determination of the mutual radiation resistances of a rectangular plate and their impact on the radiated sound power abstract the mutual radiation resistances resulting from cross modal coupling have been mostly excluded from sound power calculations on the belief or premise that either for some reasons they have an insignificant impact on the power radiation or consideration of them can be an enormous computational burden in this paper the characteristics of the mutual radiation resistances are investigated of a simply supported rectangular plate it is shown that once the self radiation resistances or the so called modal radiation efficiencies have been calculated the mutual radiation resistances can be readily obtained at virtually no cost of equal importance because no approximation is made the present formulation is fully accurate in the entire frequency range an asymptotic expression is also derived for large modal wavenumbers numerical results are presented to illustrate the spectral characteristics of the mutual radiation resistances and the corresponding impact on the radiated sound power

acoustic shape sensitivity analysis using the boundary integral equation boundary integral equations are formulated for the shape sensitivity analysis of the acoustic problems the concept of the material derivative is employed in deriving the sensitivity equations since the equation is derived by the direct differentiation of the boundary integrals containing the field values it is expected that the sensitivity would be computed more effectively and accurately than the conventional finite difference method in addition the equation has the potential to be applied to many complex acoustic problems because the derived equation is regularized by using the integral identity that incorporates the one dimensional propagating wave and its material derivative the validity of the formulations is demonstrated through examples having regular shapes such as the three dimensional pulsating sphere and the one dimensional duct for which the analytical solutions are available as an example for an irregular domain the two dimensional model of an automotive interior cavity is dealt with in the view point of the noise level at the passenger s ear position the results show that the present method can be an effective tool for the shape optimization in designing the desired sound field it is noted that the present method permits accurate sensitivities of the acoustic pressure on the boundary as well as at the field points the present method is thought to be an alternative to the previous finite difference techniques for computing the shape sensitivity using the boundary element method and the formal derivative method using the finite element method

an improved algorithm for the multidimensional moment constrained maximum entropy problem the maximum entropy principle is a versatile tool for evaluating smooth approximations of probability density functions with the least bias beyond specified constraints in the recent paper we introduced new computational framework for the moment constrained maximum entropy problem in a multidimensional domain and developed a simple numerical algorithm capable of computing maximum entropy problem in a two dimensional domain with moment constraints of order up to 4 here we design an improved numerical algorithm for computing the maximum entropy problem in a two and higher dimensional domain with higher order moment constraints the algorithm features multidimensional orthogonal polynomial basis in the dual space of lagrange multipliers to achieve numerical stability and rapid convergence of newton iterations the new algorithm is found to be capable of solving the maximum entropy problem in the two dimensional domain with moment constraints of order up to 8 in the three dimensional domain with moment constraints of order up to 6 and in the four dimensional domain with moment constraints of order up to 4 corresponding to the total number of moment constraints of 44 83 and 69 respectively the two and higher dimensional maximum entropy test problems in the current work are based upon long term statistics of numerical simulation of the real world geophysical model for wind stress driven oceanic currents such as the gulf stream and the kuroshio

local likelihood density estimation based on smooth truncation two existing density estimators based on local likelihood have properties that are comparable to those of local likelihood regression but they are much less used than their counterparts in regression we consider truncation as a natural way of localising parametric density estimation based on this idea a third local likelihood density estimator is introduced our main result establishes that the three estimators coincide when a free multiplicative constant is used as an extra local parameter

a boundary element formulation for acoustic shape sensitivity analysis the helmholtz integral equation forms a conventional basis for acoustic boundary element analysis bea implicit differentiation of the discretized helmholtz integral equation is shown to yield an effective approach for the computation of rates of change sensitivities of acoustic response quantities with respect to changes in the shape of an acoustic model a theoretical formulation is presented that allows for the reuse of the factorization of the overall bea system left hand side matrix formed in a previous analysis thus obviating the need to factor perturbed matrices in the sensitivity analysis process the singularity strengths of the new kernel functions utilized to compute sensitivities of matrix coefficients required by this approach are shown to be the same as those present in ordinary bea an indirect approach for the computation of the diagonal contributions to sensitivity matrices associated with these new kernels is also discussed the sensitivity analysis formulation includes surface pressures and normal gradients velocities surface tangential pressure gradients and pressure and pressure gradients at arbitrary domain sample points it is concluded that the overall efficiency of implementations of these formulations is significant numerical results for a series of example problems are presented to quantify the accuracy and efficiency of this approach

vibroacoustic analysis of rectangular plates with elastic rotational edge restraints this investigation deals with the vibration of and the acoustic radiation from a simply supported rectangular plate with elastic restraints against edge rotations the displacement of the plate is first sought as a series expansion in terms of the beam functions each of the beam functions is then expressed as the linear combination of a fourier sine series and a complementary sufficiently smooth function that is introduced to ensure and improve the convergence of the fourier series expansion to facilitate the acoustic analysis the plate displacement is eventually simplified to a standard fourier sine series the modal and acoustic characteristics of square plates are studied for different restraining stiffnesses and configurations it is shown that the modes of the restrained plates can be considerably different from those in the simply supported case so are the corresponding modal radiation efficiencies the proposed method is generally applicable to rectangular plates elastically restrained along any edge s and the acoustic calculations are valid for an arbitrary acoustic or structural modal wave number

boundary integral equations for recovery of design sensitivities in shape optimization a new formulation for obtaining design sensitivities in shape optimization has been developed the formulation is based on a direct application of the material derivative concept to the appropriate boundary integral equations for displacements and stresses in an elastic solid as a check on accuracy the approach was applied to a uniformly loaded infinite plate containing an elliptical hole in this case the availability of an analytical solution made it possible to calculate errors exactly furthermore a wide range of stress states could be considered simply by varying the aspect ratio of the elliptical hole for convenience the design sensitivities were calculated with respect to changes in the major axis numerical convergence was established by comparing results based on four successive boundary meshes in general the predictions for both displacement and stress sensitivities were remarkably accurate

a sherman morrison approach to the solution of linear systems we propose a new direct method to solve linear systems this method is based on the sherman morrison formula and uses a finite iterative formula to compare our method with the restarted generalized minimum residual method and the gaussian elimination method with partial pivoting we use two classes of test problems linear systems having pascal cauchy and vandermonde matrices as coefficient matrices and randomly generated linear systems

