wave number based assessment of the doubly asymptotic approximation i frequency domain wet surface impedance the doubly asymptotic approximation daa is a canonical relationship for the interaction between surface normal velocity and pressure its validity for a slender hemicapped cylinder is examined by formulating a frequency domain version of daa using the global basis functions employed in the wave number based formulation of the surface variational principle k wu and j h ginsberg asme j vib acoust 120 392 400 1998 the wet surface impedance matrix which relates the spectral representation of normal velocity to a corresponding representation of pressure is obtained according to a second order version of daa and according to the surface variational principle comparison and interpretation of the results reveals that daa fails to account for highlights associated with transition from supersonic to subsonic surface waves as the surface wavelength decreases with frequency held constant

calculation of acoustic radiation using equivalent sphere methods among the methods generally used to solve a problem in the domain of acoustic radiation the equivalent sources method offers an interesting alternative it consists in replacing the vibrating surface with a distribution of acoustic sources placed inside the structure the contribution of each source is determined in such a way that the acoustic field radiated by these sources verifies the same boundary conditions on the structure the number of unknowns in the problem is no longer directly linked to the number of mesh points on the structure as with boundary elements methods but to the number of equivalent sources employed in the model the equivalent source method is therefore of major interest if the acoustic radiation of the structure can be approximated with a sufficiently low number of sources this paper proposes its application when the equivalent source is a sphere in this case the number of unknowns is equal to the number of modes in contrast to the one point multipole the sphere has a surface surrounding a closed volume to express the boundary conditions although sphere multipole equivalence has been demonstrated the surface of the sphere allows normalization of the functions used leading to stabilization of the system to be resolved first the main acoustic radiation characteristics of a sphere and of the linear system verified by the modal coefficients of an equivalent sphere are presented the different parameters of the model are then studied position and radius of the equivalent sphere truncation of the series and influence of the spatial sampling mesh in the same vein a second approach is presented it consists of making each point of the structure correspond to a point of the sphere and the vibrating field at the surface of the sphere is deduced from that of the structure by simple geometric projection results can be obtained very quickly as no matrix inversion is required the accuracy of the results depends on the distance between the sphere and the structure finally an experimental validation that uses both methods is presented and shows interesting results when the structure is closed and when its shape is not too far removed from a sphere

doubly asymptotic approximations for transient poroelastodynamics a doubly asymptotic approximation daa is an approximate temporal impedance relation at the boundary of a continuous medium here first and second order daas are formulated for an infinite external poroelastic medium described by biot s equations as with their acoustic elastodynamic and electromagnetic predecessors the poroelastodynamic daas approach exactness in both the early time high frequency and late time low frequency limits effecting a smooth transition between they also lend themselves to straightforward boundary element discretization producing matrix ordinary differential equations in time that are readily solved by numerical integration an initial examination of poroelastodynamic daa accuracy is presented for two problems with spherical symmetry

a comparison of numerical collocation and variational procedures to the hypersingular acoustic integral operator abstract a major difficulty in implementing many of the more innovative acoustic formulations for the solution of submerged three dimensional thin shells of arbitrary geometry in an unbounded fluid medium has been the difficulty of numerically approximating a hypersingular integral operator a variational approach given by hamdi reduces this hypersingularity cauchy singularity to a weak singularity allowing for its accurate numerical approximation recently mariem and hamdi a new boundary finite element method for fluid structure interaction internat j numer methods engrg 24 1987 1251 1267 presented an acoustic formulation for thin shells where the pressure difference across the shell is related to the shell s normal velocity solely in terms of this integral operator despite its advantage of generating a symmetric fluid matrix a double surface integration is required to form this matrix some researchers have endeavoured to develop a collocation method of approximating this highly singular operator in this paper a novel solution to the numerical approximation of this operator is given in the implementation of both the variational and collocation methodologies quadratic quadrilateral elements are used to interpolate for the acoustic and geometric variables results are then presented for thin shell scattering and radiation problems for both closed and non closed thin shells demonstrating the validity and accuracy of both methods

frequency measures on time scales with applications the concept of frequency measures of subsets of a time scale is introduced and the relevant properties are discussed then frequent oscillation is defined to strengthen the classical concept of oscillation applications are shown by deriving oscillation criteria for first order dynamic equations on time scales

acoustic coupled fluid structure interactions using a unified fast multipole boundary element method this paper presents a numerical model for the acoustic coupled fluid structure interaction fsi of a submerged finite elastic body using the fast multipole boundary element method fmbem the helmholtz and elastodynamic boundary integral equations bies are respectively employed to model the exterior fluid and interior solid domains and the pressure and displacement unknowns are coupled between conforming meshes at the shared boundary interface to achieve the acoustic fsi the low frequency fmbem is applied to both bies to reduce the algorithmic complexity of the iterative solution from o n2 to o n1 5 operations per matrix vector product for n boundary unknowns numerical examples are presented to demonstrate the algorithmic and memory complexity of the method which are shown to be in good agreement with the theoretical estimates while the solution accuracy is comparable to that achieved by a conventional finite element boundary element fsi model

