a symplectic analytical wave based method for the wave propagation and steady state forced vibration of rectangular thin plates abstract a semi analytical method is used to investigate the wave propagation characteristics and steady state forced vibration response for rectangular thin plates by way of a rigorous but simple derivation the governing differential equations for transverse vibration of rectangular thin plates are first converted into hamiltonian canonical equations following the method of separation of variables a symplectic eigenproblem is formed whose solution gives analytically the dispersion equation and the wave mode shape using the wave modes i e the wave propagation parameters and wave shapes and combining the directly excited waves the wave propagation within the plate and the wave reflection at the boundary the forced response of the plate can be computed in the wave domain with high precision and high efficiency the present method is based on the basic elasticity equations of the plate and can give the symplectic analytical solutions for the wave modes for any combination of simple boundary conditions along the plate edges the present method eliminates the limitation of the traditional analytical wave propagation method which can only obtain wave modes for plates with two opposite edges simply supported in contrast to numerical wave propagation methods the present method provides symplectic analytical solutions for the wave modes and hence the computations are of high precision and well conditioned also continuously distributed external forces can be easily considered in the numerical examples the wave propagation characteristics are analyzed for plates with three different combinations of boundary conditions i e with two opposite edges either both simply supported or both clamped or one simply supported and the other clamped the steady state forced responses are also computed for plates excited by point forces as well as for line and area distributed forces for the three combinations of boundary conditions comparison of the present results with analytical results wave finite element and finite element results validates the high accuracy and high efficiency of the present method

wave reflection from the free end of a cylinder with an arbitrary cross section elastic wave scattering at the free end of a cylinder due to an incident monochromatic wave is investigated the cross section may have an arbitrary geometry with any number of distinct elastic rectilinear anisotropic materials comprising its planar profile the governing equations are based on a semi analytical finite element method in which the cross sectional behavior is modeled by general two dimensional finite elements with the axial dependence and time left unspecified at the outset first all the modal data for the cylinder are established two eigenproblems are posed for this purpose that are obtained by inserting a wavelike solution form into the governing equations these eigenproblems allow all propagating waves and end modes for the cylinder to be determined propagating modes are traveling waves with energy transport capabilities while the end modes are standing vibrations which in contrast do not transport any energy into the interior of the cylinder these eigendata are the basis for representing the wave reflection phenomenon at the free end the amplitudes of the traveling waves and end modes that satisfy traction free end conditions may be determined by least squares minimization or by a virtual work method four cylinders with different cross sectional geometries were considered to illustrate the analysis procedure and reveal some physical insight into the frequency dependent wave reflection phenomena in them

stability and euler approximation of one sided lipschitz differential inclusions ordinary differential and functional differential inclusions with compact right hand sides are considered stability theorems of filippov s type in the convex and nonconvex case are proved under a one sided lipschitz condition which extends the notions of lipschitz continuity dissipativity and the uniform one sided lipschitz condition for set valued mappings the accuracy of approximation of the solution sets by means of the euler discretization scheme for both types of inclusions is estimated

polynomial particular solutions based boundary element analysis of acoustic eigenfrequency problems the boundary element formulation for acoustic eigenfrequency analysis based on treating the forcing function in the governing differential equation as an initially unknown distributed source within the domain is presented the volume integral due to this distributed source is eliminated by approximating the internal source by global interpolation and polynomial function representations and finding particular solutions for the governing inhomogeneous equations the resulting non symmetric system matrix is solved by using arnoldi s algorithm modified to take advantage of the special structure of the substructured boundary element method the techniques described here are embedded in a computer program gpbest and the numerical results are obtained by using this computer code

a spectral super element for modelling of plate vibration part 1 general theory the dynamic response of vibrating structures is studied with a proposed merger of the standard finite element method with the more computationally efficient spectral finite element method first a plate structure is modelled with a newly developed spectral super element then this element is coupled to other parts that can have a more complex geometry and are modelled entirely with conventional finite elements some numerical examples are given to illustrate and validate the developed method and studies of numerical stability are also presented in an accompanying paper the predicted and measured response of a turbulence excited aircraft panel are compared

a boundary element method for anisotropic inhomogeneous elasticity this paper is concerned with obtaining boundary integral equations for the numerical solution of the partial differential equations governing static deformations of inhomogeneous anisotropic elastic materials the elastic parameters for the inhomogeneous materials are assumed to vary continuously with the spatial variables

lanczos algorithm for the quadratic eigenvalue problem in engineering applications abstract a new approach of employing the lanczos two sided recursion to solve the quadratic eigenvalue problem is presented the methodology employed retains the n order quadratic problems as posed without the need to use the method of matrix augmentation traditionally used to cast the problem as a linear eigenvalue problem of order 2n pursuing the concept of finding a characteristic matrix to yield an eigenvalue square matrix the lanczos recursion has been devised to solve the quadratic eigenvalue problem appropriate proofs showing the lanczos biorthogonal transformation are included the example problems presented validate the algorithm and show the effectiveness of the method for large quadratic eigenproblems