a unified approach for the formulation of interaction problems by the boundary element method a unified formulation is presented based on boundary element method in a form suitable for performing the interaction analyses by substructure method for solid solid and soil structure problems the proposed formulation permits the evaluation of all the elements of impedance and input motion matrices simultaneously at a single step in terms of system matrices of the boundary element method without solving any special problem such as unit displacement or load problem as required in conventional methods it eliminates further the complicated procedure and the need for using scattering analysis in the evaluation of input motion functions to explain the formulation it is first given for an inclusion interacting with an infinite surrounding medium under the influence of a seismic input where both the inclusion and surrounding medium are treated as viscoelastic it is shown that the formulation for a rigid inclusion may be obtained from that for flexible inclusion as a special case through a transformation then the formulation is extended to other types of interaction problems a multi inclusion problem and an interaction problem involving a foundation embedded in a viscoelastic half space it is found that the proposed formulation remains essentially the same for all kinds of interaction problems and it can be used not only in regular interaction analysis but also in the analysis involving diffraction of waves in a medium containing holes copyright 2005 john wiley sons ltd

a bem sensitivity formulation for three dimensional active noise control summary in this paper a novel boundary element formulation for sensitivity analysis of local active noise control in a three dimensional field is presented the formulation is based on the helmholtz differential equation and is valid for internal as well as for scattering wave propagation problems the primary noise is attenuated within an enclosure called control volume by adding a control source modelled as an object with a vibrating surface both the optimum position of the control volume and the optimum location orientation of the secondary source are determined by minimisation of a suitable cost function the sensitivities are determined by implicit differentiation a hierarchical adaptive cross approximation approach in conjunction with the generalised minimal residual solver is implemented to accelerate the convergence four numerical examples are presented to demonstrate the accuracy and efficiency of the proposed formulations copyright 2012 john wiley sons ltd

numerical solutions of the acoustic eigenvalue equation in the rectangular room with arbitrary uniform wall impedances two numerical procedures for finding the acoustic eigenvalues in the rectangular room with arbitrary uniform wall impedances are developed one numerical procedure applies newton s method here starting with soft walls the eigenvalues are found by increasing the impedances of each wall pair in small increments up to the terminal impedances another procedure poses the eigenvalue problem as one of homotopic continuation from a non physical reference configuration in which all eigenvalues are known and obvious the continuation is performed by the numerical integration of two differential equations the latter procedure was found to be faster and finds all possible solutions the set of eigenvalues allowed the room modal natural frequencies and damping constants to be obtained from sound decays measured in a hard walled rectangular room and from the collective modal decay curve the impedances of the hard walls are estimated these are then used to find the reverberation times of the modes in the room with the floor lined with sound absorbing material of known acoustic impedance it was found that a single reverberation time for all modes is only supported in the rectangular room with hard walls and at the higher frequency bands consistent with sabine s theory which assumes a diffuse sound field in the rectangular room with hard walls and at the lower frequency bands and in the rectangular room with the floor lined with sound absorbing material and for all frequency bands modes with rather distinctive reverberation times may produce sound decays not always consistent with sabine s prediction

a semiparametric approach to density estimation abstract one method of fitting a parametric density function f x is first to estimate by maximum likelihood say and then to estimate f x by on the other hand when the parametric model does not hold the true density f x may be estimated nonparametrically as in the case of a kernel estimate the key idea proposed is to fit a combination of the parametric and nonparametric estimates namely where 0 1 is unknown the parameter is estimated from the data and its estimate is then used in as the proposed density estimate the main point is that we expect to be close to unity when the parametric model prevails and close to zero when it does not hold we show that under certain conditions converges to the parametric density when the parametric model holds and approaches the true f x when the parametric model does not hold the procedure was applied to a number of actual data sets in each case the maximum likelihood estimate was readily obtained and the semiparametric density es

dual methods in entropy maximization application to some problems in crystallography this paper is devoted to some infinite dimensional optimization problems with finitely many constraints these deal with entropy maximization and this paper is particularly concerned with those or

the radiation efficiency of baffled plates and strips the average radiation efficiency of point excited rectangular plates including those with a very large aspect ratio strips is investigated by using a modal summation method based on the farfield sound intensity by taking an average over all possible forcing positions on the plate the cross modal contributions average out to zero the numerical results from the modal summation are compared with established formulae for rectangular plates for wavenumbers where acoustic circulation takes place it is shown that the previously published formulae are not applicable for predicting the average radiation efficiency for a strip the analysis for the strip reveals that the radiation efficiency at frequencies below the first structural natural frequency of the strip is proportional to the square of the shortest edge length at frequencies between the fundamental natural frequency and that of the second order mode of bending across the strip the average radiation efficiency is found to be proportional to the structural damping loss factor but differs from the results obtained from the usual model of the nearfield radiation from the forcing point of a rectangular plate approximate expressions for calculating the average radiation efficiency of the strip are derived the maximum radiation efficiency around the critical frequency is found to vary less with helmholtz number kca where kc is the wavenumber at the critical frequency and a is the width than previously published models suggest

on the short wave acoustic radiation from planar panels or beams of rectangular shape an exact representation which involves single as opposed to double integrals is established for the time average power output generated by individual modes of normal surface velocity on a simply supported and baffled rectangular panel fluid loading is not taken into account the representation enables analytical estimates to be found in the short wavelength range and provides details hitherto unresolved by numerical analysis

fluid structure coupling for an unbaffled elastic panel immersed in a diffuse field abstract the study of the structural response of a panel excited by a multiple plane wave acoustic field is presented a new semi analytical approach based on the integral equation method is proposed the two major difficulties lie in the fact that the panel is unbaffled and is excited by an acoustic field a system for which the fluid structure coupling cannot be neglecteda priori using the free space green function and a variational approach a linear system is obtained for the two unknowns of the problem the sound pressure jump and the panel deflection the formulation allows one to obtain a simple physical interpretation in terms of the diffraction and radiation phenomenon an efficient computation scheme is introduced for the admittance matrix as well as a multiexcitation procedure for the acoustic plane waves convergence of the method is discussed and a comparison with a modal cavity approach is presented finally the importance of the diffraction by the panel is discussed with regards to approximations usually performed in some numerical techniques

near field sound radiation from simply supported rectangular plates the sound radiation efficiency of a harmonically point forced and simply supported rectangular plate is obtained numerically and is compared with that of a circular plate the effect of aspect ratio and thickness on sound radiation efficiency is also studied since the radiation of sound from the plate is analyzed in the near field its characteristics near the critical frequency are revealed in numerical analysis the technique of co ordinate transformation which enables a quadruple integral of sound power to be shown in single integral representations is employed the radiation efficiency is at a maximum when the frequency of the applied force is slightly higher than the critical frequency when the aspect ratio of a rectangular plate is nearly equal to unity or its shape is similar to a square the radiation efficiency depends only on the frequency of the applied force but when the aspect ratio differs from unity the influence of the mode number on the radiation efficiency cannot be ignored in the frequencies below the critical frequency

