modified helmholtz integral equation for bodies sitting on an infinite plane this article presents a modified version of the helmholtz integral equation for bodies sitting on an infinite plane by using dummy integration elements on the bottom surface the coefficient c p of the helmholtz integral equation can be evaluated by a closed contour two different integral forms for c p are derived for p off the infinite plane and on the infinite plane respectively numerical results for radiation and scattering from bodies of several different shapes sitting on a rigid infinite plane are given to verify this formulation

a new acoustic interface element for fluid structure interaction problems a new comprehensive acoustic 2 d interface element capable of coupling the boundary element be and finite element fe discretizations has been formulated for fluid structure interaction problems the helmholtz equation governing the acoustic pressure in a fluid is discretized using the be method and coupled to the fe discretization of a vibrating structure that is in contact with the fluid since the be method naturally maps the infinite fluid domain into finite node points on the fluid structure interface the formulation is especially useful for problems where the fluid domain extends to infinity details of the be matrix computation process adapted to fe code architecture are included for easy incorporation of the interface element in fe codes the interface element has been used to solve a few simple fluid structure problems to demonstrate the validity of the formulation also the vibration response of a submerged cylindrical shell has been computed and compared with the results from an entirely finite element formulation

the effect of structural elasticity on the efficiency of noise barriers the efficiency of noise barriers is usually estimated neglecting their elastic behaviour in this paper the total vibro acoustical response of simple barriers is considered a variational approach with a boundary element technique is used it is a generalization of an existing formalism developed for the study of two dimensional acoustical problems the case of straight and thin barriers is studied it is found that at low frequencies their vibrations can modify their insertion losses by several decibels

numerical techniques for three dimensional steady state fluid structure interaction the application of a coupled finite element boundary integral approach to the analysis of vibrating elastic arbitrary shaped three dimensional structures in an infinite media is presented a feature of the methodologies implemented is the utilization of the isoparametric concept from finite element theory the same shape functions are used both to model the surface of the structure and to interpolate the acoustic variables over the radiating surface the boundary integral formulation used for the exterior acoustic field is a formulation that ensures uniqueness and existence of solutions for the entire frequency range an assessment of the accuracy was made after comparing the solutions attained for a vibrating submerged sphere for various excitation loads and frequencies with the exact solution

solution of fluid structure interaction problems using a coupled finite element and variational boundary element technique this work is concerned with the numerical modeling of elasto acoustic problems applied to thin shells and specifically curved plates a finite element formulation of the elastic problem is coupled to a variational boundary element solution of the acoustic problem this solution to the acoustic problem proposed by mariem and hamdi j b mariem and m a hamdi int j num methods eng 24 1251 1267 1987 is implemented using high order isoparametric elements and attention is given to techniques of accelerating the numerical implementation for solutions at multiple frequencies these techniques include a reduction in the problem size through the use of symmetry and more importantly the interpolation of the fluid impedance matrix within the frequency regime the advantages in using this variational formulation are first the manner in which a highly singular integral operator is made amenable to numerical approximation second its application to nonclosed thin shells and third its numerical im

a symmetric formulation of coupled bem fem in solving responses of submerged elastic structures for large degrees of freedom this work presents a symmetric formulation for the coupling of boundary element method bem with finite element method fem to compute responses of submerged elastic structures in a heavy acoustic medium the acoustic loading derived from bem is formulated in a symmetric complex matrix the symmetry of the acoustic loading matrix is proven by an acoustic reciprocal principle which relate two sets of arbitrary surface normal velocities and surface pressures in terms of surface integrals the structural equation is represented by fem the fact that the acoustic loading and the structural equation are symmetric allows us to take the storage and computational advantages of the banded matrix which has been widely used in conventional finite element methods consequently the computational efficiency of the proposed coupled fem bem is significantly increased the proposed method involving 20 000 degrees of freedom can be implemented on a personal computer numerical results are verified by analytical solutions of a constant thickness spherical shell subject to a point alternating force as well as the previously published variational solution of a constant thickness spheroidal shell excited by a concentrated force

about boundary values in a omega assume that c n is a balanced bounded domain with a holomorphic support function e g strictly pseudoconvex domain with c 2 boundary we denote f 2 z 1 0 f e 2 it z 2 dt let e 0 and be a circular invariant borel probability measure on if g a and h is a continuous function on with g h on then we construct nonconstant functions f 1 f 2 a with g f 1 z h z g f 2 z max 1 h z for z and additionally if is a circular bounded strictly convex domain with c 2 boundary then we give the construction of f 3 o the holomorphic function with h g f 3 z 0 for all z where f denotes the radial limit of f we also construct f 4 a with g f 4 z h z for z in all cases we can make f i arbitrarily small on a given compact subset f c and make it vanish to a given order at the point 0

