higher order boundary infinite elements abstract higher order approximations are implemented in a novel approach to infinite element formulations for exterior problems of time harmonic acoustics this approach is based on a functional which provides a general framework for domain based computation of exterior problems two prominent features of this formulation simplify the task of discretization the lack of integration over the unbounded domain and weak enforcement of continuity between finite elements and infinite elements consequently the infinite elements mesh the interface only and need not match the finite elements on the interface various infinite element approximations for two dimensional configurations with circular interfaces are presented numerical results demonstrate the good performance of this scheme

reducing spurious dispersion anisotropy and reflection in finite element analysis of time harmonic acoustics abstract galerkin and stabilized galerkin least squares and galerkin gradient least squares finite element methods for solving problems of time harmonic acoustics are presented and analyzed the error of discretization is related to spurious representation of physical phenomena namely dispersion anisotropy and reflection all of which decrease with mesh refinement the performance of the stabilized methods in terms of dispersion and anisotropy is identical both are superior to the galerkin method relaxing wave resolution requirements further insight into the design of these methods is provided by the analyses the stabilized methods differ in the degree of spurious reflection that is engendered by transitions in mesh size the performance of galerkin gradient least squares deteriorates on non uniform meshes however galerkin least squares maintains its enhanced performance exhibiting low sensitivity to transitions in mesh size thereby reducing spurious dispersion anisotropy and reflection in finite element analysis of time harmonic acoustics guidelines for discretization pertaining to mesh orientation and wave resolution are presented

finite elements with increased freedom in choosing shape functions starting with a mathematical statement of the convergence requirements for an element stiffness matrix the paper discusses displacement shape functions that may be used in connection with the potential energy principle in short these functions must be force orthogonal and energy orthogonal but they need not be conforming satisfy interelement compatibility it is shown that the requirements to the displacement functions may be greatly relaxed through slight modifications of the coupling stiffness between fundamental and higher order displacement modes several alternative formulations are examined in particular a new free formulation is suggested using this form which is very simple the only requirement to the displacement patterns used is that they should contain the fundamental deformation modes and be linearly independent applications of the theory to triangular and rectangular plate bending elements are shown the simple stiffness matrix for the latter is given explicitly the numerical results compare favourably with other types of finite elements

on the free vibration of stiffened shallow shells abstract a finite element analysis for free vibration behaviour of doubly curved stiffened shallow shells is presented the stiffened shell element is obtained by the appropriate combinations of the eight nine node doubly curved isoparametric thin shallow shell element with the three node curved isoparametric beam element the shell types examined are the elliptic and hyperbolic paraboloids the hypar and the conoidal shells the accuracy of the formulation is established by comparing some of the authors results of specific problems with those available in the literature numerical results of additional stiffened shells are also presented to study the effects of various parameters of shells and stiffeners such as orientation i e along x y both x and y directions type concentric eccentric at top and eccentric at bottom and number of stiffeners stiffener depth to shell thickness ratio and aspect ratio shallowness and boundary conditions of shells on free vibration characteristics

existence and subharmonicity of solutions for nonlinear non smooth periodic systems with a p laplacian abstract in the present paper we consider the nonlinear periodic systems driven by a vectorial p laplacian with a locally lipschitz nonlinearity some existence multiplicity and subharmonic results are obtained by using non smooth critical point theory

improved finite element methods for elastic waves abstract in this work we develop finite element methods for exterior problems of time harmonic elastic waves we employ dtn exterior boundary conditions on an artificial boundary to obtain a well posed equivalent problem in a bounded region that is suitable for domain based computation galerkin galerkin least squares and galerkin gradient least squares finite element methods are presented in acoustic wave problems the galerkin least squares method counters the numerical difficulties that result from employing the galerkin method but proves to be insufficient for elastic waves a specialization of the galerkin gradient least squares method to problems of elastic waves yields good results numerical tests validate these conclusions

construction and analysis of fourth order finite difference schemes for the acoustic wave equation in nonhomogeneous media in this article we construct and analyse a family of finite difference schemes for the acoustic wave equation with variable coefficients these schemes are fourth order accurate in space and time in the case of smooth media and are designed to remain stable and optimal for reflection transmission phenomena in the case of discontinuous coefficients together with a detailed mathematical study various numerical results are presented

numerical dispersion of higher order nodal elements in the finite element method the discretization inherent in the finite element method results in numerical dispersion this dispersion is investigated for a time harmonic plane wave propagating through an infinite two dimensional finite element mesh composed of uniform quadrilateral and triangular elements the effects on the dispersion due to the propagation direction of the wave the order of the elements the node density and the mesh geometry are studied results are given which can serve as a guide in selecting the appropriate element order node density and mesh geometry when applying the finite element method

an operational procedure for the symbolic analysis of the finite element method an operational procedure is presented for the symbolic analysis of different finite element discretizations which enables one to symbolically decouple the finite element equations and recover the corresponding limit differential equations which govern the finite element behavior comparison of the limit differential equations with the continuum differential equations succinctly manifests the component wise discretization effects on element behavior such as the transverse shear element locking phenomenon exhibited by thin co elements the procedure is applied to the hermitian approximation of the sturm liouville equation and to the linear approximation of the timoshenko beam

infinitely many nontrivial periodic solutions for damped vibration problems with asymptotically linear terms in this paper we study a class of damped vibration problem with asymptotically quadratic terms at infinity we obtain infinitely many nontrivial periodic solutions by variational method to the best of our knowledge there is no published result focusing on this class of damped vibration problem with asymptotically quadratic terms at infinity