recent developments in nonparametric density estimation advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research and especially the development of nonparametric data analysis procedures in particular theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics such as nonparametric regression nonparametric discrimination and nonparametric pattern recognition this article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject the early density estimation methods such as the histogram kernel estimators and orthogonal series estimators are still very popular and recent research on them is described different types of restricted maximum likelihood density estimators including order restricted estimators maximum penalized likelihood estimators and sieve estimators are discussed where restrictions are imposed upon the class of densities or on the form of the likelihood function nonparametric density estimators that are data adaptive and lead to locally smoothed estimators are also discussed these include variable partition histograms estimators based on statistically equivalent blocks nearest neighbor estimators variable kernel estimators and adaptive kernel estimators for the multivariate case extensions of methods of univariate density estimation are usually straightforward but can be computationally expensive a method of multivariate density estimation that did not spring from a univariate generalization is described namely projection pursuit density estimation in which both dimensionality reduction and density estimation can be pursued at the same time finally some areas of related research are mentioned such as nonparametric estimation of functionals of a density robust parametric estimation semiparametric models and density estimation for censored and incomplete data directional and spherical data and density estimation for dependent sequences of observations

a class of local likelihood methods and near parametric asymptotics observations in the neighbourhood of t the paper studies the sense in which f t t is closer to the true distribution g t than the usual estimate f t is asymptotic results are presented for the case in which the model misspecification becomes vanishingly small as the sample size tends to1 i n this setting the relative entropy risk of the local method is better than that of maximum likelihood the form of optimum weights for the local likelihood is obtained and illustrated for the normal distribution

a state space coupling method for fluid structure interaction analysis of plates a state space coupling method is presented for the direct solution of fluid loaded natural frequencies and mode shapes of plates this method expands the frequency dependent term in the rayleigh integral in a power series on circular frequency after factoring out the frequency term from the integrands integration involved in setting up the acoustic impedance coefficient matrices is confined to a frequency independent part the acoustic impedance coefficient matrices are therefore frequency independent and can be coupled directly with the structural matrix into a canonical state space form to yield the fluid loaded modes via the direct eigenvalue analysis a fluid loaded stiffened plate is involved to demonstrate the method numerical results of the fluid loaded natural frequencies mode shapes and modal damping ratios are given to show the efficacy of the state space coupling method

a hybrid approach for simulating fluid loading effects on structures using experimental modal analysis and the boundary element method many structural acoustics problems involve a vibrating structure in a heavy fluid however obtaining fluid loaded natural frequencies and damping experimentally can be difficult and expensive this paper presents a hybrid experimental numerical approach to determine the heavy fluid loaded resonance frequencies and damping of a structure from in air measurements the approach combines in air experimentally obtained mode shapes with simulated in water acoustic resistance and reactance matrices computed using boundary element be analysis the procedure relies on accurate estimates of the mass normalized in vacuo mode shapes using singular value decomposition and rational fraction polynomial fitting which are then used as basis modes for the in water be analysis the method is validated on a 4 445 cm 1 75 in thick nickel aluminum bronze rectangular plate by comparing natural frequencies and damping obtained using the hybrid approach to equivalent data obtained from actual in water measurements good agreement is shown for the fluid loaded natural frequencies and one third octave loss factors finally the limitations of the hybrid approach are examined

acoustic radiation from periodic and sectionally aperiodic rib stiffened plates the far field and near field solutions for the radiated acoustic pressure from a line driven fluid loaded rib stiffened thin elastic plate have been obtained the plate has been configured to have two sets of rib stiffeners though the formulation given has been extended to include additional rib stiffener sets the stiffeners composing a given set are identical and are spaced periodically with distance l however one set of stiffeners is shifted by an amount from the other set in this manner portions of the plate may be configured with periodic repeating sections of arbitrary length l having aperiodic rib spacing the stiffeners exert reactive forces upon the plate but not angular moments fluid loading is included on the upper surface of the plate while the lower surface is unloaded except for a time harmonic line force applied normal to the lower surface the far field radiated pressure has been obtained using the method of stationary phase numerical integration techniques were used to obtain the near field acoustic pressure

shape sensitivity analysis of sequential structural acoustic problems using fem and bem abstract a shape design sensitivity formulation for structural acoustic problems using sequential finite element and boundary element methods is presented frequency response analysis is used to obtain the dynamic behavior of the structure while boundary element analysis is used to solve for the pressure response of the acoustic domain it is shown that the adjoint method which takes the reverse direction to response analysis provides a very efficient way of sensitivity calculation in addition it has been shown that the adjoint equation for the shape design problem is the same as that of the sizing design problem the only difference is the numerical integration that evaluates the sensitivity coefficient the combination of the semi analytical method for the structure and the analytical differentiation method for the acoustic cavity yields a very practical approach for the shape design sensitivity formulation the accuracy of the sensitivity information is compared with the analytical sensitivity as well as the sensitivity calculated using the finite difference method

a fast newton algorithm for entropy maximization in phase determination a long standing issue in the bayesian statistical approach to the phase problem in x ray crystallography is to solve an entropy maximization subproblem efficiently in every iteration of phase estimation the entropy maximization problem is a semi infinite convex program and can be solved in a finite dual space by using a standard newton method however the newton method is too expensive for this application since it requires o n3 floating point operations per iteration where n corresponds to the number of phases to be estimated other less expensive methods have been used but they cannot guarantee fast convergence in this paper we present a fast newton algorithm for the entropy maximization problem which uses the sherman morrison woodbury formula and the fast fourier transform to compute the newton step and requires only o n log n floating point operations per iteration yet has the same convergence rate as the standard newton we describe the algorithm and discuss related computational issues numerical results on simple test cases will also be presented to demonstrate the behavior of the algorithm

radiation impedance matrices for rectangular interfaces within rigid baffles calculation methodology and applications the coupling of sound fields through a finite sized aperture in a plane rigid baffle where the region half space on one side is unbounded can be described by an integral equation which constitutes a boundary condition for the field on the other side of the aperture such a boundary condition when the pressure and the normal velocity are expanded in basis functions defined over the aperture can be recast into a matrix form relating the coefficients of the basis functions in the expansions the principal feature being a matrix of fourfold double area integrals analogous to those encountered in studies of radiation from flexible pistons in rigid baffles a substantial analytical reduction to sums of single nonsingular integrals is derived for the elements of this radiation impedance matrix when the aperture is rectangular and the basis functions are expressible as a sum of products of exponential functions of the cartesian coordinates of the aperture plane with the exponential coefficients being arbitrary complex numbers the validity of the result is substantiated by its reduction to previously published results for less general cases its utility is demonstrated with the example of diffraction by a square hole in a screen