coupled fe be method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain summary for thin elastic structures submerged in heavy fluid e g water a strong interaction between the structural domain and the fluid domain occurs and significantly alters the eigenfrequencies therefore the eigenanalysis of the fluid structure interaction system is necessary in this paper a coupled finite element and boundary element fe be method is developed for the numerical eigenanalysis of the fluid structure interaction problems the structure is modeled by the finite element method the compressibility of the fluid is taken into consideration and hence the helmholtz equation is employed as the governing equation and solved by the boundary element method bem the resulting nonlinear eigenvalue problem is converted into a small linear one by applying a contour integral method adequate modifications are suggested to improve the efficiency of the contour integral method and avoid missing the eigenvalues of interest the burton miller formulation is applied to tackle the fictitious eigenfrequency problem of the bem and the optimal choice of its coupling parameter is investigated for the coupled fe be method numerical examples are given and discussed to demonstrate the effectiveness and accuracy of the developed fe be method copyright 2016 john wiley sons ltd

efficient analytical integration of symmetric galerkin boundary integrals over curved elements thermal conduction formulation abstract substantial improvements are reported in the computational efficiency of galerkin boundary element analysis bea employing curved continuous boundary elements a direct analytical treatment of the singular double integrations involved in galerkin bea adapting a limit to the boundary concept used successfully in collocation bea is used to obviate significant computation in the determination of the galerkin coefficient matrices symbolic manipulation has been strategically employed to aid in the analytical evaluation of the singular contributions to these double integrals the analytical regularization procedure separates the potentially singular galerkin integrands into an essentially singular but simple part plus a regular remainder that can be integrated numerically the finite contribution from the simplified singular term is then computed analytically it is shown that the key to containing the explosive growth in the length of the formulae associated with such a hybrid analytical numerical integration scheme is the strategic timing of when to take the limit to the boundary this regularization also isolates the contribution from the curvature of the boundary element thus facilitating enhanced computational efficiency in problems with many straight elements example problems are presented to quantify the performance of this approach it is concluded that with these techniques galerkin symmetric bea can be more efficient than its collocation based counterpart

a boundary integral approach for acoustic radiation of axisymmetric bodies with arbitrary boundary conditions valid for all wave numbers a boundary integral method for solving the exterior acoustic radiation problem of axisymmetric bodies with arbitrary boundary conditions is developed the new formulation derives from the method proposed by burton and miller proc r soc london ser a 323 201 210 1971 which uses a linear combination of the helmholtz integral equation and its normal derivative to ensure the uniqueness of the numerical solution at all frequencies it is shown that the use of tangential operators enables one to easily compute the hypersingular integral without much extra effort by taking advantage of the properties of axisymmetric geometry and using the expansion of the boundary conditions and the surface distribution functions in fourier series with respect to the angle of revolution the surface integral is reduced to a line integral along the generator of the body and fourier integrals of the green s function and its derivatives over the circumferential angle the fourier integrals with singular kernels are eval

complex power reciprocity and radiation modes for submerged bodies this study of the surface interaction between a submerged body and the surrounding fluid begins by developing reciprocity relations between alternative pressure and normal velocity distributions on the wetted surface a corollary of these principles is proof of the symmetry of the matrix representing the acoustic contribution to the structural impedance even in situations where the acoustic relation between surface pressure and normal velocity is not symmetric the reciprocity properties lead to two eigenvalue problems whose solution yields velocity and pressure radiation modes each of which decouples the complex surface acoustic power the matrices required to obtain the eigensolutions are shown to arise in the ordinary course of modeling fluid structure interaction further analysis reveals that the velocity and pressure modes occur in a one to one correspondence with a relative phase angle that decreases monotonically as the radiated power increases relative to the reactive power using the radiati

acoustic radiations for submerged elastic structures using natural mode expansions in conjunction with radiation modes approach this work formulates submerged elastic structures using in vacuo vibrational mode expansions with which the acoustic impedance loading is derived based on radiation mode theory the displacement of natural modes on the normal direction is expanded as linear combinations of a set of velocity radiation modes that the expansion coefficients characterize as the radiation characteristics of each vibration mode this type of expansion allows one to represent the surface pressure by the corresponding set of pressure radiation modes thus a symmetric impedance matrix associated with the natural vibration mode expansions is derived when a variational increment is applied to the virtual work done by the surface pressure against the normal displacement the equation of the submerged structures is obtained according to hamilton s principles by incorporating the description of radiation modes this equation of natural mode expansions is used to study the coupling among vibration modal amplitudes due to the modal cross impedances and the convergence of near and farfield solutions in addition a slender submerged spheroidal shell vibrating axisymmetrically serves as a numerical example to demonstrate the effectiveness of the analysis procedure this numerical example reveals that the acoustic impedances decrease with ascending mode numbers causing the high order vibration modes to react independently moreover the convergence of the surface pressure and normal velocity is examined on the basis of independent reaction of the vibration modes accurately predicting farfield solutions depends only on the convergence of the surface quantities whose components pertain to strong radiation modes the numerical example indicates that the number of vibration modes used in the expansion for predicting farfield solutions is less than the modes required for the surface solution

