the normal velocities of the target source in a noisy environment the iptf method simplifies the helmholtz integral equation to one term by constructing a green s function satisfying neumann boundary conditions for an enclosure which is generally constructed by slowly convergent modal expansions the main objective of the present work is to provide an evanescent green s function to improve the convergence of calculations a brief description of the iptf method and two sets of green s functions for a rectangular cavity are presented firstly in simulations both the green s functions are used to calculate the condition numbers of impedance matrices describing the relation between source and measurement patches and the time cost of calculation based on the two sets of green s functions at 450 hz is compared double pressure measurements are then employed as the input data instead of pressure and velocity measurements the normal velocities of two baffled loudspeakers are reconstructed by the combination of a measurement method and a green s function in the presence of a disturbing source in the frequency range of 50 1000 hz in addition the double pressure measurements are examined by an experiment the precise identification of the sources indicates that the double pressure measurements are capable of localizing sources in a noisy environment it is also found that the reconstruction with the evanescent green s functions is slightly better than that with the modal expansions

vector intensity reconstruction using the data completion method this paper presents an application of the data completion method dcm for vector intensity reconstructions a mobile array of 36 pressure pressure probes 72 microphones is used to perform measurements near a planar surface nevertheless since the proposed method is based on integral formulations dcm can be applied with any kind of geometry this method requires the knowledge of cauchy data pressure and velocity on a part of the boundary of an empty domain in order to evaluate pressure and velocity on the remaining part of the boundary intensity vectors are calculated in the interior domain surrounded by the measurement array this inverse acoustic problem requires the use of a regularization method to obtain a realistic solution an experiment in a closed wooden car trunk mock up excited by a shaker and two loudspeakers is presented in this case where the volume of the mock up is small 0 61 m3 standing waves and fluid structure interactions appear and show that dcm is a powerful tool to ident

on the reconstruction of the vibro acoustic field over the surface enclosing an interior space using the boundary element method the vibrational velocity sound pressure and acoustic power on the vibrating boundary comprising an enclosed space are reconstructed by the boundary element method based on the measured field pressures the singular value decomposition is used to obtain the inverse solution in the least square sense and to express the acoustic modal expansion between the measurement and source fields in general such an inverse operation has been considered an ill posed problem having a divergence phenomenon involved with extremely small measurement errors the ill conditioned nature of the acoustic inverse problem is caused by the singularity of the transfer matrix which produces nonradiating wave components in order to minimize the singularity and to also reduce the number of measurement points optimal measurement positions are determined by the effective independence method regularization methods are used to stabilize the reconstructed field by suppressing nonradiating components resulting in the singular transfer

acoustical inverse problems regularization direct definition of filter factors using signal to noise ratio abstract acoustic imaging aims at localization and characterization of sound sources using microphone arrays in this paper a new regularization method for acoustic imaging by inverse approach is proposed the method first relies on the singular value decomposition of the plant matrix and on the projection of the measured data on the corresponding singular vectors in place of regularization using classical methods such as truncated singular value decomposition and tikhonov regularization the proposed method involves the direct definition of the filter factors on the basis of a thresholding operation defined from the estimated measurement noise the thresholding operation is achieved using modified filter functions the originality of the approach is to propose the definition of a filter factor which provides more damping to the singular components dominated by noise than that given by the tikhonov filter this has the advantage of potentially simplifying the selection of the best regularization amount in inverse problems theoretical results show that this method is comparatively more accurate than tikhonov regularization and truncated singular value decomposition

some new exact solutions for linear thermoelastic system the general analysis of transformation group method has been developed to study the linear thermoelastic system the application of one parameter group reduces the number of independent variables consequently the governing system of second order partial differential equations reduced into systems of ordinary differential equations in this paper some of these systems are solved analytically

interval uneffectiveness distribution for a k out of n multistate reliability system with repair this paper deals with a parallel load sharing reliability system with cold standby redundancy and ample repair facilities that is we have n identical parallel units of which at most k units are operating simultaneously if less than k units are available the system operates at a proportionally reduced level for this system an approximate method is given for the calculation of the probability distribution of that proportion of the system capacity that cannot be used in a given time period the method is based on an approximation of the k out of n multistate system by a two state single component validation of the approximation using monte carlo simulation shows satisfactory performance also sensitivity results are given showing in particular a decreasing sensitivity of the measures of performance to the distributional form of the unit lifetimes and repair times as the size of the system increases furthermore it is found that the effect of the distributional form of the unit lifetimes dominates that of the unit repair times

comparison of regularization methods for solving the cauchy problem associated with the helmholtz equation in this paper several boundary element regularization methods such as iterative conjugate gradient tikhonov regularization and singular value decomposition methods for solving the cauchy problem associated to the helmholtz equation are developed and compared regularizing stopping criteria are developed and the convergence as well as the stability of the numerical methods proposed are analysed the cauchy problem for the helmholtz equation can be regularized by various methods such as the general regularization methods presented in this paper but more accurate results are obtained by classical methods such as the singular value decomposition and the tikhonov regularization methods copyright 2004 john wiley sons ltd

implicit methods of solution to integral formulations in boundary element method based nearfield acoustic holography two integral equation methods are considered which can be inverted to provide the surface velocity and or pressure given a measurement of the pressure on an imaginary surface in the nearfield of a vibrating or scattering body this problem is central to nearfield acoustical holography nah the integral equations are discretized using boundary element methods bems the integral equation methods considered are 1 an indirect formulation method based on the single layer integral equation and 2 a direct formulation method based on a system of equations derived from the helmholtz kirchhoff integral equation the formation of integral equations from the mentioned methods will not involve the explicit inversion of matrices but instead will require this inversion to be done implicitly since these methods back track the sound field from the measurement surface to the surface of the source vibrator they are ill posed in nature and tikhonov regularization are used to stabilize the reconstruction problems a