the multidimensional moment constrained maximum entropy problem a bfgs algorithm with constraint scaling in a recent paper we developed a new algorithm for the moment constrained maximum entropy problem in a multidimensional setting using a multidimensional orthogonal polynomial basis in the dual space of lagrange multipliers to achieve numerical stability and rapid convergence of the newton iterations here we introduce two new improvements for the existing algorithm adding significant computational speedup in situations with many moment constraints where the original algorithm is known to converge slowly the first improvement is the use of the bfgs iterations to progress between successive polynomial reorthogonalizations rather than single newton steps typically reducing the total number of computationally expensive polynomial reorthogonalizations for the same maximum entropy problem the second improvement is a constraint rescaling aimed to reduce relative difference in the order of magnitude between different moment constraints improving numerical stability of iterations due to reduced sensitivity of different constraints to changes in lagrange multipliers we observe that these two improvements can yield an average wall clock time speedup of 5 6 times compared to the original algorithm

evaluation of 2 d green s boundary formula and its normal derivative using legendre polynomials with an application to acoustic scattering problems this paper presents the non singular forms in a global sense of two dimensional green s boundary formula and its normal derivative the main advantage of the modified formulations is that they are amenable to solution by directly applying standard quadrature formulas over the entire integration domain that is the proposed element free method requires only nodal data the approach includes expressing the unknown function as a truncated fourier legendre series together with transforming the integration interval a b to 1 1 the series coefficients are thus to be determined the hypersingular integral interpreted in the hadamard finite part sense and some weakly singular integrals can be evaluated analytically the remaining integrals are regular with the limiting values of the integrands defined explicitly when a source point coincides with a field point the effectiveness of the modified formulations is examined by an elliptic cylinder subject to prescribed boundary conditions the regularization is further applied to acoustic scattering problems the well known burton miller method using a linear combination of the surface helmholtz integral equation and its normal derivative is adopted to overcome the non uniqueness problem a general non singular form of the composite equation is derived comparisons with analytical solutions for acoustically soft and hard circular cylinders are made copyright 2001 john wiley sons ltd

a numerical method for the computation of the resonance frequencies and modes of a fluid loaded plate application to the transient response of the system in previous papers we have shown that the time response of a fluid loaded structure can be expressed in terms of the resonance modes of the fluid structure system we first show the efficiency of such a representation by comparing numerical predictions to experimental results the main objective of this paper is to consider the numerical aspects of this representation namely the computation of the coupling term in the variational equation and the computation of the resonance frequencies and modes three methods are proposed to compute the resonance frequencies an iterative technique a warburton approximation and a perturbation technique light fluid approximation numerical results are presented to compare these three methods for air and water loading the last part of the paper discusses the choice of the number of resonance modes which is required to obtain a representation of the transient radiated pressure with a sufficient accuracy

a practical computational framework for the multidimensional moment constrained maximum entropy principle the maximum entropy principle is a versatile tool for evaluating smooth approximations of probability density functions with a least bias beyond given constraints in particular the moment based constraints are often a common prior information about a statistical state in various areas of science including that of a forecast ensemble or a climate in atmospheric science with that in mind here we present a unified computational framework for an arbitrary number of phase space dimensions and moment constraints for both shannon and relative entropies together with a practical usable convex optimization algorithm based on the newton method with an additional preconditioning and robust numerical integration routine this optimization algorithm has already been used in three studies of predictability and so far was found to be capable of producing reliable results in one and two dimensional phase spaces with moment constraints of up to order 4 the current work extensively references those earlier studies as practical examples of the applicability of the algorithm developed below

on the radiation impedance of a rectangular piston abstract single integral representations for the resistive and reactive components of the radiation impedance appropriate to a rectangular piston are established thereby enabling a systematic refinement of estimates at both short and long wavelengths comparisons with previous analyses are made explicit as well as extensions and corrections thereto

a general formulation for the sound radiation from rectangular baffled plates with arbitrary boundary conditions the radiation of sound from a baffled rectangular plate with edges elastically restrained against deflection and rotation is analyzed the elastic constants along the contour can be varied to reproduce simply supported clamped free or guided edges as limiting cases the formulation is based on a variational method for the vibration of the plate and assumes no fluid loading of the structure the elastic boundary conditions appear in the hamiltonian of the plate through a dynamic contribution which is expressed in terms of nondimensional edge parameters the extremalization of the hamiltonian is achieved using a rayleigh ritz method and both the free vibrations and the forced vibrations of the plate are presented the radiation of sound from the plate is analyzed in the far field and is calculated from one dimensional fourier transforms numerical results are presented for the radiation efficiency of modes of simply supported clamped free and guided plates the values found agree well with predic

a series expansion of the acoustic power radiated from planar sources a series expansion in ascending powers of the wavenumber k is derived for the acoustic power delivered by baffled or unbaffled planar sources this series provides a relatively simple means of deriving expressions for the power radiated by a baffled source with a known velocity distribution and can be used for unbaffled plates when the velocity field outside the plate is also known the terms in the series are calculated from the moments of this velocity distribution in the plane containing the source if these moments are written as derivatives in wavenumber space it is shown that a maclaurin expansion of the fourier transformed velocity provides an easy technique for computing the first few terms of the acoustic power examples are provided for baffled rectangular plates with various boundary conditions the arbitrarily shaped plate with free boundaries is particularly interesting it is proven that the volume flow across its surface must be zero and as a result corner and edge mode radiation cannot e

the energy aspect of the reciprocal interactions of pairs of two different vibration modes of a clamped annular plate abstract the standardized mutual active and reactive sound power of a clamped plate representing the energy aspect of the reciprocal interactions of two different in vacuo modes has been computed it was assumed that the vibrations are axisymmetric elastic and time harmonic the plate s transverse deflection is small as compared with the plate s size and that the vibration velocity is small as compared with the acoustic wavenumber generated the kirchhoff love theory of a perfectly elastic plate was used the integral formulae for the mutual sound power were transformed into their hankel representations which made possible their subsequent computation a closed path integral was used to express the integral in its hankel representation to compute the mutual active sound power the asymptotic stationary phase method was used to compute the two magnitudes i e the mutual active and reactive sound power the results obtained are the asymptotic formulae valid for the acoustically fast waves the oscillating as well as the non oscillating terms have been identified in the formulae to make possible their further separate analysis the availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power moreover the formulae presented herein together with those for the individual modes known from the literature make a complete basis for further computations of the total sound power of the plate s damped and forced vibrations in fluid