formulation and solution of the non linear damped eigenvalue problem for skeletal systems this paper presents and discusses an arnoldi based eigensolution technique for evaluating the complex natural frequencies and mode shapes from frequency dependent quadratic eigenproblems associated with vibration analysis of damped structures the new solution technique is used in conjunction with a mixed finite element modelling procedure which utilizes both the polynomial and frequency dependent displacement fields in formulating the system matrices this modelling provides the ability to represent a frequency dependent damping matrix in vibration analysis of skeletal systems the eigensolution methodology presented here is based upon the ability to evaluate a specific set of parametrized curves for the non linear eigenvalue problem at given values of the parameter numerical examples illustrate that this method used in conjunction with a secant interpolation accurately evaluates the complex natural frequencies and modes of the quadratic non linear eigenproblem and verifies that the new eigensolution technique coupled with the mixed finite element modelling procedure is more accurate than the conventional finite element models

acoustic boundary element eigenproblem with sound absorption and its solution using lanczos algorithm a damped system eigenvalue analysis of acoustical cavities using the boundary element method is presented the acoustic boundary element eigenproblem formulation found in the literature is extended to include sound absorption in acoustical cavities a dissipative term is included in the eigenvalue matrix equation to account for boundary absorption the resulting damped system eigenvalue problem is solved using a new lanczos subspace algorithm for quadratic eigenproblems since the boundary element matrices are unsym metric the lanczos algorithm presented is in its most general form for unsymmetric quadratic eigenprob lems examples are presented to show the application of the method in computing the eigenfrequencies of acoustic cavities with sound absorption

dynamic dispersion curves for non homogeneous anisotropic beams with cross sections of arbitrary geometry abstract to accurately predict the dynamic behaviour of spanwise uniform non homogeneous anisotrophic beams with arbitrary cross sectional geometry is an important part of engineering analysis classical one dimensional beam theory fails in this endeavour and development of more sophisticated one dimensional theories is an important task a basis for development of improved one dimensional theory is the dispersion curve analysis a means to find the dispersion curves is discussed in this paper the code is developed to calculate the dispersion curves as well as corresponding mode shapes the code is based on finite element discretization over the cross sectional domain use of this code provides benchmark results for the testing of any existing one dimensional theory as well as facilitating the construction of new one dimensional theories dispersion information can also be useful in non destructive evaluation as an example of a case where non classical effects are particularly important results obtained from this code for an i beam are presented qualitative comparisons with the well known case of isotropic rectangular beam is provided features that are common for all beams are emphasized along with pointing out qualitative differences that exist for beams other than rectangular or circular

a refined use of the residue theorem for the evaluation of band averaged input power into linear second order dynamic systems abstract in a recent work a strategy was proposed which exploits the residue theorem as an efficient tool for evaluating the frequency averaged input power into vibrating systems in this paper such a technique is generalised and further insight and improvements are presented evaluating band averages requires the solution of a weighted integral over a real frequency variable in this paper the integration path is moved to the complex plane where the input mobility shows a smoother behaviour consequently a smaller number of quadrature points are needed to perform an accurate integration which leads to a significant reduction of computational time in addition the connection between the use of quadrature rules in the complex plane and weighting functions on real frequencies is considered two application examples prove the accuracy of the present strategy for different quadrature rules adaptive integration schemes are also investigated

computation of propagative waves in free rail using a finite element technique abstract a method is presented for the numerical computation of the wavenumbers and associated modes of the cross section of solid waveguides the method based on the finite element technique is well suited to the computation of both the propagative and the evanescent waves in a straight waveguide with an arbitrary cross section the solution is obtained by factorization with the cross section of the waveguide being modelled by numerical discretization the dispersion curves of propagative waves in a free rail are computed by using triangular and quadrilateral finite elements of the cross section the evolution of cross section modes as the frequency increases is evaluated and discussed

an asymptotically correct model for initially curved and twisted thin walled composite beams abstract the variational asymptotic method has been applied to develop an asymptotically correct model for initially curved and twisted thin walled composite beams of arbitrary cross sectional shapes and arbitrary anisotropic materials in a two step asymptotic reduction procedure the three dimensional strain energy is asymptotically reduced first to a two dimensional shell strain energy and then to a one dimensional beam strain energy this is a new attempt where initially curved and twisted thin walled composite beams with open or closed sections have been modeled in an asymptotically correct unified framework