subgrid modeling in a galerkin method for the helmholtz equation abstract we improve the accuracy of finite element acoustic wave solutions without introducing additional degrees of freedom with physically inspired subgrid models the models explored here will not adversely impact system matrix storage or bandwidth can be used for structured or unstructured meshes do not require the solution of any auxiliary value problems and have minimal marginal overall computational cost one interpretation of the new models is as momentum transferred to and from modes at length scales below the local mesh dimension we show a method to approximate the effects of all subgrid modes on the grid scale solution and the significant improvements in local accuracy that the new models provide the new subgrid models also improve global or pollution accuracy through a reduction in the element dispersion error in addition we draw comparisons between this proposed method and much of the alternative and related work in this area

residual based methods for fluid loaded beams abstract in this paper residual based modifications to standard finite element approximations for structural acoustics are developed and analyzed results for symmetric residual based modifications for the coupled problem are presented the accuracy of symmetric and unsymmetric methods is determined in a two dimensional setting a symmetric form of the residual based modification results in lower computational costs than the other methods the inclusion of new fluid structure coupling and fluid stiffness terms arising from the consistent integration into the coupled formulation of residual modifications to the structural equations is shown to dramatically decrease the l 2 error

existence theorems of periodic solutions for a class of damped vibration problems abstract in the present paper we research the following damped vibration problem 1 1 u t g t u t f t u t a e t 0 t u 0 u t u 0 u t 0 where t 0 g l 0 t r g t 0 t g s ds g t 0 and f 0 t r n r the variational principle is given and three existence theorems for periodic solutions are obtained

soft and hard db boundary conditions defined by a skewon axion medium a novel set of electromagnetic boundary conditions is defined in terms of an interface of a medium belonging to the class of skewon axion media such a medium class can be introduced in a simple and natural manner applying four dimensional representation of electromagnetic media it is shown that the novel boundary conditions generalize soft and hard sh and db boundary conditions to shdb conditions as an application reflection of a plane wave from a planar shdb boundary is studied it is shown that the two eigenvectors of the reflection dyadic define eigenwaves for which the shdb boundary can be replaced by equivalent pec or pmc boundaries the theory is tested with numerical examples which reveal an interesting narrow beamed reflection phenomenon associated to the shdb boundary condition

complex wave number dispersion analysis of galerkin and galerkin least squares methods for fluid loaded plates abstract the technique of complex wave number dispersion analysis is used to examine the accuracy of discretized systems in the representation of wave propagation phenomena this technique was applied to study finite element approximations to in vacuo and fluid loaded plates considering discretizations of kirchhoff and reissner mindlin plate theories coupled to an acoustic medium the allowed evanescent waves in the finite element approximation of the in vacuo plate are obtained and compared with theory the finite element dispersion relation for the coupled plate fluid system is derived results for the galerkin structural approximation coupled to galerkin and galerkin least squares gls fluid formulations are presented quantitative errors are reported and the significance of these errors in view of an analytical solution to the problem is given

a minimax inequality and its applications to ordinary differential equations the aim of this paper is to investigate the minimax inequality which plays a fundamental role in the critical points theorem of b ricceri below equivalent formulations are shown and characterization is proved in particular for a special class of functionals as an application a multiplicity result for an ordinary dirichlet problem is emphasized

grid dispersion and stability criteria of some common finite element methods for acoustic and elastic wave equations purely numerical methods based on finite element approximation of the acoustic or elastic wave equation are becoming increasingly popular for the generation of synthetic seismograms we present formulas for the grid dispersion and stability criteria for some popular finite element methods fem for wave propagation namely classical and spectral fem we develop an approach based on a generalized eigenvalue formulation to analyze the dispersive behavior of these fems for acoustic or elastic wave propagation that overcomes difficulties caused by irregular node spacing within the element and the use of high order polynomials as is the case for spectral fem analysis reveals that for spectral fem of order four or greater dispersion is less than 0 2 at four to five nodes per wavelength and dispersion is not angle dependent new results can be compared with grid dispersion results of some classical finite difference methods fdm used for acoustic or elastic wave propagation analysis reveals that fdm and classical fem require a larger sampling ratio than a spectral fem to obtain results with the same degree of accuracy the staggered grid fdm is an efficient scheme but the dispersion is angle dependent with larger values along the grid axes on the other hand spectral fem of order four or greater is isotropic with small dispersion making it attractive for simulations with long propagation times

a three critical points theorem revisited abstract in this paper the following result is proved let x be a reflexive real banach space i r an interval x r a sequentially weakly lower semicontinuous c 1 functional bounded on each bounded subset of x whose derivative admits a continuous inverse on x j x r a c 1 functional with compact derivative assume that lim x x j x for all i and that there exists r such that sup i inf x x x j x inf x x sup i x j x then there exist a non empty open set a i and a positive real number r with the following property for every a and every c 1 functional x r with compact derivative there exists 0 such that for each 0 the equation x j x x 0 has at least three solutions in x whose norms are less than r

acoustic diffraction from the junction of two flat plates a general solution is developed for the acoustic and structural scattered response from the junction of two flat plates under unilateral fluid loading the plates are modelled by the classical theory of flexure and the solution is found using the wiener hopf technique for the dual integral equations for the unknown pressure on the plates explicit formulae are obtained for the pressure transform when the plates are in welded or clamped contact and corresponding explicit expressions are given for the various diffraction coefficients associated with the fluid structure interaction the magnitudes of the reflection and transmission coefficients of structural waves display very simple analytic forms at low frequency

finite element dispersion of cylindrical and spherical acoustic waves a reference solution for cylindrical waves is obtained by wkb approximation finite element representations of both cylindrical and spherical waves satisfy the resolution dependent plane wave dispersion relation and approximate the desired decay rates independent of mesh resolution