a unified boundary element method for the analysis of sound and shell like structure interactions i formulation and verification a unified boundary element method bem is developed in this paper to model both the exterior acoustic field and the elastic shell like structure in a coupled analysis the conventional boundary integral equation bie for three dimensional 3d elastodynamics is applied to thin shell like structures which can have arbitrary shapes and small thicknesses the nearly singular integrals existing in the bie when applied to thin bodies are transformed to nonsingular line integrals and are evaluated accurately and efficiently for the exterior 3d acoustic domain the burton and miller composite bie formulation is employed to overcome the fictitious eigenfrequency difficulty fed and the thin shape breakdown tsb conforming c0 quadratic elements are employed in the discretization of the two sets of bies the developed bie formulations are valid for both radiation and scattering problems and for all wave numbers numerical examples using spherical and cylindrical shells including nonuniform thickness and nond

coupled finite element boundary element approach for fluid structure interaction a new computational capability is described for calculating the sound pressure field radiated or scattered by a harmonically excited submerged arbitrary three dimensional elastic structure this approach called nashua couples a nastranfinite element model of the structure with a boundary element model of the surrounding fluid the surface fluid pressures and normal velocities are first calculated by coupling the finite element model of the structure with a discretized form of the helmholtz surfaceintegral equation for the exterior fluid after generation of the fluid matrices most of the required matrix operations are performed using the general matrix manipulation package available in nastran farfield radiated pressures are then calculated from the surface solution using the helmholtz exterior integral equation the overall capability is very general highly automated and requires no independent specification of the fluid mesh an efficient new out of core block equation solver was written so that very large problems could be solved the use of nastran as the structural analyzer permits a variety of graphical displays of results including computer animation of the dynamic response the overall approach is illustrated and validated using known analytic solutions for submerged spherical shells subjected to both incident pressure and uniform and nonuniform applied mechanical loads

a high order discontinuous galerkin approach to the elasto acoustic problem abstract we address the spatial discretization of an evolution problem arising from the coupling of elastic and acoustic wave propagation phenomena by employing a discontinuous galerkin scheme on polygonal and polyhedral meshes the coupled nature of the problem is ascribed to suitable transmission conditions imposed at the interface between the solid elastic and fluid acoustic domains we state and prove a well posedness result for the strong formulation of the problem present a stability analysis for the semi discrete formulation and finally prove an a priori h p version error estimate for the resulting formulation in a suitable mesh dependent energy norm we also discuss the time integration scheme employed to obtain the fully discrete system the convergence results are validated by numerical experiments carried out in a two dimensional setting

a coupled fe and boundary integral equation method based on exterior domain decomposition for fluid structure interface problems abstract a coupled finite element and exterior domain decomposition based boundary integral formulations for the solutions of two or three dimensional time harmonic fluid structure interaction problems is described in this paper it is known that the memory limitation of computers has been one of the major obstacles for solving large scale high frequency fluid structure interface systems using various existing nonlocal finite element and boundary integral equation coupling techniques due to the fully populated resultant matrix generated from the boundary integral equation representation the essence of this study is to decompose through domain decomposition of the exterior region the original exterior problem into arbitrary subproblems with data sharing only at the interfaces by decomposing the exterior infinite domain into an appropriate number of infinite subdomains this method not only ensures the validity of the formulation for all frequencies but also leads to a diagonalized blockwise banded system of discretized equations the size of an individual submatrix i e a block that is associated with an exterior subdomain may be decided by the user and may be selected such that the restriction due to the memory limitation of a given computer may be accommodated in addition the method is suited for parallel processing since the data associated with each subdomain impedance matrices load vectors etc may be generated in parallel and the communication needed will be only for the interface values most significantly unlike the existing coupled finite element and boundary integral equation techniques that are valid for all frequencies our method avoids the use of both the hypersingular operator and the double integrals therefore reducing the computational complexity numerical experiments have been performed for elastic cylindrical shells subjected to a plane incident wave the results have demonstrated the accuracy of the method for wavenumbers ranging from 0 to 30 both directly on the shell and in the far field and have confirmed that the procedure is valid for all frequencies

a higher order on surface radiation condition derived from an analytic representation of a dirichlet to neumann map on surface radiation conditions are useful for obtaining approximate solutions to scattering problems involving compact obstacles an analytic representation of the dirichlet to neumann map for a circle is derived and used to construct a higher order on surface radiation condition for a generally convex perfectly conducting body in two dimensions this approach is based on a hankel function in which a tangential operator appears in the index in the high frequency limit this analytic representation approaches the square root of a differential operator which commonly arises in the application of parabolic equation techniques to propagation problems treating the scattered field propagation angle relative to the surface normal and the surface curvature as independent parameters the representation is fit to a rational function to provide an accurate and efficient on surface radiation condition that is tested for various examples

an infinite boundary element formulation for three dimensional potential problems an infinite boundary element ibe is presented for the analysis of three dimensional potential problems in an unbounded medium the ibe formulations are done to allow their coupling with the finite element fe matrices for finite domains and to obtain the overall matrices without destroying the banded structure of the fe matrices the infinite body is divided into a number of zones whose contributions are expressed in terms of the nodal quantities at fe nodes by employing suitable decay functions and performing mainly analytical integrations of the boundary element kernels the continuity and compatibility conditions for the potential and the flux at the fe ibe interface are developed the relationships for the contributions of the ibe flux vectors to the fe load vectors are given the final equations for the ibe are obtained in the usual fe stiffness load vector form and are easily assembled with the fe matrices for the finite object a series of numerical examples in heat transfer and electromagnetics were solved and compared with alternative solutions to demonstrate the validity of the present formulations