an alternating iterative algorithm for the cauchy problem associated to the helmholtz equation in this paper the iterative algorithm proposed by kozlov et al comput maths math phys 31 1991 45 for obtaining approximate solutions to the ill posed cauchy problem for the helmholtz equation is analysed the technique is then numerically implemented using the boundary element method bem the numerical results confirm that the iterative bem produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data an efficient stopping regularising criterion is also proposed

hybrid near field acoustic holography hybrid near field acoustical holography nah is developed for reconstructing acoustic radiation from an arbitrary object in a cost effective manner this hybrid nah is derived from a modified helmholtz equation least squares hels formula that expands the acoustic pressure in terms of outgoing and incoming waves the expansion coefficients are determined by solving an overdetermined linear system of equations obtained by matching the assumed form solution to measured acoustic pressures through the least squares measurements are taken over a conformal surface around a source at close range so that the evanescent waves can be captured next the modified hels is utilized to regenerate as much acoustic pressures on the conformal surface as necessary and take them as input to the helmholtz integral formulation implemented numerically by boundary element method bem the acoustic pressures and normal velocities on the source surface are reconstructed by using a modified tikhnov regularization tr with its regularization parameter determined by generalized cross validation gcv method results demonstrate that this hybrid nah combines the advantages of hels and inverse bem this is because a majority of the input data are regenerated but not measured thus the efficiency of reconstruction is greatly enhanced meanwhile the accuracy of reconstruction is ensured by the helmholtz integral theory and modified tr together with gcv method provided that hels converges fast enough on the measurement surface numerical examples of reconstructing acoustic quantities on the surface of a simplified engine block are demonstrated work supported by nsf

structural source identification using a generalized tikhonov regularization abstract this paper addresses the problem of identifying mechanical exciting forces from vibration measurements the proposed approach is based on a generalized tikhonov regularization that allows taking into account prior information on the measurement noise as well as on the main characteristics of sources to identify like its sparsity or regularity to solve such a regularization problem efficiently a generalized iteratively reweighted least squares girls algorithm is introduced proposed numerical and experimental validations reveal the crucial role of prior information in the quality of the source identification and the performance of the girls algorithm

local patch acoustic holography methods in enclosed spaces the paper compares reconstruction accuracy and computational cost of three patch acoustic holography algorithms applicable in the enclosed spaces for prediction of sound field near sources algorithms under investigation were dl sonah ibem and classical nah with spatial transformations and hologram aperture enlargement all of the selected algorithms take an advantage of using double layer microphone array for measurement of sound pressure field the reconstruction accuracy of all algorithms is determined by using of simple 3d model of curved radiating surface on the basis of calculation of difference between true acoustic quantity pressure velocity or intensity values very close to the surface and predicted sound field at same positions all these methods use different calculation procedure to obtain predicted sound field near source surface thus comparison of effectiveness of these algorithms including prediction accuracy to computational cost ratio is useful to determination their applicability in

fading regularization mfs algorithm for the cauchy problem associated with the two dimensional helmholtz equation abstract in this paper we combine the fading regularization method with the method of fundamental solutions mfs and investigate its application to the cauchy problem for the two dimensional helmholtz equation we present a numerical reconstruction of the missing data on an inaccessible part of the boundary from the knowledge of overprescribed noisy data taken on the remaining accessible boundary part for both smooth and piecewise smooth two dimensional geometries the accuracy convergence stability and efficiency of the proposed numerical algorithm as well as its capability to deblur the noisy data are validated by three numerical examples

reconstructing interior acoustic pressure fields via helmholtz equation least squares method this paper extends the helmholtz equation least squares hels method previously developed by wang and wu j acoust soc am 102 2020 2032 1997 to reconstruction of acoustic pressure fields inside the cavity of a vibrating object the acoustic pressures are reconstructed through an expansion of the acoustic modes generated by the gram schmidt orthonormalization with respect to the particular solutions to the helmholtz equation such an expansion is uniformly convergent because the selected acoustic modes consist of a uniformly convergent series of legendre functions the coefficients associated with these acoustic modes are determined by requiring the assumed form solution to satisfy the pressure boundary condition at the measurement points the errors incurred in this process are minimized by the least squares method numerical examples of partially vibrating spheres and cylinders with various half length to radius aspect ratios subject to different frequency excitations are demonstrated the recon

reconstruction of vibroacoustic responses of a highly nonspherical structure using helmholtz equation least squares method the vibroacoustic responses of a highly nonspherical vibrating object are reconstructed using helmholtz equation least squares hels method the objectives of this study are to examine the accuracy of reconstruction and the impacts of various parameters involved in reconstruction using hels the test object is a simply supported and baffled thin plate the reason for selecting this object is that it represents a class of structures that cannot be exactly described by the spherical hankel functions and spherical harmonics which are taken as the basis functions in the hels formulation yet the analytic solutions to vibroacoustic responses of a baffled plate are readily available so the accuracy of reconstruction can be checked accurately the input field acoustic pressures for reconstruction are generated by the rayleigh integral the reconstructed normal surface velocities are validated against the benchmark values and the out of plane vibration patterns at several natural frequencies are compared with the natural modes of a simply supported plate the impacts of various parameters such as number of measurement points measurement distance location of the origin of the coordinate system microphone spacing and ratio of measurement aperture size to the area of source surface of reconstruction on the resultant accuracy of reconstruction are examined