electromagnetic wave reflection from boundaries defined by general linear and local conditions electromagnetic boundaries defined by the most general linear and local conditions are considered in this paper the conditions relate the normal components of the d and b vectors to the tangential components of the e and h vectors at each point of the boundary reflection of a plane wave from a planar boundary in an isotropic half space is analyzed and an analytic expression for the reflection dyadic is derived it is shown that any plane wave can be decomposed in two components which do not interact in reflection properties of plane waves matched to the general boundary are given certain special cases arising naturally from the general theory and labeled as e boundary h boundary and eh boundary conditions are introduced as interesting novelties and some of their properties are studied other special cases with known results are considered in verifying the theory a possible realization of the general boundary in terms of an interface of a bianisotropic medium is discussed in the appendix

locking spurious mechanisms and pressure divergence in penalty finite element methods for stokes flow problems abstract solution locking spurious mechanisms and pressure divergence exhibited in the stokes flow calculations by the penalty finite element methods are analyzed employing a fourier analysis technique comparison of the approximate discrete operator components with the corresponding continuum ones enables one to explicitly identify the conditions for avoiding locking spurious mechanisms and pressure divergence in terms of discrete operator components which are applicable to either the finite difference or finite element discretizations a synthesis approach is explored to eliminate the solution locking spurious mechanisms and pressure divergence in uniformly reduced integrated four noded elements extensions of the present analysis and synthesis approach to navier stokes equations appear to be straightforward if one deals with a set of consistently linearized operators

a stabilization procedure for the quadrilateral plate element with one point quadrature a stabilization procedure is developed for controlling the kinematic modes of the four node bilinear quadrilateral element when single point quadrature is used these kinematic modes manifest themselves by spatial oscillations or singularity of the total stiffness in this stabilization procedure additional generalized strains are defined which are activated by the kinematic modes these generalized modes are furthermore not activated by rigid body motions regardless of the shape of the quadrilateral by using a scaling law developed in an earlier paper the stabilization parameters are defined so they do not adversely affect the element s performance several problems which are subject to kinematic modes are presented to illustrate the performance of this stabilization procedure for linear problems

a symbolic fourier synthesis of a one point integrated quadrilateral plate element a symbolic fourier analysis is performed on both one point and four point spatially integrated four noded c0 plate elements the analysis shows that the effects of different integration rules is characterized by a single fourier component called the directional averaging operator in addition the conditions for avoiding locking and spurious mechanisms are explicitly identified in a general plate operator expressed in fourier form encouraged by these results a c0 plate element is synthesized employing only one point integrated attributes the stiffness matrix of the new element consists of two parts the usual one point integrated part and the rank compensating part that is identified as the difference between the synthesized and one point integrated plate operators the present element achieves the same accuracy of elements employing the four point spatial integration rule which is not realized in the one point integrated elements using hour glass control techniques preliminary numerical experiments corroborate the present theoretical results and demonstrate the usefulness of the present symbolic analysis and fourier synthesis techniques

complex wave number decomposition of structural vibrations a high resolution parameter estimation technique is used to analyze the spatial dependence of the steady state vibrations of finite structures the complex wave number dependence is extracted using a modified version of the prony method along with model order overdetermination this prony technique forms the basis of an automated algorithm for the robust and efficient estimation of the structural system parameters a specific algorithm is described and implemented using a wave viewpoint of the spatial response the algorithm is used to deconvolve the helical wave spectrum of a point driven cylindrical shell from analytic response data the effects of added noise are studied

solvability of second order hamiltonian systems with impulses via variational method in this paper a class of second order impulsive hamiltonian systems are considered some new existence results are obtained by using a variational method and critical point theorem due to tang and wu some recent results are extended three examples are presented to illustrate the feasibility and effectiveness of our results

extension of mitc to higher order beam models and shear locking analysis for compact thin walled and composite structures summary a class of mixed interpolated beam elements is introduced in this paper under the framework of the carrera unified formulation cuf to eliminate the detrimental effects due to shear locking the mixed interpolation of tensorial components mitc method is adopted to generate locking free displacement based beam models using general 1d finite elements an assumed distribution of the transverse shear strains is employed for the derivation of the virtual work and the full gauss legendre quadrature is used for the numerical computation of all the components of the stiffness matrix linear quadratic and cubic beam elements are developed using the unified formulation and applied to linear static problems including compact laminated and thin walled structures a comprehensive study of how shear locking affects general beam elements when different classical integration schemes are employed is presented evidencing the outstanding capabilities of the mitc method to overcome this numerical issue refined beam theories based on the expansion of pure and generalized displacement variables are implemented making use of lagrange and legendre polynomials over the cross sectional domain allowing one to capture complex states of stress with a 3d like accuracy the numerical examples are compared to analytic numerical solutions from the literature and commercial software solutions whenever it is possible the efficiency and robustness of the proposed method is demonstrated throughout all the assessments illustrating that mitc elements are the natural choice to avoid shear locking and showing an unprecedent accuracy in the computation of transverse shear stresses for beam formulations this article is protected by copyright all rights reserved

design of galerkin generalized least squares methods for timoshenko beams abstract a class of finite element methods the galerkin generalized least squares methods are developed and applied to model the steady state response of timoshenko beams an optimal method is designed using a linear interpolation of the response such that there is zero finite element dispersion error the classical method of selective reduced integration and a modified version of selective reduced integration with mass lumping are shown to fall under the galerkin generalized least squares framework numerical experiments in wave propagation demonstrate the dramatic superiority of the new optimal method over the standard approaches the goal of the new methods is to decrease the computational burden required to achieve a desired accurcy level at a particular frequency thereby enabling larger scale higher frequency computations for a given platform

periodic solutions for second order systems with not uniformly coercive potential abstract the existence and multiplicity of periodic solutions are obtained for the nonautonomous second order systems with locally coercive potential that is f t x as x for a e t in some positive measure subset of 0 t by using an analogy of egorov s theorem the properties of subadditive functions the least action principle and a three critical point theorem proposed by brezis and nirenberg