a non singular boundary integral equation for acoustic problems abstract a weakly singular boundar integral equation and a non singular one are derived for acoustic problems by using the one dimensional wave propagation mode the degree of the singularities appearing in the conventional boundary integral equation can be reduced since the strong singularity is removed in the weakly singular equation the jump term of the field pressure expression in the very vicinity of the boundary disappears it is shown that the weak singularity can be also removed for a smooth boundary in the non singular representation and thus special treatments for singular integral are no longer needed in order to test the proposed method several simple problems have been solved by employing the triangular element with standard gaussian quadrature integration points the results obtained show the accuracy of the method in the near field as well as on the boundary

analytical approximations for the modal acoustic impedances of simply supported rectangular plates coupling of the in vacuo modes of a fluid loaded vibrating structure by the resulting acoustic field while known to be negligible for sufficiently light fluids is still only partially understood a particularly useful structural geometry for the study of this problem is the simply supported rectangular flat plate since it exhibits all the relevant physical features while still admitting an analytical description of the modes here the influence of the fluid can be expressed in terms of a set of doubly infinite integrals over wave number the modal acoustic impedances closed form solutions for these impedances do not exist and while their numerical evaluation is possible it greatly increases the computational cost of solving the coupled system of modal equations there is thus a need for accurate analytical approximations in this work such approximations are sought in the limit where the modal wavelength is small in comparison with the acoustic wavelength and the plate dimensions it is shown that contour integration techniques can be used to derive analytical formulas for this regime and that these formulas agree closely with the results of numerical evaluations previous approximations davies j sound vib 15 1 107 126 1971 are assessed in the light of the new results and are shown to give a satisfactory description of real impedance components but in general erroneous expressions for imaginary parts

an improved state space method for coupled fluid structure interaction analysis this paper presents an improved state space method for incorporating fluid structure interaction into structural acoustic analyses giordano and koopmann j a giordano and g h koopmann state space boundary element finite element coupling for fluid structure interaction analysis j acoust soc am 98 363 372 1995 introduced a state space approach for the coupled analysis of fluid loaded structures giordano s method employed a third order interpolation of the fluid impedance coupled with state space formalism permitting the direct eigenvalue analysis of the coupled system and thereby yielding the fluid loaded modes and natural frequencies this is in contrast to the common technique of sweeping through a range of frequencies so as to identify the natural frequencies and mode shapes the original state space approach yielded system matrices of order 4n where n is the number of degrees of freedom in the underlying model where giordano s method employed an interpolation based on surface velo

analytical and experimental investigation on transmission loss of clamped double panels implication of boundary effects the air borne sound insulation performance of a rectangular double panel partition clamp mounted on an infinite acoustic rigid baffle is investigated both analytically and experimentally and compared with that of a simply supported one with the clamped or simply supported boundary accounted for by using the method of modal function a double series solution for the sound transmission loss stl of the structure is obtained by employing the weighted residual galerkin method experimental measurements with al double panel partitions having air cavity are subsequently carried out to validate the theoretical model for both types of the boundary condition and good overall agreement is achieved a consistency check of the two different models based separately on clamped modal function and simply supported modal function is performed by extending the panel dimensions to infinite where no boundaries exist the significant discrepancies between the two different boundary conditions are demonstrated in terms of the stl versus frequency plots as well as the panel deflection mode shapes

the kernel estimate of a regression function in likelihood based models abstract smoothing splines have a penalized likelihood motivation good and gaskins 1971 allowing direct application to nonparametric regression in likelihood based models the notion of a weighted likelihood for the nonparametric kernel estimation of a regression function is proposed generalizing the local likelihood theory of tibshirani and hastie 1987 let the data be of the form xi yi i 1 n where xi 0 1 d are lattice points and the yi are independent random variables from a family of distributions with parameter i g xi with g having continuous partial derivatives of order k 2 the goal is to arrive at a nonparametric estimate o of o g xo for a fixed point xo 0 1 d we consider the estimator o that maximizes the weighted likelihood function w n i 1 w xo xi b log f yi with f the density of yi w a symmetric kernel with compact support and b the bandwidth that controls the degree of smoothing sufficient conditions for consistency and asympt

modal decomposition of exterior acoustic structure interaction a modal decomposition technique to analyze individual modal contributions to the sound power radiated from an externally excited structure submerged in a heavy fluid is presented the fluid loaded structural modes are calculated by means of a polynomial approximation and symmetric linearization of the underlying nonlinear eigenvalue problem the eigenvalues and eigenfunctions of a fluid loaded sphere with and without internal structures are presented the modal sound power contributions using both fluid loaded structural modes and acoustic radiation modes are presented the results for the resistive and reactive sound power obtained from the superposition of the individual modal sound power contributions are compared to the harmonic solution of the forced problem

local likelihood estimation abstract a scatterplot smoother is applied to data of the form x 1 y 1 x 2 y 2 xn yn and uses local fitting to estimate the dependence of y on x a simple example is the running lines smoother which fits a least squares line to the y values falling in a window around each x value the value of the estimated function at x is given by the value of the least squares line at x a smoother generalizes the least squares line which assumes that the dependence of y on x is linear in this article we extend the idea of local fitting to likelihood based regression models one such application is to the class of generalized linear models nelder and wedderburn 1972 we enlarge this class by replacing the covariate form 0 x 1 with an unspecified smooth function s x this function is estimated from the data by a technique we call local likelihood estimation the method consists of maximum likelihood estimation for 0 and 1 applied in a window around each x value multiple covariates are incor

a simple calculation method for the self and mutual radiation impedance of flexible rectangular patches in a rigid infinite baffle a numerical model has been developed to calculate the self and mutual radiation impedance in the cases of uniformly and flexibly vibrating rectangular patches in a rigid infinite baffle the spatial convolution approach is employed here to derive general expressions for the radiation impedance of a rectangular radiator in the form of simple integrals which allows a fast evaluation numerically the presented integral solution agrees with that obtained for the mutual radiation impedance of a uniformly vibrating rectangular piston by the use of the classical approach the numerical results of self radiation impedance of a square piston are compared with the tabulated values published previously as examples of flexibly vibrating rectangular patch a closed form expression is first given for the radiation impedance in the normal mode of vibration the numerical results reveal that the computation time in obtaining accurate calculations is greatly reduced by using the proposed method