micromechanical modeling of transient waves from matrix cracking and fiber fracture in laminated beams abstract a micromechanical model for excitation of waves resulting from fiber fracture and matrix cracking in laminated beams is presented the source is described as a time dependent displacement discontinuity and the wave propagation in the beam is modeled by a higher order beam theory the equations of motion defined by the beam model are then formally solved by employing integral transforms asymptotically valid solutions are subsequently found using residue calculus and the stationary phase method as an example a 90 0 2 90 beam with a width to thickness ratio of 10 is considered the dispersion curves resulting from the beam theory and three dimensional finite element computations are compared and a maximum frequency for applicability of the beam theory is determined the time response from fiber fracture and transverse matrix cracking is presented the applications of the results to the analysis of acoustic emission experiments are also discussed

wave scattering by cracks in inhomogeneous continua using biem elastic wave scattering by cracks in inhomogeneous geological continua with depth dependent material parameters and under conditions of plane strain is studied in this work a restricted case of inhomogeneity is considered where poisson s ratio is fixed at one quarter while both shear modulus and density profile vary with depth but proportionally to each other furthermore time harmonic conditions are assumed to hold for this type of material the body wave speeds remain macroscopically constant and it becomes possible to recover exact green functions for the crack free inhomogeneous continuum by using an algebraic transformation method proposed in earlier work as a first step in a subsequent step the complete elastodynamic fundamental solution along with its spatial derivatives and an asymptotic expansion for small argument are all derived in closed form using the radon transform next a non hypersingular traction based boundary integral equation method biem formulation for solving boundary value problems with internal cracks is presented specifically the biem is used for computing stress intensity factors and scattered wave displacement amplitudes for an inclined line crack in an otherwise inhomogeneous continuum that is being swept by either pressure waves or vertically polarized shear waves at an arbitrary angle of incidence with respect to the horizontal direction the numerical results obtained herein reveal substantial differences between homogeneous and continuously inhomogeneous materials containing a crack in terms of their dynamic response where the latter case is assumed to give a more realistic representation of geological deposits compared to the former one finally these types of examples plus the benchmark case used for validation serve to illustrate the present approach and to show its potential for solving complex problems not just in geophysics but also in mechanics

finite element analysis of the vibrations of waveguides and periodic structures many structural components can be regarded as waveguides they are uniform in one direction so that the cross section of the waveguide has the same physical and geometric properties at all points along the axis of the waveguide in this paper a method is presented to calculate the forced response of such a structure using a combination of wave and finite element fe approaches the method involves post processing a conventional but low order fe model in which the mass and stiffness matrices are typically found using a conventional fe package a section of the waveguide is meshed and the eigenvalues and eigenvectors of the resulting transfer matrix found the eigenvectors form a set of basis functions for the analysis of the structure as a whole allowing the global dynamic stiffness matrix to be built easily and then the forced response to be calculated very efficiently the main advantage of the approach over the alternative waveguide fe approach often termed the spectral fe method is that conventional fe packages can be used to form the stiffness and mass matrices so that structures with complex geometries or material distributions can be analysed with relative ease to demonstrate the efficacy of the method examples of the forced response for a finite beam and plate strip are presented

on the use of the residue theorem for the efficient evaluation of band averaged input power into linear second order dynamic systems abstract an alternative to numerical quadrature is proposed to compute the power injected into a vibrating structure over a certain frequency band instead of evaluating the system response at several sampling frequencies within the considered band the integral is computed by estimating the residue at a few complex frequencies corresponding to the poles of the weighting function this technique provides considerable benefits in terms of computation time since the integration is independent of the width of the frequency band two application examples show the effectiveness of the approach firstly the use of a butterworth filter instead of a rectangular weighting function is assessed secondly the accuracy of the approximation in case of hysteretic damping is proven finally the computational performance of the technique is compared with classical numerical quadrature schemes

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

best strip beam properties derivable from classical lamination theory this paper presents a simple method to extract classical beam properties for composite strips with general anisotropy from an asymptotically correct classical lamination theory derived using the variational asymptotic method none of the ad hoc approximations common in the literature of beam theory are used rather this approach discovers the necessary and su cient engineering assumptions for obtaining the correct cross sectional constants and stress recovery relations for a strip numerical examples are provided to illustrate that the resulting theory resulting elastic constants agree well with those from well established methods of calculating cross sectional constants and the accuracy deteriorates as the strip thickness to width ratio increases

development of a block lanczos algorithm for free vibration analysis of spinning structures this paper is concerned with the development of an efficient eigenproblem solution algorithm and an associated computer program for the economical solution of the free vibration problem of complex practical spinning structural systems thus a detailed description of a newly developed block lanczos procedure is presented in this paper that employs only real numbers in all relevant computations and also fully exploits sparsity of associated matrices the procedure is capable of computing multiple roots and proves to be most efficient compared to other existing similar techniques