time domain analysis of transient structural acoustics problems based on the finite element method and a novel absorbing boundary element this paper is concerned with the development of an efficient and accurate finite element procedure for the solution directly in the time domain of transient problems involving structures submerged in an infinite acoustic fluid the central feature of the procedure is a novel impedance or absorbing boundary element that is used to render the computational domain finite this element is local in both time and space and is completely defined by a pair of symmetric stiffness and damping matrices it thus can be attached directly to the adjoining fluid elements within the computational domain using standard assembly procedures due to its local nature it also preserves the overall structure of the global equations of motion including symmetry and sparseness thus the new impedance element makes it possible to solve complex transient exterior structural acoustics problems via existing finite element software for interior problems by just incorporating this element into current finite element libraries st

new kamenev type oscillation criteria for second order nonlinear advanced dynamic equations this paper presents a new kamenev type oscillation criterion for a second order advanced dynamic equation on a time scale two examples are included to show that the result obtained complements and improves those reported in the literature

oscillation criteria for a class of second order emden fowler delay dynamic equations on time scales abstract by means of riccati transformation technique we establish some new oscillation criteria for the second order emden fowler delay dynamic equations x t p t x t 0 on a time scale t here is a quotient of odd positive integers with p t real valued positive rd continuous functions defined on t to the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales our results in this paper not only extend the results given in r p agarwal m bohner s h saker oscillation of second order delay dynamic equations can appl math q 13 1 2005 1 18 but also unify the oscillation of the second order emden fowler delay differential equation and the second order emden fowler delay difference equation

on inequalities of lyapunov for linear hamiltonian systems on time scales in this paper we establish several new lyapunov type inequalities for linear hamiltonian systems on an arbitrary time scale t when the end points are not necessarily usual zeroes but rather generalized zeroes which generalize and improve all related existing ones including the continuous and discrete cases

existence of nonoscillatory solutions to neutral dynamic equations on time scales abstract in this paper we give an analogue of the arzela ascoli theorem on time scales then we establish the existence of nonoscillatory solutions to the neutral dynamic equation x t p t x g t f t x h t 0 on a time scale to dwell upon the importance of our results three interesting examples are also included

doubly asymptotic approximations for vibration analysis of submerged structures doubly asymptotic approximations daa s are differential equations for boundary element analysis of the dynamic interaction between a complex structure and a surrounding infinite medium t l geers j acoust soc am 64 1500 1508 1978 p g underwood and t l geers int j solids struct 17 687 697 1981 in this paper the use of first and second order daa s for vibration analysis of submerged structures is examined first the governing discrete element equations for the general problem are set down and discussed then the accuracy of three daa forms is studied through the generation of numerical results for a submerged spherical shell although the first order daa is found to be inadequate the two second order forms show considerable promise work supported by the david w taylor naval ship r d center

fast bem fem mortar coupling for acoustic structure interaction a coupling algorithm based on lagrange multipliers is proposed for the simulation of structure acoustic field interaction finite plate elements are coupled to a galerkin boundary element formulation of the acoustic domain the interface pressure is interpolated as a lagrange multiplier thus allowing the coupling of non matching grids the resulting saddle point problem is solved by an approximate uzawa type scheme in which the matrix vector products of the boundary element operators are evaluated efficiently by the fast multipole boundary element method the algorithm is demonstrated on the example of a cavity backed elastic panel

a new bem fem coupling strategy for two dimensional fluid solid interaction problems we present a numerical method to solve a fluid solid interaction problem posed in the plane in this scheme we use a finite element method to approximate the solid vibrations and the near wave field the far field effects are taken into account by means of boundary integral equations posed on an artificial interface that contains the obstacle the boundary unknown involved in our formulation is approximated by a spectral method we obtain a fully discrete galerkin procedure whose main advantage is the simplicity of the quadratures used to approximate the weakly singular boundary integrals we provide numerical results that illustrate the accuracy of our method and the stability of the algorithm used to solve the linear systems of equations that arise from this discretization technique

precorrected fft accelerated bem for large scale transient elastodynamic analysis using frequency domain approach summary a precorrected fast fourier transform pfft accelerated boundary element method bem for large scale transient elastodynamic analysis is developed and described in this paper the frequency domain approach is used to overcome the wrap around problem associated with the discrete fourier transform the exponential window method ewm is employed and incorporated in the frequency domain bem an improved implementation scheme of the pfft method based on polynomial interpolation technique is developed and applied to accelerate the elastodynamic bem this new scheme reduces the memory required to save the convolution matrix by a factor of 8 to further improve the efficiency of the code a newly developed linear system solver based on the induced dimension reduction method is employed its performance is investigated and compared with that of the well known gmres the accuracy and computational efficiency of the method are evaluated and demonstrated by three examples a classical benchmark a plate subject to an impact loading and a porous cube with nearly half million dofs subject to a step traction loading both analytical and experimental results are employed to validate the method it has been found that the ewm can effectively resolve the wrap around problem and accurate time responses for an arbitrarily chosen time period can be obtained copyright 2011 john wiley sons ltd