a new form of the hypersingular boundary integral equation for 3 d acoustics and its implementation with c0 boundary elements abstract an improved weakly singular form of the hypersingular boundary integral equation hbie for 3 d acoustic wave problems is presented in this paper compared with the weakly singular form of the hbie published earlier y j liu and f j rizzo a weakly singular form of the hypersingular boundary integral equation applied to 3 d acoustic wave problems comput methods appl mech engrg 96 1992 271 287 this new form involves only tangential derivatives of the density function and thus its discretization using the boundary element method bem is easier to perform instead of using nonconforming and c1 continuous boundary elements advocated earlier c0 continuous conforming quadratic elements are employed in the discretization of this weakly singular form of the hbie some justifications on using c0 elements for hbies are provided to reflect the current views on this crucial issue for hbies it is postulated that the original c1 continuity requirement for the density function in the analytical hbie formulation can be relaxed to piecewise c1 continuity in the numerical implementation of the weakly singular forms of the hbie numerical examples of both scattering and radiation problems clearly demonstrate the accuracy and versatility of the new weakly singular form of the hbie for 3 d acoustics

sound power radiation from a vibrating structure in terms of structure dependent radiation modes abstract as a good supplement of conventional acoustic radiation modes a modes a set of so called structure dependent radiation modes s modes is introduced to describe the sound power radiation from a vibrating structure differing from a modes s modes are determined by not only the acoustic resistance matrix of the structure but also the frequency independent normal modes of the structure such a new definition has the following main advantages over the conventional one 1 it can reflect directly the influences of dynamic properties e g boundary conditions of the structures on its sound power radiation 2 the number of s modes generated is generally less than that of a modes since the former depends on the number of structural modes involved in the vibration while the latter depends on the number of segmented elemental radiators of the structure and consequently the demand for large data storage can be greatly alleviated especially for large structures and or higher frequency vibrations 3 the set of s modes possesses a better convergence than that of a modes because the higher ordered s modes can decay more rapidly than the same ordered a modes two baffled finite models i e a simple beam and a thin plate are employed to investigate numerically the acoustic properties of s modes and then compared with those of a modes it has been shown that the two sets of radiation modes share a very similar frequency dependent behavior in that the radiation efficiency falls off very rapidly with increasing mode order at low frequency range typically with kl

symmetric galerkin boundary formulations employing curved elements accounts of the symmetric galerkin approach to boundary element analysis bea have recently been published this paper attempts to add to the understanding of this method by addressing a series of fundamental issues associated with its potential computational efficiency a new symmetric galerkin theoretical formulation for both the harmonic heat conduction and the biharmonic elasticity problem that employs regularized singular and hypersingular boundary integral equations bies is presented the novel use of regularized bies in the galerkin context is shown to allow straightforward incorporation of curved isoparametric elements a symmetric reusable intrinsic sample point risp numerical integration algorithm is shown to produce a galerkin i e double integration strategy that is competitive with its counterpart i e singular integration procedure in the collocation bea approach when the time saved in the symmetric equation solution phase is also taken into account this new formulation is shown to be capable of employing hypersingular bies while obviating the requirement of c 1 continuity a fact that allows the employment of the popular continuous element technology the behavior of the symmetric galerkin bea method with regard to both direct and iterative equation solution operations is also addressed a series of example problems are presented to quantify the performance of this symmetric approach relative to the more conventional unsymmetric bea in terms of both accuracy and efficiency it is concluded that appropriate implementations of the symmetric galerkin approach to bea indeed have the potential to be competitive with if not superior to collocation based bea for large scale problems

causality and model abstraction abstract much of science and engineering is concerned with characterizing processes by equations describing the relations that hold among parameters of objects and govern their behavior over time in formal descriptions of processes in terms of parameters and equations the notion of causality is rarely made explicit formal treatments of the foundations of sciences have avoided discussions of causation and spoken only of functional relations among variables nevertheless the notion of causality plays an important role in our understanding of phenomena even when we describe the behavior of a system formally in terms of acausal mathematical relations we often give an informal intuitive explanation of why the system behaves the way it does in terms of cause effect relations in this paper we will present an operational definition of causal ordering the definition allows us to extract causal dependency relations among variables implicit in a model of a system when a model is represented as a set of acausal mathematical relations our approach is based on the theory of causal ordering first presented by simon 22 the paper shows how to use the theory and its extension in reasoning about physical systems further the paper studies the relation of the theory to the problems of model aggregation