convergence of curved shell elements based on assumed covariant strain interpolations a c0 9 node shell element based on assumed interpolations of covariant strain components defined with respect to the element natural co ordinate system has recently been proposed in this formulation the covariant strains are obtained directly from the cartesian strains by tensor transformation without any need to compute laminar co ordinate based strains in the present work the interpolated covariant strains used in this element are analysed to determine their satisfaction of the basic requirements for successful strain interpolation these basic requirements are stated as invariance to rigid body motions and ability to represent constant and linear strain states in the finite element formulation the weak form of momentum balance is expressed in terms of covariant strains and contravariant stresses the corresponding elasticity tensor is a function of the components of the metric tensor associated with the element natural co ordinate system the invariance properties of the metric tensor in the context of the finite element approximation are also discussed

uniform surface integral equation formulation for mixed impedance boundary conditions a numerical approach based on the surface integral equation sie method is developed for the analysis of time harmonic electromagnetic scattering by impenetrable objects equipped with mixed impedance boundary conditions mibcs mibc is an axially anisotropic generalization of the conventional isotropic leontovich impedance boundary condition the developed sie formulation utilizes surface helmholtz decomposition the self dual formulation of yan and jin and loop and star rwg functions a combined field formulation is applied to avoid internal resonances

estimation of plate material properties by means of a complex wavenumber fit using hankel s functions and the image source method abstract this paper presents a new wave fitting approach to estimate the frequency dependent material properties of thin isotropic plate structures from an experimentally obtained vibrational field exciting the plate at a single point the method projects the measurement data on to an analytical image source model in which hankel s functions are used for a description of the wave fields emanating from the point of excitation including the reflected wave fields from the edges of the finite plate by minimizing the error between the projected field and the measured field varying the complex wave number and the source strengths of the image sources an optimum fit is searched for thus the source strengths of the image sources do not need to be determined theoretically but are estimated from the fit on to the experimental data instead thus avoiding difficulties in theoretically assessing the reflection coefficient of the edges of the plate the approach uses a complex wavenumber fit enabling the determination of the dynamic stiffness of the plate structure and its damping properties as function of frequency the method is especially suited for plates with a sufficient amount of damping excited at high frequencies

grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics summary the spatial discretisation of a continuum by the fem introduces dispersion errors to the numerical solution of stress wave propagation errors of phase and group velocities and the scatter of wave propagation are induced when these propagating phenomena are modelled by the fem the speed of a single harmonic wave depends on its frequency parasitic effects do not exist in an ideal unbounded continuum with higher order finite elements there are optical modes in the spectrum resulting in spurious oscillations of stress and velocity distributions near the sharp wavefronts in principle the dispersion errors and the spurious oscillations cannot be removed from these solutions but can be suppressed to a certain extent for reliable numerical solutions by the fem the dispersion errors should be analysed and determined the dispersion properties of a plane square biquadratic serendipity finite element are examined and compared with a bilinear one dispersion analysis is carried out for the consistent and lumped mass matrices a dispersive improved lumped mass matrix for biquadratic serendipity elements is proposed the paper closes with the recommendation of a choice of permissible dimensionless wavelengths for bilinear and biquadratic serendipity finite element meshes copyright 2013 john wiley sons ltd

a study of stabilization and projection in the 4 node mindlin plate element in this paper a mindlin plate element is formulated based on the hellinger reissner principle and the technique the stiffness consists of a constant stress one point quadrature matrix and a stabilization matrix the stabilization matrix is compared with those previously proposed in addition the element uses a projection to modify the nodal displacements so that the patch test is satisfied the projection matrix is based on a mode decomposition several numerical cases are presented and it is shown that the mode decomposition projection is necessary both for satisfaction of the patch test and convergence

field consistent strain interpolations for the quadratic shear flexible beam element a shear flexible i e timoshenko quadratic isoparametric beam element with two degrees of freedom per node is critically examined from the point of view of the consistency of the constrained strain fields that arise in the thin beam limits the errors in terms of convergence of displacement fields and violent oscillations of stress fields that emerge when exactly integrated elements are used are predicted a priori and confirmed with numerical experiments the rationale behind the use of optimal stress sampling at gaussian points is also derived directly from these arguments

geometric methods for determining system poles from transient response the problem treated is that of identifying the poles of a finite order system by observing its transient decay after cessation of input for a limited time using possibly multiple observation points and experimental repetition various approaches are studied having the common characteristic that a homogeneous matrix equation must be solved several techniques that have been given scant attention in the literature are consolidated by a geometric treatment together with new results including an analytical treatment of the consequences of assuming an excessively high system order derivation of a statistically unbiased estimate for an intermediate parameter in the solution new theorems on error effects a recipe for effective use of the singular value decomposition and a new method for suppression of extraneous poles

numerical issues concerning the wave and finite element method for free and forced vibrations of waveguides the wave and finite element wfe method is a numerical approach to the calculation of the wave properties of structures of arbitrary complexity the method starts from a finite element fe model of only a short segment of the structure typically by using existing element libraries and commercial fe packages the dynamic stiffness matrix of the segment is obtained a periodicity condition applied and an eigenvalue problem formed whose solution gives the dispersion equations and wave mode shapes these define a wave basis from which the forced response can be found straightforwardly although straightforward in application the wfe method is prone to numerical difficulties these are discussed in this paper and methods to avoid or remove them described attention is focused on 1 dimensional waveguide structures for which numerical problems are most severe three ways of phrasing the eigenvalue problem for free wave propagation are presented and a method based on singular value decomposition is proposed to determine eigenvectors at low frequencies discretisation errors are seen to occur if the segment is too large while round off errors occur if the segment is too small this can be overcome by forming a super segment from the concatenation of two or more segments the forced response is then considered the use of a reduced wave basis removes many problems direct calculation of the waves excited by a point force is very prone to poor numerical conditioning but can be circumvented by exploiting the orthogonality of the left and right eigenvectors numerical examples are presented