multilevel fast multipole algorithm for elastic wave scattering by large three dimensional objects multilevel fast multipole algorithm mlfma is developed for solving elastic wave scattering by large three dimensional 3d objects since the governing set of boundary integral equations bie for the problem includes both compressional and shear waves with different wave numbers in one medium the double tree structure for each medium is used in the mlfma implementation when both the object and surrounding media are elastic four wave numbers in total and thus four fma trees are involved we employ nystrom method to discretize the bie and generate the corresponding matrix equation the mlfma is used to accelerate the solution process by reducing the complexity of matrix vector product from o n 2 to o nlogn in iterative solvers the multiple tree structure differs from the single tree frame in electromagnetics em and acoustics and greatly complicates the mlfma implementation due to the different definitions for well separated groups in different fma trees our nystrom method has made use of the cancellation of leading terms in the series expansion of integral kernels to handle hyper singularities in near terms this feature is kept in the mlfma by seeking the common near patches in different fma trees and treating the involved near terms synergistically due to the high cost of the multiple tree structure our numerical examples show that we can only solve the elastic wave scattering problems with 0 3 0 4 millions of unknowns on our dell precision 690 workstation using one core

the bergman kernel function and proper holomorphic mappings it is proved that a proper holomorphic mapping f between bounded complete reinhardt domains extends holomorphically past the boundary and that if in addition f 1 0 01 then f is a polynomial mapping the proof is accomplished via a transformation rule for the bergman kernel function under proper holomorphic mappings

solution of discontinuous interior helmholtz problems by the boundary and shell element method the helmholtz equation governing an interior domain with shell discontinuities is not efficiently solvable by the traditional boundary element method in this paper it is shown how the helmholtz equation can be recast as an integral equation known as the boundary and shell integral equation the application of collocation to the integral equation gives rise to a method termed the boundary and shell element method the associated problem of finding the eigenvalues and eigenfunctions of the helmholtz equation in a discontinuous domain via the same method is also considered this leads to a non linear eigenvalue problem such a problem may be solved through polynomial interpolation of the matrix components in this paper methods for solving the helmholtz equation and the associated eigenvalue problem are implemented and applied to a test problem

oscillation of second order damped dynamic equations on time scales abstract the study of dynamic equations on time scales has been created in order to unify the study of differential and difference equations the general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so called time scale which may be an arbitrary closed subset of the reals this way results not only related to the set of real numbers or set of integers but those pertaining to more general time scales are obtained in this paper by employing the riccati transformation technique we will establish some oscillation criteria for second order linear and nonlinear dynamic equations with damping terms on a time scale t our results in the special case when t r and t n extend and improve some well known oscillation results for second order linear and nonlinear differential and difference equations and are essentially new on the time scales t h n h 0 t q n for q 1 t n 2 etc some examples are considered to illustrate our main results

transient spheroidal elements for unbounded wave problems a wave envelope element numerical scheme is applied to the solution of unbounded wave problems the scheme is based on a fourier transformation of a discrete model formulated in the frequency domain this yields a discrete system of ordinary differential equations in time which are local in space oblate and prolate spheroidal element geometries are used the accuracy of the scheme is demonstrated by a comparison of computed and analytic solutions for axisymmetric test cases time harmonic and transient solution are presented an indirect solution procedure is also presented which permits the sparsity of the transient equations to be utilised more effectively

oscillation criteria for second order nonlinear neutral variable delay dynamic equations abstract this paper is concerned with oscillation of second order nonlinear neutral dynamic equations on time scales with a variable delay by using the generalized riccati technique and integral averaging technique new oscillation criteria are obtained for all solutions of the equation some results extend known results for difference equations when the time scale is the set z of positive integers and for differential equations when the time scale is r several examples are given to illustrate the results of the paper

oscillation criteria for second order nonlinear neutral delay dynamic equations in this paper we will establish some oscillation criteria for the second order nonlinear neutral delay dynamic equation r t y t p t y t f t y t 0 on a time scale t here 0 is a quotient of odd positive integers with r t and p t real valued positive functions defined on t to the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales so this paper initiates the study

positive solutions of second order half linear dynamic equations on time scales necessary and sufficient conditions are obtained for the existence of positive solutions of a second order half linear dynamic equation on time scales relations between this equation and an advanced type dynamic equation are also discussed

a fast high order algorithm for the solution of surface scattering problems basic implementation tests and applications we present a new algorithm for the numerical solution of problems of acoustic scattering by surfaces in three dimensional space this algorithm evaluates scattered fields through fast high order solution of the corresponding boundary integral equation the high order accuracy of our solver is achieved through use of partitions of unity together with analytical resolution of kernel singularities the acceleration in turn results from use of a novel approach which based on high order two face equivalent source approximations reduces the evaluation of far interactions to evaluation of 3 d fast fourier transforms ffts this approach is faster and substantially more accurate and it runs on dramatically smaller memories than other fft and k space methods the present algorithm computes one matrix vector multiplication in o n6 5logn to o n4 3logn operations where n is the number of surface discretization points the latter estimate applies to smooth surfaces for which our high order algorithm provides accurate solutions with small values of n the former more favorable count is valid for highly complex surfaces requiring significant amounts of subwavelength sampling further our approach exhibits super algebraic convergence it can be applied to smooth and nonsmooth scatterers and it does not suffer from accuracy breakdowns of any kind in this paper we introduce the main algorithmic components in our approach and we demonstrate its performance with a variety of numerical results in particular we show that the present algorithm can evaluate accurately in a personal computer scattering from bodies of acoustical sizes of several hundreds