on local likelihood density estimation this paper considers a class of local likelihood methods introduced by eguchi and copas unified asymptotic results are presented in the usual smoothing context of the bandwidth h tending to zero as the sample size tends to infinity we present our results pointwise in the univariate case but then go on to extend them to global properties and to indicate how to cope with the multivariate case specific members of the class due to copas and hjort and jones are seen to be members of a subset of the whole class with the same and best small h behavior further comparisons between members of the class are alluded to based on the complementary large h asymptotic results of eguchi and copas

relative efficiencies of kernel and local likelihood density estimators summary local likelihood methods enjoy advantageous properties such as good performance in the presence of edge effects that are rarely found in other approaches to nonparametric density estimation however as we argue in this paper standard kernel methods can have distinct advantages when edge effects are not present we show that whereas the integrated variances of the two methods are virtually identical the integrated squared bias of a conventional kernel estimator is less than that of a local log linear estimator by as much as a factor of 4 moreover the greatest bias improvements offered by kernel methods occur when they are needed most i e when the effect of bias is particularly high similar comparisons can also be made when high degree local log polynomial fits are assessed against high order kernel methods for example although as is well known high degree local polynomial fits offer potentially infinite efficiency gains relative to their kernel competitors the converse is also true indeed the asymptotic value of the integrated squared bias of a local log quadratic estimator can exceed any given constant multiple of that for the competing kernel method in all cases the densities that suffer problems in the context of local log likelihood methods can be chosen to be symmetric either unimodal or bimodal either infinitely or compactly supported and to have arbitrarily many derivatives as functions on the real line they are not pathological however our results reveal quantitative differences between global performances of local log polynomial estimators applied to unimodal or multimodal distributions

local likelihood based on kernel censoring by drawing an analogy with likelihood for censored data a local likelihood function is proposed which gives more weight to observations near a region of interest in the sample space resulting methods can be used for assessing local departures from a parametric model and for semiparametric density estimation some theory and three examples is given

locally parametric nonparametric density estimation this paper develops a nonparametric density estimator with parametric overtones suppose f x is some family of densities indexed by a vector of parameters we define a local kernel smoothed likelihood function which for each x can be used to estimate the best local parametric approximant to the true density this leads to a new density estimator of the form f x o x thus inserting the best local parameter estimate for each new value of x when the bandwidth used is large this amounts to ordinary full likelihood parametric density estimation while for moderate and small bandwidths the method is essentially nonparametric using only local properties of data and the model alternative ways more general than via the local likelihood are also described the methods can be seen as ways of nonparametrically smoothing the parameter within a parametric class properties of this new semiparametric estimator are investigated our preferred version has approximately the same variance as the ordinary kernel method but potentially a smaller bias the new method is seen to perform better than the traditional kernel method in a broad nonparametric vicinity of the parametric model employed while at the same time being capable of not losing much in precision to full likelihood methods when the model is correct other versions of the method are approximately equivalent to using particular higher order kernels in a semiparametric framework the methodology we develop can be seen as the density estimation parallel to local likelihood and local weighted least squares theory in nonparametric regression

eigenpairs of a coupled rectangular cavity and its fundamental properties this paper deals with the eigenvalue problem of a coupled rectangular cavity comprising five rigid walls and one flexible panel frequently employed in much literature it is the purpose of this paper to derive explicitly the eigenpairs of the coupled cavity which are yet to be found first the coupling orthogonality conditions the eigenpairs need to satisfy are derived thereby enabling the verification of the eigenpairs newly sought or already existent using the coupling orthogonality conditions the modal equation of the coupled cavity system is then obtained permitting one to deal with a forced response of the coupled cavity it is shown that the eigenfunctions governing the dynamics of the sound field are expressed as the infinite sum of degenerate eigenfunctions the characteristic matrix equation is then derived specifying the eigenpairs of the coupled cavity in order to investigate the fundamental properties of the eigenpairs derived a numerical analysis is conducted revealing the presence of evanescent modes in addition to the conventional standing wave modes finally an experiment is carried out verifying the validity of the eigenpairs derived in the article

monte carlo study of three data based nonparametric probability density estimators abstract although the theoretical properties of modern nonparametric probability density estimators have been studied for 25 years there remains the practical problem of how to specify the amount of bias or smoothing in a density estimate based on a random sample in this paper we review and evaluate three recently developed data based algorithms that completely specify a density estimate from a random sample using monte carlo techniques we compare the statistical accuracy of these algorithms as measured by the integrated mean squared error in addition we examine the sensitivity of these algorithms to outliers and estimate computer time requirements one conclusion we draw is that the statistical accuracy of these data based algorithms seems comparable to levels predicted by theoretical models

the effect of different combinations of boundary conditions on the average radiation efficiency of rectangular plates the boundary conditions of a vibrating plate are known to have an influence on its sound radiation for frequencies below the critical frequency to investigate this effect in a systematic way the average radiation efficiency and radiated power are calculated for a rectangular plate set in an infinite baffle using a modal summation approach whereas analytical expressions exist for simply supported boundary conditions a numerical approach is required for other cases nine combinations of boundary conditions are considered consisting of simply supported clamped and free edges on different plate edges the structural vibration is approximated by using independent beam functions in orthogonal directions allowing simple approximate formulae for mode shapes and natural frequencies this assumption is checked against a finite element model and shown to give reliable results it is shown that a free plate has the lowest radiation efficiency and a clamped plate the highest for most frequencies between the fundamental panel natural frequency and the critical frequency other combinations of boundary condition give intermediate results according to the level of constraint introduced the differences depend on frequency excluding the extreme case of a fully free plate all the other boundary conditions give results within a range of 8 db in the middle part of the short circuiting region decreasing towards the critical frequency at low frequency the differences can be even greater in some cases up to 20 db these conclusions are shown to hold for a range of plate thicknesses and dimensions

local likelihood density estimation local likelihood was introduced by tibshirani and hastie as a method of smoothing by local polynomials in non gaussian regression models in this paper an extension of these methods to density estimation is discussed and comparison with other methods of density estimation presented the local likelihood method has particularly strong advantages over kernel methods when estimating tails of densities and in multivariate settings suppose constraints are incorporated in a simple manner asymptotic properties of the estimate are discussed a method for computing the estimate is outlined c code to implement the estimation procedure described in this paper together with s interfaces for graphical display of results are available at http cm bell labs com stat project locfit index html