accuracy of finite difference and finite element modeling of the scalar and elastic wave equations numerical solutions of the scalar and elastic wave equations have greatly aided geophysicists in both forward modeling and migration of seismic wave fields in complicated geologic media and they promise to be invaluable in solving the full inverse problem this paper quantitatively compares finite difference and finite element solutions of the scalar and elastic hyperbolic wave equations for the most popular implicit and explicit time domain and frequency domain techniques in addition to versatility and ease of implementation it is imperative that one choose the most cost effective solution technique for a fixed degree of accuracy to be of value a solution technique must be able to minimize 1 numerical attenuation or amplification 2 polarization errors 3 numerical anisotropy 4 errors in phase and group velocities 5 extraneous numerical parasitic modes 6 numerical diffraction and scattering and 7 errors and transmission coefficients this paper shows that in homogeneous media the

finite difference approximations of first derivatives for three dimensional grid singularities explicit finite difference approximations of first derivatives are developed for two dimensional three way and five way grid singularities the schemes for three way singularities also apply for six way singularities the development objectives are such that the finite difference schemes are non dissipative and compatible with regular difference approximations for convection dominated phenomena special emphasis is given to the directional dependency of numerical phase speeds and stability limits for explicit time integration for that purpose free coefficients are used to minimize the isotropy error of the numerical phase velocity it is shown that numerical phase speeds and stability limits are almost isotropic hence employment of the proposed schemes is nearly independent of the local orientation of the differencing stencil the time step limits are greater than those of regular finite differences indicating that the overall time step of a computation is not reduced by employing the proposed schemes the developed schemes for three way singularities are of second fourth and sixth order of accuracy whereas the five way difference approximations are second and fourth order accurate respectively the spectral characteristics the formal order of accuracy and the stability limits of the proposed schemes imply that they can favorably be used in combination with regular difference approximations of the same order of accuracy on block structured grids

maximum likelihood estimation of structural wave components from noisy data in this paper a general framework is developed for determining the underlying parameters of general signal models through the application of maximum likelihood estimation theory for functions whose variables separate this method extends previous work in sinusoidal and exponential estimation to include models with other functional bases such as exponential functions with nonconstant amplitudes and bessel functions nonuniform spatial sampling is also possible with this technique the maximum likelihood method is applied to the identification of wave components along one dimensional structural elements results are given which demonstrate the viability and accuracy of the technique estimating exponential and bessel function model parameters from noisy simulation data

a uniform strain hexahedron and quadrilateral with orthogonal hourglass control the treatment of zero energy modes which arise due to one point integration of first order isoparametric finite elements is addressed a method for precisely isolating these modes for arbitrary geometry is developed two hourglass control schemes viscous and elastic are presented and examined in addition a convenient one point integration scheme which analytically integrates the element volume and uniform strain modes is presented

periodic solutions of non autonomous second order systems we obtain an existence theorem of periodic solutions of non autonomous second order systems with classical theorems of variational calculus

finite element formulation for a baffled fluid loaded finite cylindrical shell a new method for obtaining the response of a baffled fluid loaded finite cylindrical shell using the finite element method is presented the galerkin finite element formulation for this problem utilizes a neumann green s function representation of the pressure loading on the shell by representing the pressure loading in this manner only the structure need be discretized both c0 and c1 finite element discretizations of the shell are considered the finite element results are compared with the analytic solutions of the fluid loaded cylinder which are obtained using an expansion of the displacement in terms of the in vacuo modes of the naghdi cooper and flugge shell theories

new existence of periodic solutions for second order non autonomous hamiltonian systems abstract by using mountain pass theorem and local link theorem some existence theorems are obtained for periodic solutions of second order non autonomous hamiltonian systems under local superquadratic condition and other suitable conditions

acoustic radiation from an insonified elastic plate with a line discontinuity this paper deals with the development of analytic models for the prediction of the acoustic radiated field from an infinite elastic plate with a single line force and line moment impedance discontinuity due to an incident plane acoustic wave the solution is in the form of a fourier integral with a kernel having ten poles the integral is evaluated by three methods the first uses the steepest descent path sdp method leading to a solution that decays as 1 k0r 1 2 the second method used conformal transformations and the modified saddle point msp method where all ten poles of the integrand are factored out this second method yields a solution that has complementary error functions and an asymptotic series in k0r the third method employs a transformation of the integrand to effect an efficient and fastly convergent numerical integration algorithm in general the msp asymptotic series solution and the numerical integration yielded numerically identical results however while the sdp solution pre

spurious reflection of elastic waves due to gradually changing finite element size summary when a homogeneous elastic continuum is modelled by a non uniform finite element grid the differences in the size of adjacent finite elements can cause a spurious wave reflection which does not exist in the continuum extending previous studies in which the spurious wave reflection was investigated for the case of two uniform grids with a sudden element size change from one grid to the other the present study deals with the case when the two uniform grids of different element sizes are separated by a transition zone through which the element size varies gradually either by a geometric progression or by an arithmetic progression the solution is carried out in complex variables and numerical plots of the results are given when the ratio of wavelength to the largest element size is as low as 4 1 the spurious wave reflection is very significant while for the ratios over 10 1 it is insignificant inserting a transition zone with gradually varying element size between the two uniform parts of the grid somewhat mitigates the phenomenon of spurious reflection but this is significant only when the ratio of element sizes in the uniform grids is small less than about 1 5 1 varying the element size throughout the transition zone in an arithmetic progression seems slightly better than in a geometric progression the spurious wave reflection is less pronounced for higher order elements in particular for linear strain elements as compared to constant strain elements the spurious reflection is also less severe for consistent mass than for lumped mass