on dowell s simplification for acoustic cavity structure interaction and consistent alternatives a widely employed description of the acoustical response in a cavity whose walls are compliant which was first proposed by dowell and voss 1962 aiaa j 1 476 477 uses the modes of the corresponding cavity with rigid walls as basis functions for a series representation of the pressure it yields a velocity field that is not compatible with the movement of the boundary and the system equations do not satisfy the principle of reciprocity the simplified formulation is compared to consistent solutions of the coupled field equations in the time and frequency domains in addition this paper introduces an extension of the ritz series method to fluid structure coupled systems that satisfies all continuity conditions by imposing constraint equations to enforce any such conditions that are not identically satisfied by the series a slender waveguide terminated by an oscillator is analyzed by each method the simplified formulation is found to be very accurate for light fluid loading except for the pressure field at frequencies below the fundamental rigid cavity resonance whereas the ritz series solution is found to be extremely accurate in all cases

stability assessment of a unified variational boundary integral method applicable to thin scatterers and scatterers with corners abstract the objective of this study is to assess the stability especially at and near critical frequencies of a new unified stable symmetric domain finite element and boundary integral methodology for solving time harmonic interface problems for scatterers of arbitrary shape the validity of this energy based variational procedure for rigid and penetrable smooth scatterers including the existence uniqueness and optimal convergence of the corresponding numerical approximations has been proved rigorously in the context of fluid structure interaction problems the emphasis here is on investigating the applicability of this procedure to the case of scatterers with corners using square and thin rectangular two dimensional rigid obstacles as prototypes we also establish that the apparently distinct direct boundary integral formulation due to burton and miller and the combined single and double layer indirect formulation due to leis brakhage and werner and panich introduced to insure that boundary integral equations for scattering problems are uniquely solvable for all wavenumbers are entirely equivalent within our variational setting by examining the condition number of the matrix of coefficients of the discretized equations as well as the resulting solutions both directly on the surface of the scatterers and in the far field it is demonstrated that the new methodology is robust and completely insensitive to critical frequencies even for thin objects most significantly the precise singular behaviour of the pressure field at corners is also predicted quite accurately by using standard finite elements along the boundary of the scatterer without having to introduce special singularity functions which for general interface problems may not be known in advance

a construction of inner functions on the unit ball in c p in their recent paper 1 hakim and sibony came very close to constructing inner functions on the unit ball in c e in fact only some minor modifications of their arguments are necessary to produce bona fide inner functions the present paper carries out these modifications since we need to point out some information not explicitly stated but clear from the context in their paper and to make the exposition self contained we repeat most of the material in their paper our lemma 1 for instance is identical to their lemma 3 and our application of lemma 1 in the proof of lemma 2 is the same as theirs in the proof of theorem 1 the following notations are used b is the unit ball in c p br z cp izl r we use the distance

responses of partially immersed elastic structures using a symmetric formulation for coupled boundary element and finite element methods using a coupled bem fem this work describes a numerical method to compute the response and acoustic radiation for structures partially immersed in fluid the structures and their responses are assumed to be symmetric about a symmetric plane a symmetric complex matrix derived from the bem and a reciprocal principle for surface acoustics is also used to represent the acoustic loading against the structures in addition selecting a proper green s function based on image source method satisfies the boundary conditions of pressure release on the fluid surface and null normal velocity on the symmetric plane moreover a boundary integral equation emerges when the field point approaches the structural surface where the normal derivative of the green s function over partial infinitesimal spheres is evaluated these limiting values depend on locations of the field point on the surface owing to the symmetry of the acoustic loading matrix the matrix for the coupled bem fem is a banded symmetric one thereby allowing us to employ a variable banded storage method and invert of the matrix doing so markedly increases computational efficiency furthermore an analytical solution of a spherical thin shell with the lower semi sphere immersed in water is carried out by characteristic function expansions for shell equation and acoustic loading these analytical solutions compare with the results obtained from the proposed numerical method a good correlation for low frequencies is obtained and minor discrepancies are observed with an increasing frequency

fluid solid interaction acoustic scattering by a smooth elastic obstacle a bounded three dimensional elastic obstacle is surrounded by an unbounded inviscid compressible fluid acoustic waves are scattered by the obstacle the problem is to find the scattered waves and the response of the obstacle this problem is formulated mathematically existence and uniqueness theorems are proved various systems of boundary integral equations over the interface between the fluid and the solid are derived and analysed these systems include a system obtained by a straightforward direct method and a smaller system for a single vector field

a method to compute the radiated sound power based on mapped acoustic radiation modes application of modal expansion approach for the exterior acoustic field has drawn wide research interests in recent years this is primarily due to the acoustic radiation modes arm that can diagonalize the impedance matrix hence significantly simplifying the computation of radiated sound power the orthogonal arm are typically calculated via a standard eigenvalue analysis of the impedance matrix which normally leads to numerical difficulties especially for wideband frequency and large scale problems in this paper a theory of mapped arm is proposed to avoid the cumbersome computation of arm for convex structures a mapping relationship between the arm on the surface of an equivalent spherical source and the mapped arm on the surface of a convex structure is obtained based on the equivalent source method multipole expansion method and boundary integral method furthermore analytical expressions for the radiated sound power of structures vibrating in its mapped arm as well as that of spheres are derived finally a simple method is proposed to approximate the radiated sound power based on the modal decomposition method and the mapping relationship numerical simulations are conducted to validate the accuracy and efficiency of the proposed approach and different vibrating structures with various geometries are considered results demonstrate that the proposed methodology for calculating the radiated sound power of convex structures is very efficient and accurate as compared with the traditional approach