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

numerical oscillation and non oscillation for differential equation with piecewise continuous arguments of mixed type the paper deals with the oscillation and non oscillation of the runge kutta methods for a differential equation with piecewise continuous arguments of mixed type the conditions of the oscillation and non oscillation for the runge kutta method are obtained it is proved that oscillation of the analytic solution is not preserved by the runge kutta method under any conditions the conditions under which the non oscillation of analytic solutions is preserved by the runge kutta method are obtained some numerical experiments are given

a fast and high order method for the three dimensional elastic wave scattering problem in this paper we present a fast and high order boundary integral equation method for the elastic scattering by three dimensional large penetrable obstacles the algorithm extends the method introduced in 5 for the acoustic surface scattering to the fully elastic case in our algorithm high order accuracy is achieved through the use of the partition of unity and a semi classical treatment of relevant singular integrals the computational efficiency associated with the nonsingular integrals is attained by the method of equivalent source representations on a cartesian grid and fast fourier transform fft the resulting algorithm computes one matrix vector product associated with the discretization of the integral equation with o n 4 3 log n operations and it shows algebraic convergence several numerical experiments are provided to demonstrate the efficiency of the method

asymptotic behavior of solutions of a third order nonlinear dynamic equation on time scales in this paper we will establish some sufficient conditions which guarantee that every solution of the third order nonlinear dynamic equation c t a t x t q t f x t 0 t t0 oscillates or converges to zero

oscillation criteria for second order matrix dynamic equations on a time scale we obtain oscillation criteria for a second order self adjoint matrix differential equation on a measure chain in terms of the eigenvalues of the coefficient matrices and the graininess function we illustrate our results with some nontrivial examples

asymptotic behavior of solutions of third order nonlinear dynamic equations on time scales in this paper we will study asymptotic behavior of solutions to third order nonlinear dynamic equations on time scales of the form 1a 2 t 1a 1 t x d t a 1 d a 2 d q t f x t 0 by using the riccati technique and integral averaging technique two different types of criteria are established one of which extends some existing results and the other is new two examples of dynamic equations on different time scales are given to show the applications of the obtained results

an efficient and high order frequency domain approach for transient acoustic structure interactions in three dimensions this paper is concerned with numerical solution of the transient acoustic structure interaction problems in three dimensions an efficient and higher order method is proposed with a combination of the exponential window technique and a fast and accurate boundary integral equation solver in the frequency domain the exponential window applied to the acoustic structure system yields an artificial damping to the system which eliminates the wrap around errors brought by the discrete fourier transform the frequency domain boundary integral equation approach relies on accurate evaluations of relevant singular integrals and fast computation of nonsingular integrals via the method of equivalent source representations and the fast fourier transform numerical studies are presented to demonstrate the accuracy and efficiency of the method copyright 2016 john wiley sons ltd

partitioned formulation of internal fluid structure interaction problems by localized lagrange multipliers abstract a partitioned formulation of compressible internal fluid structure interaction problems is presented by employing a displacement model for both the fluid and structure partitioning is effected by a localized version of the method of lagrange multipliers which assigns two independent sets of lagrange multipliers to the structural and fluid interfaces two major features of the present formulation include an interface compliance normalization that helps capture the predominant physics of interaction phenomena when the interfaces are characterized by two radically different rigidities and a novel transformation of the displacement model into a fluid pressure model that is suitable for both transient and vibration analyses the present formulation first solves for the interface lagrange multipliers which are subsequently used to solve for the structural displacements and the fluid displacement or pressure by employing two independent analysis modules

a space time finite element method for structural acoustics in infinite domains part 1 formulation stability and convergence abstract a space time finite element method for solution of the exterior structural acoustics problem involving the interaction of vibrating elastic structures submerged in an infinite acoustic fluid is formulated in particular time discontinuous galerkin and galerkin least squares gls variational formulations for coupled structural acoustics in unbounded domains are developed and analyzed for stability and convergence the formulation employs a finite computational fluid domain surrounding the structure and incorporates time dependent non reflecting boundary conditions on the fluid truncation boundary energy estimates are obtained which allow us to prove the unconditional stability of the method for the coupled fluid structure problem with absorbing boundaries the methods developed are especially useful for the application of adaptive solution strategies for transient acoustics in which unstructured space time meshes are used to track waves propagating along space time characteristics an important feature of the space time formulation is the incorporation of temporal jump operators which allow for finite element interpolations that are discontinaous in time for additional stability least squares operators based on local residuals of the structural acoustics equations including the non reflecting boundary conditions are incorporated the energy decay estimates and high order accuracy predicted by our a priori error estimates are demonstrated numerically in a simple canonical example