a finite element based method for the analysis of free wave propagation in stiffened cylinders abstract a finite element based method is developed to evaluate elastic wave propagation characteristics in orthogonally stiffened cylindrical shells the method is general and allows for detailed modelling of the shell and stiffners it is assumed that identical stiffeners are spaced at regular intervals in both the axial and circumferential directions so that the structure is periodic in these two dimensions wave propagation techniques are applied to a finite element model of a single periodic unit to determine propagation constants the shell variables are expanded in a fourier series in the circumferential direction and the axial propagation constants are presented for different values of the circumferential wavenumber as a function of frequency the method is verified for unstiffened cylinders by comparing results with exact solutions

the influence of the mass matrix on the dispersive nature of the semi discrete second order wave equation abstract the application of discrete solution methods to the second order wave equation can yield a dispersive representation of the non dispersive wave propagation problem resulting in a phase speed that depends not only upon the wavelength of the signal being propagated but also upon the direction of propagation in this work the dependence of the dispersive errors on the wave propagation direction mesh aspect ratio and wave number is investigated with the goal of understanding and hopefully reducing the phase and group errors associated with the two dimensional bilinear finite element an analysis of the dispersive effects associated with the consistent row sum lumped and higher order mass matrices has led to a reduced coupling penta diagonal mass matrix that yields improved phase and group errors with respect to wavelength and propagation direction the influence of row sum lumping the finite element mass matrix is demonstrated to always introduce lagging phase and group error while a linear combination of the lumped and consistent mass matrices i e a higher order mass matrix is shown to improve the dispersion characteristics of both the reduced and full integration element using a 2 5 phase error metric the higher order mass matrix can reduce the mesh resolution requirements relative to the lumped mass matrix by nearly a factor of two in one dimension a factor of 4 in two dimensions similarly the reduced coupling mass matrix can reduce the grid requirements by a factor of approximately four relative to the lumped mass matrix a factor of 16 in two dimensions although the reduced coupling mass matrix requires additional storage relative to the lumped mass the factor of 16 reduction in grid requirements promises tremendous overall savings for computing a fixed wavelength spectrum or alternatively for resolving shorter wavelengths with a fixed grid resolution

mixed impedance boundary conditions a novel set of isotropic electromagnetic boundary conditions generalizing some of the recently introduced boundary conditions is introduced for a planar boundary it is required that the boundary appears as an impedance boundary for the te and tm components of the field with different surface impedances in the general case thus such conditions can be dubbed as mixed impedance boundary conditions it is shown that the conditions can be alternatively expressed in terms of normal components of the fields at the boundary and in this form they can be defined for non planar boundaries as well the conditions generalize those of the isotropic impedance boundary and the more recently considered db and d b boundaries as a numerical example scattering from a mixed impedance sphere is considered and it is found that the sphere could be useful as a cloaking device

periodic solutions of a class of non autonomous second order systems some existence theorems are obtained by the least action principle for periodic solutions of nonautonomous second order systems with a potential which is the sum of a subconvex function and a subquadratic function

on variational methods for a class of damped vibration problems abstract in the present paper the following damped vibration problems 1 1 u t q t u t a t u t f t u t a e t 0 t u 0 u t u 0 e q t u t 0 and 1 1 u t q t u t a t u t f t u t a e t 0 t u 0 u t u 0 e q t u t 0 are studied where t 0 0 q l 1 0 t r q t 0 t q s d s a t a i j t is a symmetric n n matrix valued function defined in 0 t with a i j l 0 t for all i j 1 2 n and there exists a positive constant such that a t 2 for all r n and a e t 0 t the variational principles are given and an existence theorem and three multiplicity theorems of periodic solutions are obtained

boundary infinite elements for the helmholtz equation in exterior domains a novel approach to the development of infinite element formulations for exterior problems of time harmonic acoustics is presented this approach is based on a functional which provides a general framework for domain based computation of exterior problems special cases include non reflecting boundary conditions such as the dtn method a prominent feature of this formulation is the lack of integration over the unbounded domain simplifying the task of discretization the original formulation is generalized to account for derivative discontinuities across infinite element boundaries typical of standard infinite element approximations continuity between finite elements and infinite elements is enforced weakly precluding compatibility requirements various infinite element approximations for two dimensional configurations with circular interfaces are presented implementation requirements are relatively simple numerical results demonstrate the good performance of this scheme 1998 john wiley sons ltd

transformation method for problems involving perfect electromagnetic conductor pemc structures perfect electric conductor pec and perfect magnetic conductor pmc can be generalized to perfect electromagnetic conductor pemc a medium where certain linear combinations of electromagnetic fields are required to vanish in differential form representation the corresponding medium is characterized as the simplest possible medium it is defined through a scalar admittance parameter whose zero and infinite limits yield the pmc and pec media respectively in this paper a duality transformation is found that has the property of transforming pemc to pec and an isotropic medium to itself thus problems involving pemc objects in air can be transformed to problems with pec objects in air which can be solved through traditional techniques and then transformed back several simple examples are treated to demonstrate the principle pemc has the potential of having similar applications as pmc in antenna engineering and finding structures for its realization is a challenge

computation of scattering by db objects with surface integral equation method electromagnetic scattering by objects with a db boundary condition normal components of the electric and magnetic flux densities d and b vanish at the boundary surface is investigated scattering of arbitrary shaped three dimensional objects is analyzed with the surface integral equation method a significant difference compared to the more conventional boundary conditions is that the uniqueness of the solution to the scattering problem with db boundary depends on the connectivity of the object for a simply connected object the solution is unique but for a multiply connected object some additional conditions are required it appears that these additional conditions are satisfied if divergence free basis functions are used to expand the unknown surface current densities the developed method is applied to calculate polarizabilities scattering efficiencies and radar cross sections rcs of the db sphere and cube and the results are compared with those of the pec cube and sphere