a peak set of hausdorff dimension 2n 1 for the algebra a in the boundary of a domain with c boundary in c ⁿ

an acoustic boundary integral formulation for open shells allowing different impedance conditions top and bottom surfaces abstract in the automotive aerospace industries as well as the underwater acoustics defense applications the addition of coatings to modify the response of the vibrating structure is commonplace the formulation developed is an extension of the existing thin body formulation currently found in commercial noise prediction codes such as sysnoise in order to allow problems requiring different boundary condition on both sides of the thin shell to be solved for instance a generalised thin body acoustic formulation would allow for a local impedance boundary condition to be specified on the top surface and a hard neumann boundary condition to be specified on the bottom surface such a formulation would allow for different local impedance coatings to be specified on the top and bottom surfaces due to the lack of analytical solutions for such problems even for the simplest geometries it is difficult to validate such a formulation however three test cases are presented two flat plate examples and a open cylinder with a point monopole source excitation at its centre

implementation of a constrained ritz series modeling technique for acoustic cavity structural systems a prior study ginsberg j h 2010b j acoust soc am 127 2749 2758 used ritz series in conjunction with hamilton s principle to derive general equations describing the time domain response of an acoustic cavity bounded by an elastic structure the equations of motion are supplemented by constraint equations that explicitly enforce velocity continuity at the cavity s surface these constraints are imposed by the surface traction which is represented by unknown coefficients of ritz type series the resulting set of equations are differential algebraic type three methods are presented to convert the governing equations to forms that are familiar to structural acoustics including one that transforms them from differential algebraic type to the standard ordinary differential equations associated with linear multi degree of freedom vibratory systems in cases where only the structure is excited the formulation offers options as to how displacement velocity boundary conditions on the nonstructural b

solving the hypersingular boundary integral equation in three dimensional acoustics using a regularization relationship regularization of the hypersingular integral in the normal derivative of the conventional helmholtz integral equation through a double surface integral method or regularization relationship has been studied by introducing the new concept of discretized operator matrix evaluation of the double surface integrals is reduced to calculate the product of two discretized operator matrices such a treatment greatly improves the computational efficiency as the number of frequencies to be computed increases the computational cost of solving the composite helmholtz integral equation is comparable to that of solving the conventional helmholtz integral equation in this paper the detailed formulation of the proposed regularization method is presented the computational efficiency and accuracy of the regularization method are demonstrated for a general class of acoustic radiation and scattering problems the radiation of a pulsating sphere an oscillating sphere and a rigid sphere insonified by a plane acoustic wave are solved using the new method with curvilinear quadrilateral isoparametric elements it is found that the numerical results rapidly converge to the corresponding analytical solutions as finer meshes are applied

acoustic scattering by a hard or soft body across a wide frequency range by the helmholtz integral equation method in this paper the acoustic scattering by an obstacle across a wide frequency range of sound waves is investigated on the basis of the helmholtz integral formulation to overcome the nonuniqueness difficulties the methods proposed by burton npl report nac 30 jan 1973 and by burton and miller proc r soc london ser a 323 201 210 1971 are adopted for the dirichlet and neumann problems respectively the aim of this paper is twofold the first is to bring together completely regular formulations of the helmholtz integral equation and its normal derivative the second is to extend these formulations to treat the higher frequency problems the weakly singular integrals are regularized by subtracting out one term and adding it back depending on the problem concerned the additional integral can finally be expressed in an explicit form or results in solving a surface source distribution of the equipotential body the hypersingular kernels are regularized by the method of using some properties of the associated laplace equation originally proposed by chien et al j acoust soc am 88 918 937 1990 the completely regularized integral equations are amenable to computation by direct use of the standard quadrature methods to study the acoustic scattering due to higher frequency waves filon s quadrature method proc r soc edinburgh 49 38 47 1928 is extended to treat the rapidly oscillatory integrands numerical examples consist of acoustic scattering from a hard or soft sphere of radius a across a wide spectrum of wave numbers ka 20 comparisons of the numerical results with the exact solutions demonstrate the validity and efficiency of the implementation

a boundary integral equation method for two dimensional acoustic scattering problems this work formulates the singularity free integral equations to study 2 d acoustic scattering problems to avert the nonuniqueness difficulties burton s and burton and miller s methods are employed to solve the dirichlet and neumann problems respectively the surface helmholtz integral equations and their normal derivative equations in bounded form are derived the weakly singular integrals are desingularized by subtracting a term from the integrand and adding it back with an exact value depending on the relevant problem the additional integral can finally be either expressed in an explicit form or transformed to form a surface source distribution of the related equipotential body the hypersingular kernel is desingularized further using some properties of an interior laplace problem the new formulations are advantageous in that they can be computed by directly using standard quadrature formulas also discussed is the contour a unique feature of 2 d problems instead of dividing the boundary surface into several small elements a parametric representation of a 2 d boundary curve is further proposed to facilitate a global numerical implementation calculations consist of acoustic scattering by a hard and a soft circular cylinder respectively comparing the numerical results with the exact solutions demonstrates the proposed method s effectiveness