isogeometric indirect boundary element method for solving the 3d acoustic problems abstract this paper provides an isogeometric indirect boundary element method igibem based on nurbs non uniform rational b splines and pht splines polynomial splines over hierarchical t meshes for analyzing the three dimensional 3d acoustic problems in the classical procedure the geometries are discretized by lagrange polynomials elements which leads to both substantial geometrical error and time consuming meshing steps however these deficiencies can be eliminated by the isogeometric analysis iga directly incorporating the geometry description generated from the cad computer aided design software into cae computer aided engineering analysis unlike the dbem direct boundary element method the ibem indirect boundary element method allows different types of boundary conditions on the two sides of a surface moreover the hypersingular integrals in ibem can be transformed to a weakly singular form in addition the pht based ibem is used to investigate the influence of local refinement on the accuracy of solutions finally the non uniqueness problem is solved which is a fatal defect in the acoustic bem for the exterior problem four different methods to handle the non uniqueness problem are discussed and compared the results obtained by the proposed method were compared with analytical solutions and the results computed by lagrange based ibem several benchmark examples demonstrate 1 the present method i e igibem has super accuracy over conventional ibem for the acoustic problems 2 local refinement has a significant influence on the convergence rate of the solutions and the numerical accuracy is relevant to the distance to the boundary where the local refinement acted 3 as for the non uniqueness problem the imposition of specific interior boundary conditions not only obtains the best calculation result over the entire range of frequencies but also has a simple integral formulation

oscillation criteria of second order half linear dynamic equations on time scales in this paper by using the riccati transformation technique chain rule and inequalitya l lab l 1 l 1 b l 0 l 1 where a and b are positive constants we will establish some oscillation criteria for the second order half linear dynamic equation p t x d t c d q t x c t 0 t a b on time scales where c 1 is an odd positive integer our results not only unify the oscillation of half linear differential and half linear difference equations but can be applied on different types of time scales and improve some well known results in the difference equation case some examples are considered here to illustrate our main results

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

lyapunov inequality for linear hamiltonian systems on time scales the principal aim of this paper is to state and prove some lyapunov inequalities for linear hamiltonian system on an arbitrary time scale t so that the well known case of differential linear hamiltonian systems t r and the recently developed case of discrete hamiltonian systems t z are unified applying these inequalities a disconjugacy criterion for hamiltonian systems on time scales is obtained

a new boundary finite element method for fluid structure interaction problems in order to study problems on fluid structure interaction we have used a mixed formulation which couples the classical functional of the structure with a new variational formulation by integral equations for the fluid this formulation has the advantage over the finite element methods of avoiding the discretization of the fluid domain furthermore unlike collocation methods the explicit calculation of the hadamard finite part of the singular integrals is avoided this leads after discretization by boundary finite elements to a small and symmetrical algebraic system typical examples are presented that demonstrate the efficiency of this variational formulation by studying the sound transmission through a baffled plane structure and through a flexible panel backed by a rigid cavity these include the calculation of the transmission loss factor and the determination of which modes dominate the noise transmission good agreement is obtained between numerical results and analytical results found in the literature

three dimensional wave envelope elements of variable order for acoustic radiation and scattering part i formulation in the frequency domain a variable order infinite wave envelope element scheme is formulated for transient unbounded acoustical problems the transient formulation which is local in space and time is obtained by applying an inverse fourier transformation to a time harmonic wave envelope model whose formulation is described in a companion article this procedure yields a coupled system of second order differential equations which can be integrated in time to yield transient pressure histories at discrete nodal points far field transient pressures can also be obtained at adjusted times the method can be applied quite generally to two dimensional and three dimensional problems and is compatible with a conventional finite element model in the near field the utility of the method is confirmed by the presentation of transient solutions for axisymmetric and fully three dimensional test problems an implicit time integration scheme is used and computed results are compared to analytic solutions and to solutions obtained from alternative numerical schemes close correspondence is demonstrated and the scheme is shown to be stable for the problems which are presented cpu times for a large three dimensional problem are shown to compare favorably with those required for an equivalent transient boundary element computation

displacement pressure based mixed finite element formulations for acoustic fluid structure interaction problems summary we present reliable finite element discretizations based on displacement pressure interpolations for the analysis of acoustic fluid structure interaction problems the finite element interpolations are selected using the inf sup condition and emphasis is given to the fact that the boundary conditions must satisfy the mass and momentum conservation we show that with our analysis procedure no spurious non zero frequencies are encountered as heretofore calculated with other displacement based discretizations 1997 by john wiley sons ltd

existence of weak solutions of two point boundary value problems for second order dynamic equations on time scales abstract in this paper by using critical point theory we establish the existence of weak solutions of the two point boundary value problem for a second order dynamic equation on an arbitrary time scale t so that the well known case of differential dynamic systems t r and the recently developed case of discrete dynamic systems t z are unified to the best of our knowledge this is the first time that boundary value problems of dynamic equations on time scales have been dealt with by using critical point theory

on the formulation of the acoustic boundary element eigenvalue problems acoustic algebraic eigenvalue analysis by the boundary element method bem can be formulated by the dual reciprocity method drm of nardini and brebbia or by the complementary function particular integral method pim proposed by ahmad and banerjee but both drm and pim require inversion of a matrix of size at least as large as the system matrices before the equations can be cast in the form of generalized eigensystem this makes these methods inefficient for large problems of practical interest in this paper a rather simple technique is proposed which eliminates the need to invert any matrix in the process of setting up the algebraic eigenvalue problem especially for the most important case where all the boundary walls are acoustically hard p n 0 a few example problems having known analytical and experimental results are solved in order to demonstrate the validity of the new technique it is also demonstrated that unlike in elasticity here the boundary element domain must be adequately zoned or an adequate number of internal points must be incorporated in order to solve truly 2 d or 3 d problems