state space boundary element finite element coupling for fluid structure interaction analysis state space coupling is a new approach for handling computational fluid structure interaction problems in the low to medium frequency range the method is based on standard boundary element bem and finite element fem discretizations of the acoustic and structural domains respectively the implicit frequency dependence of a traditional acoustic impedance matrix is made explicit through a power series expansion on circular frequency and considering time harmonic motion once expanded the acoustic energy of the fluid is directly coupled to that of the structure via hamilton s principle the coupled system is then recast in a canonical state space form which is also in the form of a standard eigenvalue problem solution of this system produces a series of complex eigenvalues and eigenvectors which represent a modal decomposition of the fluid loaded structure biorthogonality properties of the state space eigensystem allow for an uncoupled modal solution of the forced problem results for a submerged spherical shell and a finite plate in an infinite ridged baffle are given to illustrate the state space approach

modal parameter estimation for fluid loaded structures from reduced order models a model reduction method is developed to estimate modal parameters of fluid loaded structures the method uses a matrix free formulation of rational krylov projection to construct reduced order models of the fluid loaded structures from forced responses at selected interpolation frequencies due to small sizes of the reduced order models eigenpairs of the associated eigenvalue problems are available at a very low computational cost resonance frequencies modal damping ratios and mode shapes of the original systems are recovered from the forced responses and the eigenpairs of the reduced order models nonphysical modes introduced by the model reduction process are filtered out by a modal damping ratio test and double checked by the condition number of the dynamic stiffness matrix efficiency and accuracy of the present method are demonstrated on a benchmark model of a water loaded plate clamped in a baffle

modal sound transmission loss of a single leaf panel asymptotic solutions in a previously published paper c wang j acoust soc am 137 6 3514 3522 2015 the modal sound transmission coefficients of a single leaf panel were discussed with regard to the inter modal coupling effects by incorporating such effect into the equivalent modal radiation impedance which is directly related to the modal sound transmission coefficient of each mode the overall sound transmission loss for both normal and randomized sound incidences was computed through a simple modal superposition benefiting from the analytical expressions of the equivalent modal impedance and modal transmission coefficients in this paper behaviors of modal sound transmission coefficients in several typical frequency ranges are discussed in detail asymptotic solutions are also given for the panels with relatively low bending stiffnesses for which the sound transmission loss has been assumed to follow the mass law of a limp panel results are also compared to numerical analysis and the renowned mass law theories

acoustic modeling of a three dimensional rectangular opened enclosure coupled with a semi infinite exterior field at the baffled opening a modeling method is proposed for the acoustic analysis of a three dimensional 3d rectangular opened enclosure coupled with a semi infinite exterior field by a rectangular opening of arbitrary size and with general wall impedance in contrast to existing modeling methods that solve the differential equations the energy principle in combination with a 3d modified fourier cosine series is employed in the present method for the modeling of this system under this theoretical framework the effect of an opening in the wall of a rectangular enclosure is taken into account via the work done by the sound pressure acting on the opening between the finite enclosure and exterior domain the sound pressure inside the opened enclosure is expressed as the combination of a 3d trigonometric cosine series and one supplementary 2d expansion introduced to ensure uniform convergence of the solution over the entire solution domain including opening boundary the acoustic responses of the opened enclosure are obtained bas

the sound power of an individual mode of a clamped free annular plate abstract the main aim of this study is an analysis of sound radiation of some clamped free and free clamped annular plates the plates are embedded in some infinite perfectly rigid baffles and vibrate with the free field condition satisfied the kirchhoff love linear theory of a perfectly elastic plate is used to solve the plates equations of motion the sound pressure at the plates surfaces is expressed by its hankel transform the closed path integral technique known from the literature and the stationary phase method are used to find the standardized active and reactive sound power of an individual mode in the form of some high frequency asymptotic formulae useful for some highly efficient engineering computations their non oscillating and oscillating parts have been separated it is assumed that the vibration and sound radiation are axisymmetric and time harmonic low fluid loading is also assumed the complex sound power of an individual mode forms the basis for computing the total sound power of some excited and damped vibrations in the fluid the total sound power is not discussed in this study

the forced sound transmission of finite single leaf walls using a variational technique the single wall is the simplest element of concern in building acoustics but there still remain some open questions regarding the sound insulation of this simple case the two main reasons for this are the effects on the excitation and sound radiation of the wall when it has a finite size and the fact that the wave field in the wall is consisting of two types of waves namely forced waves due to the exciting acoustic field and free bending waves due to reflections in the boundary the aim of the present paper is to derive simple analytical formulas for the forced part of the airborne sound insulation of a single homogeneous wall of finite size using a variational technique based on the integral differential equation of the fluid loaded wall the so derived formulas are valid in the entire audible frequency range the results are compared with full numerical calculations measurements and alternative theory with reasonable agreement

the solution of coupled interior exterior acoustic problems using the boundary element method the boundary element method bem is used to solve a class of problems in which an interior domain and an exterior domain are coupled by an interface surface such as when sound propagates along a duct and radiates from the open end into the surrounding space in the current approach integral equations for the interior and exterior domains are coupled using continuity conditions at the interface surface between the two domains the integral equations are reduced to numerical form using second order boundary elements the coupled interior exterior boundary element method presented here overcomes numerical error and excess computer time problems present when traditional boundary element formulations are applied to this class of problems the current approach is illustrated using several examples including the radiation of sound from an open duct the radiation of sound from a source within a partial enclosure and the acoustical response of a slotted cavity due to an incident plane wave

acoustic radiation from a rectangular plate reinforced by springs at arbitrary locations abstract the vibration of a simply supported rectangular plate which is reinforced by a finite number of springs at arbitrary locations is sought as a linear combination of the flexural modes of the corresponding unloaded or simple plate although these modes cannot be directly used to decouple the dynamic equations of the motion of the reinforced plate it is still advantageous to use them as a complete set of basis functions to represent the interested quantities such as the deflection of the plate a linear transformation is established between the two modal spaces spanned by the modes respectively for the reinforced and the unloaded plates the radiation characteristics of the spring reinforced plate are investigated by using a near field formulation in order to reduce computational burden a frequency interpolation technique is employed so that numerical integration now needs to be carried out only at some key frequencies the specific radiation resistances of the basis modes are first determined as a set of invariants from which the modal radiation efficiency of the reinforced plate can be readily extracted the effects of cross modal coupling between the basis modes have been considered which is necessary for an accurate determination of the modal radiation efficiency for the reinforced plate a qualitative procedure is also described for locating the coincidence frequencies where the modal radiation efficiencies of the reinforced plate tend to reach their peak values