response to comments on on dowell s simplification for acoustic cavity structure interaction and consistent alternatives j acoust soc am 127 22 32 2010 dowell j acoust soc am 128 1 2 2010 commented on several aspects of an approximation commonly invoked to model the coupling of an acoustic cavity and a surrounding structure additional observations regarding these issues are provided herein as well as an explanation of discrepancies in the low frequency pressure predicted by the approximation

carleson sobolev measures for weighted bloch spaces abstract carleson sobolev measures for weighted bloch spaces on the unit ball of c n are described the classical carleson measures for growth spaces on special circular domains are characterized

impulse response functions based on a causal approach to residual orthogonalization in vector autoregressions abstract a data determined method for testing structural models of the errors in vector autoregressions is discussed the method can easily be combined with prior economic knowledge and a subjective analysis of data characteristics to yield valuable information concerning model selection and specification in one dimension it turns out that standard t statistics can be used to test the various overidentifying restrictions that are implied by a model in another dimension the method compares a priori knowledge of a structural model for the errors with the properties exhibited by the data thus this method may help to ensure that orderings of the errors for impulse response and forecast error variance decomposition analyses are sensible given the data two economic examples are used to illustrate the method

solving the hypersingular boundary integral equation for the burton and miller formulation this paper presents an easy numerical implementation of the burton and miller bm formulation where the hypersingular helmholtz integral is regularized by identities from the associated laplace equation and thus needing only the evaluation of weakly singular integrals the helmholtz equation and its normal derivative are combined directly with combinations at edge or corner collocation nodes not used when the surface is not smooth the hypersingular operators arising in this process are regularized and then evaluated by an indirect procedure based on discretized versions of the calderon identities linking the integral operators for associated laplace problems the method is valid for acoustic radiation and scattering problems involving arbitrarily shaped three dimensional bodies unlike other approaches using direct evaluation of hypersingular integrals collocation points still coincide with mesh nodes as is usual when using conforming elements using higher order shape functions with the boundary element method model size kept fixed reduces the overall numerical integration effort while increasing the solution accuracy to reduce the condition number of the resulting bm formulation at low frequencies a regularized version ik k2 of the classical bm coupling factor i k is proposed comparisons with the combined helmholtz integral equation formulation method of schenck are made for four example configurations two of them featuring non smooth surfaces

hypersingular boundary integral equations for exterior acoustic problems a bounded form of the hypersingular helmholtz integral equation for 3 d acoustic problems is developed in this paper all integrals with singular kernels are regularized within each regular surface element in the sense of kellogg with twice continuous differentiability the standard gaussian quadrature formula is applied without any special treatment for all the computational points the collocation points are chosen to be the gauss legendre nodes and no interpolation function is assumed for acoustic variables

complete proper holomorphic embeddings of strictly pseudoconvex domains into balls abstract we construct a complete proper holomorphic embedding from any strictly pseudoconvex domain with c 2 boundary in c n into the unit ball of c n for n large enough thereby answering a question of alarcon and forstneric 2013

long time behavior of a coupled heat wave system arising in fluid structure interaction this paper is devoted to the analysis of the long time behavior of a coupled wave heat system in which a wave and a heat equation evolve in two bounded domains with natural transmission conditions at a common interface these conditions couple in particular the heat unknown with the velocity of the wave solution this model may be viewed as a simplified version of linearized models which arise in fluid structure interaction first we show the strong asymptotic stability of solutions to this system then based on the construction of ray like solutions by means of geometric optics expansions and a careful analysis of the transfer of energy at the interface we show the lack of uniform decay in general domains further we obtain a polynomial decay result for smooth solutions of the system under a suitable geometric assumption which guarantees that the heat domain envelopes the wave domain finally in the absence of geometric conditions we show a logarithmic decay result for the same system but with simplified transmission conditions at the interface we also analyze the difficulty there is to extend this result to the more natural transmission conditions

causal ordering comparative statics and near decomposability abstract the notion of causal ordering has been explicated for systems in the form of sets of linear algebraic equations and also for dynamic models consisting of linear differential equations since we often wish to aggregate or disaggregate models of systems or to consider the static equilibrium of a dynamic model the question arises as to how these transformations from one model of a system to another affect the causal ordering of variables the present paper provides some answers to this question

an accurate and efficient scheme for acoustic structure interaction problems based on unstructured mesh abstract this paper focuses on the accurate and efficient numerical implementation of acoustic structure coupling formulations using the edge based smoothed finite element method for the flexible shell and the gradient weighted finite element method for the acoustic fluid field namely the es gw fem the shell is discretized using the simplest linear triangular elements and the edge based smoothing domain is then constructed by introducing an edge local coordinate system the edge based smoothing operation is performed on the smoothing domain as for the acoustic fluid domain the tetrahedron elements are adopted a compacted support domain is then constructed and the gradient weighted operation is performed on the support domain to model the exterior acoustic domain an artificial boundary is introduced and the dirichlet to neumann dtn boundary condition is imposed based on the appropriate compatibility and equilibrium conditions on the interface boundaries the coupled es gw fem formulation is finally obtained both the interior acoustic structure coupled problems and exterior acoustic structure coupled problems are available as the dtn boundary is considered numerical examples demonstrate that the coupled es gw fem achieves much higher accuracy and works more reliably compared with the coupled fem fem in solving practical engineering problems