oscillation of nonlinear dynamic equations on time scales by means of riccati transformation techniques we establish some new oscillation criteria for the second order nonlinear dynamic equation p t x d t d q t f x s t 0 email protected a b on time scales in terms of the coefficients and the graininess function we illustrate our results with a nontrivial example

a discontinuous enrichment method for capturing evanescent waves in multiscale fluid and fluid solid problems abstract an evanescent wave is produced when a propagating incident wave impinges on an interface between two media or materials at a sub critical angle the sub scale nature of such a wave makes it difficult to be captured computationally in this paper the discontinuous enrichment method dem developed in c farhat i harari l p franca the discontinuous enrichment method comput methods appl mech engrg 190 2001 6455 6479 c farhat i harari u hetmaniuk a discontinuous galerkin method with lagrange multipliers for the solution of helmholtz problems in the mid frequency regime comput methods appl mech engrg 192 2003 1389 1419 c farhat i harari u hetmaniuk the discontinuous enrichment method for multiscale analysis comput methods appl mech engrg 192 2003 3195 3210 c farhat r tezaur p weidemann goiran higher order extensions of a discontinuous galerkin method for mid frequency helmholtz problems int j numer methods engrg 61 2004 1938 1956 c farhat p wiedemann goiran r tezaur a discontinuous galerkin method with plane waves and lagrange multipliers for the solution of short wave exterior helmholtz problems on unstructured meshes new computational methods for wave propagation wave motion 39 4 2004 307 317 l zhang r tezaur c farhat the discontinuous enrichment method for elastic wave propagation in the medium frequency regime int j numer methods engrg 66 2006 2086 2114 r tezaur c farhat three dimensional discontinuous galerkin elements with plane waves and lagrange multipliers for the solution of mid frequency helmholtz problems int j numer methods engrg 66 2006 796 815 is extended to a class of evanescent wave problems new dem elements are constructed by enriching polynomial approximations with free space evanescent solutions in order to achieve high accuracy for problems with fluid fluid or fluid solid interfaces on which evanescent waves may occur the new dem elements are applied to the solution of various two dimensional model problems with evanescent waves their performance is observed to be better than that of the basic helmholtz type dem elements and superior to that of the classical higher order polynomial finite element method

partitioned formulation of internal and gravity waves interacting with flexible structures abstract this paper presents a partitioned modeling of internal and gravity fluid waves that interact with flexible structures the governing interaction model consists of three completely partitioned entities fluid model structural model and interface model that acts as an internal constraint on the fluid structure interface boundary thus the proposed partitioned multi physics modeling can employ two completely modular fluid and structure software modules plus an interface solver hence amenable to partitioned solution algorithms the interface discretization can exploit the nonmatching interface algorithm previously developed via the method of localized lagrange multipliers also noted is that the present fluid model can make use of widely available finite element software for standard poisson type problems

localization of the kobayashi metric and the boundary continuity of proper holomorphic mappings a classical theorem of carath6odory 8 states that every biholomorphic map f d d2 between domains in the complex plane c bounded by simple closed jordan curves extends to a homeomorphism of 31 onto 2 there are some well known generalizations of this result to domains in ie a if d t and d2 are bounded pseudoconvex domains in 112 with if2 boundary and if the infinitezimal kobayashi metric on d2 grows sufficiently fast near the boundary of d2 ko2 g x xl d z bdz for some e e 0 1 then every proper holomorphic map f dt d2 extends to a h61der continuous map of 51 onto 32 2 3 10 25 29 32 this holds in particular if 92 is strictly pseudoconvex or if it is pseudoconvex with real analytic boundary the same result holds if d2 is only piecewise smooth strongly pseudoconvex 31 further results treat exceptional cases such as the balls 1 reinhardt domains 5 24 domains with many symmetries 4 and analytically bounded hartogs domains in c 2 i1 biholomorphic maps between certain types of nonpseudoconvex domains with real analytic boundaries were treated in 13 and 27 besides the papers mentioned above there is a vast literature concerning smooth extension of proper holomorphic maps of smoothly bounded pseudoconvex domains 6 7 12 14 to mention just a few in the present paper we obtain some results on the continuous extension of proper holomorphic maps f d1 2 under local assumptions on the boundaries bd1 and bd2 one of the main results is

dynamic equations on time scales a survey the study of dynamic equations on time scales which goes back to its founder stefan hilger 1988 is an area of mathematics that has recently received a lot of attention it has been created in order to unify the study of differential and difference equations in this paper we give an introduction to the time scales calculus we also present various properties of the exponential function on an arbitrary time scale and use it to solve linear dynamic equations of first order several examples and applications among them an insect population model are considered we then use the exponential function to define hyperbolic and trigonometric functions and use those to solve linear dynamic equations of second order with constant coefficients finally we consider self adjoint equations and more generally so called symplectic systems and present several results on the positivity of quadratic functionals