modelling wave propagation in two dimensional structures using finite element analysis a method is described by which the dispersion relations for a two dimensional structural component can be predicted from a finite element fe model the structure is homogeneous in two dimensions but the properties might vary through the thickness this wave finite element wfe method involves post processing the mass and stiffness matrices found using conventional fe methods of a segment of the structure this is typically a 4 noded rectangular segment although other elements can be used periodicity conditions are applied to relate the nodal degrees of freedom and forces the wavenumbers real imaginary or complex and the frequencies then follow from various resulting eigenproblems the form of the eigenproblem depends on the nature of the solution sought and may be a linear quadratic polynomial or transcendental eigenproblem numerical issues are discussed examples of a thin plate an asymmetric laminated plate and a laminated foam cored sandwich panel are presented for the last two examples developing an analytical model is a formidable task at best the method is seen to give accurate predictions at very little computational cost furthermore since the element matrices are typically found using a commercial fe package the meshing capabilities and the wealth of existing element libraries can be exploited

a high order numerical approach with cartesian meshes for modeling of wave propagation and heat transfer on irregular domains with inhomogeneous materials abstract recently we have developed a new numerical approach for pdes with constant coefficients on irregular domains and cartesian meshes in this paper we extend it to a much more general case of pdes with variable coefficients that have a lot of applications e g the modeling of functionally graded materials the inhomogeneous materials obtained by 3 d printing and many others here we consider the 2 d wave and heat equations for isotropic and anisotropic inhomogeneous materials the idea of the extension to the case of pdes with variable coefficients is based on the representation of the stencil coefficients as functions of the mesh size this leads to the increase in the size of the local system of algebraic equations solved for each grid point of the new approach however this does not change the size of the global system of semidiscrete equations and practically does not increase the computational costs of the proposed technique similar to our previous technique the new 2 d approach with compact 9 point stencils uses trivial cartesian meshes for complex irregular domains and provides the fourth order of accuracy for the wave and heat equations with variable coefficients the calculation of the coefficients of the stencil equations is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of the new technique at similar 9 point stencils the accuracy of the new approach is much higher than that for the linear finite elements the numerical results for irregular domains show that at the same number of degrees of freedom the new approach is even much more accurate than the high order up to the third order finite elements with much wider stencils the wave and heat equations are uniformly treated with the new approach

information criteria and selection of vibration models this paper presents a method of determining an appropriate equation of motion of two dimensional plane structures like membranes and plates from vibration response measurements the local steady state vibration field is used as input for the inverse problem that approximately determines the dispersion curve of the structure this dispersion curve is then statistically treated with akaike information criterion aic which compares the experimentally measured curve to several candidate models equations of motion the model with the lowest aic value is then chosen and the utility of other models can also be assessed this method is applied to three experimental case studies a red cedar wood plate for musical instruments a thick paper subjected to unknown membrane tension and a thick composite sandwich panel these three cases give three different situations of a model selection

optimal blended spectral element operators for acoustic wave modeling spectral element methods based on high order polynomials are among the most commonly used techniques for computing accurate simulations of wave propagation phenomena in complex media however to retain computational efficiency very high order polynomials cannot be used and errors such as numerical dispersion and numerical anisotropy cannot be totally avoided in the present work we devise an approach for reducing such errors by considering modified discrete wave operators we analyze consistent and lumped operators together with blended operators weighted averages of consistent and lumped operators furthermore using the operator blending approach and a novel dispersion analysis method we develop optimal spectral element operators that have increased numerical accuracy without resorting to very high order operators the new operators are faster and computationally more efficient than consistent operators our approach is based on the tensor product decomposition of the element matrices into 1d f

electromagnetic boundary and its realization with anisotropic metamaterial a set of boundary conditions requiring vanishing of the normal components of the d and b vectors at the boundary surface is introduced and labeled as that of db boundary basic properties of the db boundary are studied in this paper reflection of an arbitrary plane wave incident with a complex propagation vector is analyzed for the planar db boundary it is shown that waves polarized transverse electric te and transverse magnetic tm with respect to the normal of the boundary are reflected as from respective perfect electric conductor and perfect magnetic conductor planes the basic problem of current source above the planar db boundary is solved by applying te and tm decomposition for the source realization of the db boundary in terms of an interface of uniaxially anisotropic metamaterial half space with zero axial medium parameters is considered it is also shown that such a medium with small axial parameters acts as a spatial filter for waves incident at the interface which could be used for narrowing the beam of a directive antenna application of db boundary as an isotropic soft surface with low interaction between antenna apertures also appears possible

realization of impedance boundary impedance boundary is generally considered as an approximate model for material interfaces considering an electromagnetic field in a certain wave guiding anisotropic material it is shown that a slab of such a material backed by a perfect electric conductor pec plane can be exactly represented by impedance boundary conditions as a result of the analysis a novel explicit relation is derived between the surface admittance dyadic of the impedance boundary and the material and geometric parameters of the anisotropic slab which can be used to realize a given admittance dyadic the relation is verified with results known for the perfect electromagnetic pemc boundary and bi axial material considered as special cases of the theory

some critical point theorems and their applications to periodic solution for second order hamiltonian systems abstract some critical point theorems without the compactness assumptions are obtained by the reduction method the perturbation argument and the least action principle as applications some existence results of periodic solutions are obtained for nonautonomous second order hamiltonian systems which unify and generalize some recent corresponding results

saddle point characterization and multiplicity of periodic solutions of non autonomous second order systems abstract in the present paper the non autonomous second order systems 1 1 u t f t u t a e t 0 t u 0 u t u 0 u t 0 and 1 2 u t t u t f t u t a e t 0 t u 0 u t u 0 u t 0 are studied and a existence result of periodic solutions with saddle point character and two new multiplicity results are obtained