a unique coupled boundary element finite element method for the elastoacoustic analysis of fluid filled thin shells a coupled boundary element finite element technique originally developed for the analysis of open thin shell problems such as propeller blades is used in this paper for the analysis of the fluid filled elastic structures for open thin shell problems the question of nonuniqueness does not arise however it was thought at the time that such a formulation would prove to be nonunique for the analysis of closed fluid filled submerged bodies the work presented in this paper will demonstrate that for submerged fluid filled closed elastic bodies this coupled formulation is unique throughout the entire frequency range an advantage in implementing the variational form of the acoustic integral operator is that the resulting fluid matrix is symmetric as such the fluid structural coupling is simplified and the computational efficiency enhanced

higher radial derivative of functions of qp spaces and its applications in this paper we give some characterizations of the integral and carleson type measure both associated with higher radial derivative for holomorphic functions of q p 0 and q p spaces in the unit ball of c n as applications some sharp forms of the relations between dirichlet type spaces and q p 0 spaces are shown by means of higher radial derivative carleson type measure and constructive methods for the cases of determinism and randomization respectively

efficient analytical integration of symmetric galerkin boundary integrals over curved elements elasticity formulation abstract substantial improvements are reported in the computational efficiency of galerkin boundary element analysis bea 1employing curved continuous boundary elements for elasticity problems a direct analytical treatment of the singular and hypersingular double integrations employing a limit to the boundary definition is adapted to gain computational economy symbolic manipulation has been employed to derive the analytical expressions for the singular contributions to these double integrals the analytical regularization procedure separates the potentially singular galerkin integrands into an essentially singular but simple part plus a regular remainder that can be integrated numerically the exact finite contributions from the simplified singular terms are then computed analytically it is shown that the key to containing the explosive growth in the length of the formulae associated with such a hybrid analytical numerical integration scheme is the strategic timing of when to take the limit to the boundary this regularization also isolates the contribution from the curvature of the boundary element thus facilitating enhanced computational efficiency in problems with many straight elements although the evaluation of the integrals of the kelvin fundamental solution essentially follows the procedures described earlier for the scalar laplace equation the analytical treatment is now more involved in terms of the complexity and number of terms present in each of these second rank tensor kernel functions the complete analytical formulation is explicitly provided in a series of tables example problems indicate that with these techniques galerkin symmetric bea can be more efficient than collocation for moderate or large scale problems

reverse estimates in growth spaces let h b d denote the space of holomorphic functions on the unit ball b d of mathbb c d given a radial doubling weight w we construct functions f g in h b 1 such that f g is comparable to w also we obtain similar results for b d d 2 and for circular strictly convex domains with smooth boundary as an application we study weighted composition operators and related integral operators on growth spaces of holomorphic functions

spaces m dp bnp and qp abstract in this paper the relations between d p and b n p m d p and b n p are discussed by means of high order radial derivative and random series the main results of this paper are 1 let i if 0 b n q d p ii if n p 2 q b n q and d p cannot included each other iii if q 3n p 2 then d p b n q 2 let 0 i if 0 b n q m d p ii if n p 2 q b n q and m d p cannot included each other iii if q 3n p 2 then m d p b n q 3 let n 1 n m d n 1 p q p

a coupling of multi zone curved galerkin bem with finite elements for independently modelled sub domains with non matching nodes in elasticity when the different parts of a structure are modelled independently by bem or fem methods it is sometimes necessary to put the parts together without remeshing of the nodes along the part interfaces frequently the nodes do not match along the interface in this work the symmetric galerkin multi zone curved boundary element is a fully symmetric formulation and is the method used for the boundary element part for bem fem coupling it is then necessary to interpolate the tractions in between the non matching nodes for the fem part finally the coupling is achieved by transforming the finite element domains to equivalent boundary element domains in a block symmetric formulation this system is then coupled with a boundary element domain with non matching nodes in between copyright 2004 john wiley sons ltd

on uniformly bounded bases in spaces of holomorphic functions the main result of the paper is the construction of explicit uniformly bounded bases in the spaces of complex homogenous polynomials on the unit ball of c 3 extending an earlier result of the author in the c 2 case

a boundary integral method for acoustic radiation and scattering in this article a computational method is proposed for computing the helmholtz integral equation for acoustic radiation and scattering problems with a three dimensional body shape unlike the previous boundary element method the integration of acoustic properties is based on the global body surface instead of local elements the approximation function of body geometry and the weighting function of numerical integration are independently chosen when the singular kernels of helmholtz equation are regularized as bounded discontinuous functions the order of integration polynomials for acoustic properties can be arbitrarily chosen therefore the accuracy and efficiency of computation can be increased