a necessary and sufficient condition for oscillation of the sturm liouville dynamic equation on time scales in this paper we investigate oscillatory properties of the second order sturm liouville dynamic equation on a time scale r t x c t x 0 using the so called trigonometric transformation we establish a necessary and sufficient condition for oscillation of this condition is then used to derive an explicit oscillation criterion for this equation

numerical solution of the helmholtz equation in 2d and 3d using a high order nystrom discretization we show how to solve time harmonic scattering problems by means of a high order nystrom discretization of the boundary integral equations of wave scattering in 2d and 3d the novel aspect of our new method is its use of local corrections to the discretized kernel in the vicinity of the kernel singularity enhanced by local corrections the new algorithm has the simplicity and speed advantages of the traditional nystrom method but also enjoys the advantages of high order convergence for controlling solution error we explain the practical details of implementing a scattering code based on a high order nystrom discretization and demonstrate by numerical example that a scattering code based on this algorithm can achieve high order convergence to the correct answer we also demonstrate its performance advantages over a high order galerkin code

oscillations of delay differential equations with variable coefficients consider the delay differential equation t p t x t 0 where p t c t0 r and is a positive constant we show that every solution of this equation oscillates if tt p t dt 1 e for sufficiently large t and t0 p t exp tt p s ds 1 e 1 dt

oscillation criteria for second order linear differential equations abstract some oscillation criteria are given for the second order linear differential equation r t u t c t u t 0 where r t c 1 t 0 0 and c t c t 0 r these results improve oscillation criteria of wintner hartman kamenev yan and philos by using a generalized riccati transformation t a t r t u t u t f t where f c 1 is a given function on t 0 and a t exp 2 t f s ds

on lyapunov type inequalities for nonlinear dynamic systems on time scales in this paper by using elementary analysis we establish several new lyapunov type inequalities for the following nonlinear dynamic system on an arbitrary time scale t x d t email protected t x s t email protected t y t p 2y t y d t email protected t x s t q 2x s t email protected t y t when the end points are not necessarily usual zeros but rather generalized zeros which generalize and improve all related existing ones including the continuous and discrete cases

boundary regularity of proper holomorphic mappings it s main result is formulated in theorem 2 below although the answer to the conjecture in the general case is still unknown it has been shown to hold in many special cases a fairly detailed history of this subject will be contained in 14 one class of positive answers deals with cases in which one knows that f21 and 2 posses fairly large classes of holomorphic automorphisms that extend holomorphically across the boundaries like for instance reinhardt domains see e g h cartan 8 w kaup 16 and st bell 6 in these situations one even often does not need a smoothness assumption on the boundaries of 1 and 22 on the other hand the first result without a priori knowledge on automorphisms which gave c extendability was proved by ch fefferman in 1974 in 15 and says

new approximations of external acoustic structural interactions derivation and evaluation new approximate models for external acoustics interacting with flexible structures are developed the basic form of the present models is obtained by a combination of the laplace transformed retarded and advanced potentials with the weighting parameter as part of the model equation it is shown that the maximum attainable time derivative of convergent approximate models is two hence any attempt to include higher orders will lead to non convergent models the present external acoustic model is implemented and interfaced with a finite element structural analyzer for the transient response analysis of submerged spherical and cylindrical shells subjected to a series of incident waves comparisons of the present results with the classical analytical solutions and the doubly asymptotic approximations daas show that proposed model offers improved accuracy especially for early time responses exhibits computational robustness and maintains the impulse response consistency that are desirable for inverse problems the present model is applied for a shock response correlation of an experimental complex ring cylinder which demonstrates the applicability of the proposed approximate model to practical engineering problems

on a disconjugacy criterion for second order dynamic equations on time scales in this paper a sufficient condition for disconjugacy of second order differential equations on time scales is given for this purpose a mean value result on time scales is employed

some oscillation results for second order nonlinear dynamic equations of neutral type abstract in this paper some oscillation results for the second order nonlinear neutral delay dynamic equation r t y t p t y t q t y t sgn y t 0 are obtained on a time scale t under the assumption t 0 1 r t 1 t where 0 is a quotient of odd positive integers

the lanczos algorithm applied to unsymmetric generalized eigenvalue problem application of the two sided lanczos recursion to the unsymmetric generalized eigenvalue problem is presented the system matrices are real and unsymmetric therefore the recursions are performed in real arithmetic and complex arithmetic is employed in the qr algorithm used to extract the eigenvalues of the transformed tridiagonal matrix the biorthonormal transformation of the unsymmetric generalized eigenvalue problem is considered in detail with appropriate proofs presented in appendices issues relating to the computer implementation of the unsymmetric generalized eigenvalue problem are discussed the example problems solved demonstrate the working of the algorithm in extracting the complex and or real eignevalues of an unsymmetric system of matrices also the algorithm is applied to extract a few of the eigenvalues of a large fluid structure interaction problem and the results are compared with the eigenfrequencies extracted by an unsymmetric subspace iteration procedure presented in the literature

the automorphism group of a domain with an exponentially flat boundary point abstract we study the automorphisms group action on a bounded domain in c n having a boundary point that is exponentially flat such a domain typically has a compact automorphism group our results enable us to generate many new examples