the average specific forced radiation wave impedance of a finite rectangular panel the average specific forced radiation wave impedance of a finite rectangular panel is of importance for the prediction of both sound insulation and sound absorption in 1982 thomasson published numerical calculations of the average specific forced radiation wave impedance of a square of side length 2e for wave number k in half octave steps of ke from 0 25 to 64 thomasson s calculations were for the case when the forced bending wave number kb was less than or equal to k thomasson also published approximate formulas for values of ke above and below the published results this paper combines thomasson s high and low frequency formulas and compares this combined formula with thomasson s numerical calculations the real part of the approximate formula is between 0 7 db higher and 1 db lower than the numerical calculations the imaginary part of the approximate formula is between 2 3 db higher and 2 6 db lower than the numerical calculations this paper also gives approximate formulas for the case when kb is greater than or equal to k the differences are between 0 8 and 1 2 db for the imaginary part and between 6 2 and 2 4 db for the real part

a unified approach for predicting sound radiation from baffled rectangular plates with arbitrary boundary conditions this paper discusses sound radiation from a baffled rectangular plate with each of its edges arbitrarily supported in the form of elastic restraints the plate displacement function is universally expressed as a 2 d fourier cosine series supplemented by several 1 d series the unknown fourier expansion coefficients are then determined by using the rayleigh ritz procedure once the vibration field is solved the displacement function is further simplified to a single standard 2 d fourier cosine series in the subsequent acoustic analysis thus the sound radiation from a rectangular plate can always be obtained from the radiation resistance matrix for an invariant set of cosine functions regardless of its actual dimensions and boundary conditions further this radiation resistance matrix unlike the traditional ones for modal functions only needs to be calculated once for all plates with the same aspect ratio in order to determine the radiation resistance matrix effectively an analytical formula is derived in the form of a power series of the non dimensional acoustic wavenumber the formula is mathematically valid and accurate for any wavenumber several numerical examples are presented to validate the formulations and show the effect of the boundary conditions on the radiation behavior of planar sources

solution of coupled acoustic problems a partially opened cavity coupled with a membrane and a semi infinite exterior field abstract there have been many attempts to understand the coupling phenomena between a solid structure and the surrounding fluid however the studies were restricted to interaction only between a structure and a finite cavity or a structure and acoustic field of infinite size the system that we have studied has a structure that faces both a cavity of finite size and an external field of semi infinite size we also allow a hole which can directly interact with the cavity as well as the external field this configuration therefore provides two different interactions or communication means one is the finite structure and the other is the hole of finite size this paper studies as to how these two components interact with the other two systems the finite cavity covered by the structure and the hole and the semi infinite fluid for simplicity a two dimensional and partially opened cavity coupled with a membrane and an exterior field was selected the solution has to be found by solving a boundary value problem but this case has to do with the boundaries that have two different conditions one is the membrane and the other is the hole the solution has been found in terms of the modal functions that satisfy the boundary conditions of finite cavity membrane and hole non dimensional coupling coefficients are obtained from the solution the results exhibit that the coupling effect gives additional peaks and troughs in the averaged pressure of the cavity these peaks and troughs are symmetrically arranged with respect to helmholtz frequency of the cavity the strong coupling occurs at the trough frequencies where the membrane interacts actively with the cavity and the exterior field

an analytical solution for the self and mutual radiation resistances of a rectangular plate it is widely accepted that for an arbitrary acoustic wavenumber the radiation resistance of a simply supported rectangular plate has to be calculated through numerical integration in this study an analytical solution for the self and mutual radiation resistances is obtained in the form of the power series of the non dimensional acoustic wavenumber unlike the previous analytical or asymptotic solutions it is not subject to any of the restrictions usually imposed upon the acoustic wavenumber a few numerical examples are given simply to verify the solution and elucidate the reliance of the self and mutual radiation resistances on the acoustic wavenumber and the plate aspect ratio it is shown that the present formulae are extremely efficient by cutting the cpu time by orders of magnitude in comparison with the traditional numerical integration scheme this investigation successfully fills the long existing gap in solutions for the moderate wavenumbers that are often of primary concern in an acoustic analysis

the sensitivity of structural acoustic response to attachment feature scale representation this paper presents a technique to assess the impact on model fidelity introduced through discretization of attachments on harmonically forced fluid loaded structural acoustic models while fluid loading is included it is not a requirement or restriction to the methods presented the perspective taken is one of knowledge of a reference state with a desire to determine the impact on the total radiated acoustic power due to perturbations in the reference state such perturbations change the predicted resonance frequencies of a structure under consideration and hence change the predicted response amplitudes the method uses a single degree of freedom response model in the local region of each fluid loaded resonance coupled with eigenvalue sensitivities to estimate the perturbation impact the sensitivity of the eigenvalues to changes in model detail is derived based on variations in the spatial representation of attached features e g point versus distributed attachments elements of the analysis me

dynamic analysis of generally supported beams using fourier series the applicability of fourier series to the dynamic analysis of beams having arbitrary boundary conditions is explored for the simplicity of presenting the analysis procedure beams having zero end displacement are used in the discussion numerical results for free vibration and dynamic response based on the present analysis procedure are compared with existing results for natural frequencies and dynamic behavior obtained by the conventional modal analysis these results indicate that the present analysis is accurate and provides a unified and systematic procedure which is seemingly simpler and more straightforward than the conventional modal analysis

computing fluid coupled resonance frequencies mode shapes and damping loss factors using the singular value decomposition in many acoustic design problems it would be useful to be able to compute fluid coupled resonance frequencies mode shapes and their associated damping levels unfortunately conventional eigenvalue solution procedures are either computationally inefficient unreliable or have limited applicability sophisticated methods for identifying modal parameters using the singular value decomposition have recently emerged in the area of experimental modal analysis where the available data typically consists of velocity to force transfer functions for several drive point locations in this paper we show that these techniques can be applied to numerically generated frequency domain data and are even more effective because full matrices of transfer function data are available this typically allows the modes to be completely separated from each other such that the modal parameters can be identified using analytical formulas several benchmark example problems are solved numerically including a rectangular cantilever plate a baffled circular plate and a baffled circular plate covered by an open ended rigid walled pipe

acoustic eigenvalues of rectangular rooms with arbitrary wall impedances using the interval newton generalized bisection method modal analysis of a rectangular room requires evaluation of the eigenvalues of the helmholtz operator while taking into account the boundary conditions imposed on the walls of the room when the walls have finite impedances the acoustic eigenvalue equation becomes complicated and a numerical method that can find all roots within a given interval is required to solve it in this study the interval newton generalized bisection in gb method is adopted for solving this problem for an efficient implementation of this method bounds are derived for the acoustic eigenvalues and their asymptotic behavior explored the accuracy of the in gb method is verified for a canonical problem by comparing the modal solution with the corresponding finite element solution furthermore reverberation times estimated using the in gb method are compared to those calculated using the finite difference method through these examples it is demonstrated that the in gb method provides a useful and efficient approach for estimat