the computation of dispersion relations for three dimensional elastic waveguides using the scaled boundary finite element method abstract in this paper a numerical approach for the computation of dispersion relations for three dimensional waveguides with arbitrary cross section is proposed the formulation is based on the scaled boundary finite element method sbfem it is an extension of the approach previously derived for plate structures it is shown that the wavenumbers of guided waves in a waveguide can be obtained as the eigenvalues of the z matrix which is well known in the sbfem the hamiltonian properties of this matrix are utilized to derive an efficient way to compute the group velocities of propagating waves as eigenvalue derivatives the cross section of the waveguide is discretized using higher order spectral elements it is discussed in detail how symmetry axes can be utilized to reduce computational costs in order to sort the solutions at different frequencies a mode tracking algorithm is proposed based on the pade expansion

determination of structural modes via the prony model system order and noise induced poles the parameters of multiple degree of freedom structural systems can be identified from their impulse response via the prony method overdetermining the system s order is shown to improve the identification accuracy in noisy situations but introduces additional mathematical poles described are methods to determine the necessary overdetermination and the true system poles a novel efficient perturbation method based on the singular value decomposition is shown to be effective under noisy situations

maximum likelihood estimation of flexural wavenumbers in lightly damped plates abstract this paper describes the use of the maximum likelihood method to estimate the flexural wavenumber characteristics of a vibrating plate from experimental measurements the motion of the plate is assumed composed of a set of plane propagating waves of unknown wavenumber and amplitude the problem of determining the wavenumbers and amplitudes that provide the best fit to the measured data is posed as a nonlinear least squares problem in which the nonlinear and linear variables can be separated the maximum likelihood method is then used to solve this problem the method is demonstrated in simulations of infinite and finite plates and the effects of nearfields damping and measurement noise are investigated practical implementation issues including model deficiency model adequacy and determining convergence are discussed the method is then applied to experimental measurements on both a steel plate and a composite orthotropic panel and the results are compared with theoretical predictions it is shown that the proposed approach can give a good indication of the propagating wavenumber characteristics of lightly damped plates

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

a fourier analysis of spurious mechanisms and locking in the finite element method a fourier analysis technique is used to examine spurious mechanisms and the element locking phenomena engendered by different finite element discretizations it is shown that these phenomena can be identified by examining the uncoupled discrete fourier operators and corresponding characteristic equations and are caused in terms of discrete filter concepts by either a spurious mode carrier or by violating the unlocking condition specified in the paper the analysis is performed for two simple problems wave propagation in a bar and vibration of a timoshenko beam which when discretized by linear shape functions succinctly manifest the two phenomena as being directly traceable to specific components of the finite element discretizations

estimation of structural wave numbers from spatially sparse response measurements a method is presented for estimating the complex wave numbers and amplitudes of waves that propagate in damped structures such as beams plates and shells the analytical basis of the method is a wave field that approximates response measurements in an aperture where no excitations are applied at each frequency the method iteratively adjusts wave numbers to best approximate response measurements using wave numbers at neighboring frequencies as initial estimates in the search in comparison to existing methods the method generally requires far fewer measurement locations and does not require evenly spaced locations the number of locations required by the method scales with the number of waves that propagate in the structure whereas the number of locations required by existing methods scales with the minimum wavelength in addition the method allows convenient inclusion of the analytic relationships between wave numbers that exist for flexural vibrations of beams and plates advantages of the method are illustrated by an example in which a beam is excited by a transverse force at one end using analytic data and experimental measurements the method produces a wave field that matches response measurements to within 1 percent one interesting feature of the new method is that when applied to analytic data it supplies more robust wave number estimates using responses at unevenly spaced locations

galerkin generalized least squares finite element methods for time harmonic structural acoustics galerkin generalized least squares ggls finite element methods are developed and implemented for modeling the response of fluid loaded structures a general formalism for the application of this methodology to problems in structural acoustics the vibration of an elastic structure in contact with an acoustic medium is presented a consistent approach for the development and implementation of the design parameters inherent to the ggls methods for coupled problems is given this general methodology is then applied to an exterior problem of a fluid loaded reissner mindlin plate complex wave number dispersion analysis and numerical experiments demonstrate clearly the reduction of storage requirements and solution time of the new ggls methods over standard discretization techniques

periodic solutions of non autonomous second order systems with γ quasisubadditive potential abstract the existence of periodic solutions to non autonomous second order systems with quasisubadditive potential is proved with classical theorems of variational calculus

periodic solutions for a class of nonautonomous second order hamiltonian systems abstract in this paper some existence theorems of periodic solutions of a class of the nonautonomous second order hamiltonian systems x t b t x t h t x t 0 t 0 t are obtained by a mountain pass theorem and a local link theorem

acoustics of a fluid loaded plate with attached oscillators part i feynman rules the fuzzy structure paradigm developed by soize and others provides a framework within which the acoustic properties of systems with complex internal structure can be explored in this two part paper the acoustic properties of one of the simplest such systems a fluid loaded plate with attached internal oscillators are explored in part i the theoretical tools needed in this investigation the representation of the neumann series in terms of feynman diagrams is presented in most ways the formal aspects of this development are identical to similar results from other disciplines but the presence of damping in the system either internal or due to radiation into the fluid requires one to make some modifications to existing theories the rules for evaluating averaged quantities such as g gg g involving higher order products of the green s function are given these quantities are necessary to determine a number of relevant properties of the system including the scattering cross section and the size

effects of spatial discretization on dispersion and spurious oscillations in elastic wave propagation the dispersive and spurious oscillation properties of one dimensional uniform finite element meshes are investigated using the information provided by the frequency response functions of the finite element meshes the modal superposition method in which the effects of temporal discretization are eliminated is employed to integrate the discretized equations of motion