oscillation of second order nonlinear neutral delay dynamic equations on time scales in this paper some sufficient conditions for oscillation of the second order nonlinear neutral delay dynamic equation r t y t p t y t f t y t 0 on a time scale t are established here 1 is an odd positive integer with r t and p t are rd continuous functions defined on t our results as a special case when t r and t n involve and improve some well known oscillation results for second order neutral delay differential and difference equations when t hn and t qn t t qk k n q 1 i e for generalized neutral delay difference and q neutral delay difference equations our results are essentially new and also can be applied on different types of time scales e g t n2 t2 t n and t tn tn n n0 where tn is the set of harmonic numbers some examples illustrating our main results are given

boundary element finite element coupled eigenanalysis of fluid structure systems the eigenanalysis of acoustical cavities with flexible structure boundaries such as a fluid filled container or an automobile cabin enclosure is considered an algebraic eigenvalue problem formulation for the fluid structure problem is presented by combining the acoustic fluid boundary element eigenvalue analysis method and the structural finite elements for many practical eigenproblems use of finite elements to discretize the fluid domain leads to large stiffness and mass matrices since the acoustic boundary element discretization requires putting nodes only on the wetted surface of the structure the size of the eigenproblem is reduced considerably thus reducing the eigenvalue extraction effort futhermore unlike in ordinary cases the finite element discretization of pressure displacement based fluid structure problem gives rise to unsymmetric matrices therefore the fact that the boundary element formulation produces unsymmetric matrices does not introduce additional difficulties here compared to the finite element case in the choice of an eigenvalue extraction procedure examples are included to demonstrate the fluid structure eigenanalysis using boundary elements for the fluid domain and finite elements for the structure

oscillation criteria for second order nonlinear delay dynamic equations abstract in this paper we consider the second order nonlinear delay dynamic equation r t x t p t f x t 0 on a time scale t by employing the generalized riccati technique we will establish some new sufficient conditions which ensure that every solution oscillates or converges to zero the obtained results improve the well known oscillation results for dynamic equations and include as special cases the oscillation results for differential equations some applications and examples are considered to illustrate the main results

a simple impedance infinite element for the finite element solution of the three dimensional wave equation in unbounded domains this paper is concerned with the development of an efficient and accurate impedance infinite element that can be used either in the frequency or directly in the time domain for the modeling and solution of problems described by the scalar three dimensional wave equation in infinite or semi infinite domains the infinite domain is truncated and the effect of the truncated infinite region is simulated by the introduction of an absorbing boundary condition prescribed on the truncation boundary a systematic procedure for the construction of a family of such conditions of increasing accuracy and complexity is developed with explicit formulas given for approximations up to second order a central feature of this high order approximation is that it can be expressed within the context of a finite element formulation as a set of local infinite elements located at the boundary of the computational domain with each element defined by a pair of symmetric time invariant stiffness and damping matrices this makes it possible to incorporate readily the new local boundary element into finite element software developed for purely interior regions for applications involving steady state harmonic or transient excitations whereas the theory has been developed formally for arbitrary smooth boundary surfaces here details are provided for ellipsoidal and spherical boundaries thus far only the latter has been implemented and tested in problems involving cavities and rigid scatterers of spherical and cubic shape numerical experiments in both the frequency and time domain attest to the efficacy and accuracy of the proposed new element

a dual primal feti method for solving a class of fluid structure interaction problems in the frequency domain summary the dual primal finite element tearing and interconnecting method feti dp is extended to systems of linear equations arising from a finite element discretization for a class of fluid structure interaction problems in the frequency domain a preconditioned generalized minimal residual method is used to solve the linear equations for the lagrange multipliers introduced on the subdomain boundaries to enforce continuity of the solution the coupling between the fluid and the structure on the fluid structure interface requires an appropriate choice of coarse level degrees of freedom in the feti dp algorithm to achieve fast convergence several choices are proposed and tested by numerical experiments on three dimensional fluid structure interaction problems in the mid frequency regime that demonstrate the greatly improved performance of the proposed algorithm over the standard feti dp method copyright 2011 john wiley sons ltd

mapped spheroidal wave envelope elements for unbounded wave problems this paper describes a family of axisymmetric spheroidal wave envelope elements for modelling exterior wave problems they are of variable radial order and can be used to represent steady and transient wave fields the formulation is presented for the axisymmetric case using elements which are based on oblate and prolate spheroidal geometries these offer the prospect of reduced dimensionality in comparison to conventional spherically formulated elements when used to represent wave fields in the vicinity of slender or flat objects conjugated weighting functions are used to give frequency independent acoustic mass stiffness and damping matrices this facilitates a simple extension of the method to transient problems the effectiveness and accuracy of the method is demonstrated by a comparison of computed and analytic solutions for sound fields generated by a rigid sphere in steady harmonic oscillation by a rigid sphere excited from rest and by a circular plate vibrating in a plane baffle

some new dynamic inequalities on time scales in this paper based on some known dynamic inequalities we investigate certain new dynamic inequalities on time scales which provide explicit bounds on unknown functions our results unify and extend some continuous inequalities and their corresponding discrete analogues