propagating waves and edge vibrations in anisotropic composite cylinders the entire dispersive spectra of a cylinder with cylindrical anisotropy are determined from three different algebraic eigenvalue problems deducible from the same finite element formulation the displacement vector v in this version of the finite element method has the form f r exp i ez n t with the radial dependence f r taken as quadratic interpolation polynomials therefore this discretization procedure allows a cylinder with radially inhomogeneous material properties to be modeled the three different algebraic eigenvalue problems that emerge depend on whether the axial wave number e or the natural frequency is regarded as the eigenvalue parameter and on the real purely imaginary or complex nature of e for e specified as real an eigenvalue problem results for the natural frequencies i for waves propagating along the z direction of a cylinder of infinite extent when e is specified to be purely imaginary then an algebraic eigenvalue problem governing the edge vibrations end modes of a semi infinite cylinder is obtained the third eigenvalue problem can be obtained by considering to be prescribed and regarding e as the eigenvalue parameter the algebraic eigenvalue problem that results is quadratic in the eigenvalue parameter and admits solutions for e which may be real purely imaginary or complex complex e s correspond to edge vibrations in a cylinder which are exponentially damped trigonometric wave forms moreover for the case 0 the eigenvalue analysis yields e as the characteristic inverse decay lengths for systems of elastostatic self equilibrated edge effects in the context of st venant s principle all the eigenvalue problems are solved by efficient techniques based on subspace iteration examples of two four layer angle ply cylinders are presented to illustrate this comprehensive finite element analysis

free vibration analysis of civil engineering structures by component wise models abstract higher order beam models are used in this paper to carry out free vibration analysis of civil engineering structures refined kinematic fields are developed using the carrera unified formulation cuf which allows for the implementation of any order theory without the need for ad hoc formulations the principle of virtual displacements in conjunction with the finite element method fem is used to formulate stiffness and mass matrices in terms of fundamental nuclei the nuclei depend neither on the adopted class of beam theory nor on the fem approximation along the beam axis this paper focuses on a particular class of cuf models that makes use of lagrange polynomials to discretize cross sectional displacement variables this class of models are referred to as component wise cw in recent works according to the cw approach each structural component e g columns walls frame members and floors can be modeled by means of the same 1d formulation a number of typical civil engineering structures e g simple beams arches truss structures and complete industrial and civil buildings are analyzed and cw results are compared to classical beam theories euler bernoulli and timoshenko refined beam models based on taylor like expansions of the displacements on the cross section and classical solid shell fem solutions from the commercial code msc nastran the results highlight the enhanced capabilities of the proposed formulation it is in fact demonstrated that cw models are able to replicate 3d solid results with very low computational efforts

approximate determination of dispersion relations and displacement fields associated with elastic waves in bars method based on matrix formulation of hamiltons principle a method for approximate determination of dispersion relations and displacement fields associated with elastic waves in long prismatic bars is established the method is based on a matrix formulation of hamilton s principle and utilizes co ordinate functions to model the displacements in the bar the method which involves the solution of an eigenvalue problem is suitable for use in a mathematical toolbox it is applied to wave propagation in bars with square and circular cross sections the results obtained agree well with the known exact and approximate solutions the convergence rate is illustrated by systematically changing the order of the co ordinate functions

fuzzy differential equations without fuzzy convexity classical fuzzy differential equations defined in terms of the hukuhara derivative depend critically on the convexity of the level sets and result in expanding level sets here hullermeier s suggestion of defining fuzzy differential equations at each level set via differential inclusions is combined with ideas of aubin on morphological equations which allow nonlocal set evolution to remove the assumption of fuzzy convexity and thus to allow fuzzy differential equations to be defined for non convex level sets this approach uses reachable sets as a more general form of set integration and in contrast to the aumann set integral does not necessarily give rise to convex sets the results presented in this paper are even more general since they concern fuzzy sets that need to be only closed without additional assumptions of convexity compactness or even normality in particular an existence and uniqueness theorem is established under the assumption that the right hand sides satisfy a one sided lipschitz condition rather than a much stronger lipschitz condition fuzzy delay differential equations are also considered from this new perspective

continuous selection of the solution map for one sided lipschitz differential inclusions abstract in the paper we deal with differential inclusions with one sided lipschitz osl continuous right hand sides and prove the existence of a continuous selection of the solution map which assigns to any point the set of solutions to the multivalued cauchy problem as an application we study the problem of the existence of viable trajectories in a prescribed closed subset of a banach space via the generalized wazewski retract method

elastodynamic green s functions for a smoothly heterogeneous half space in this paper the response of a vertically heterogeneous elastic half space with a smooth modulus variation under a set of time harmonic ring and point sources is derived analytically a method of evaluation via asymptotic decomposition for the singular green s functions is presented in the technique the green s functions are decomposed into an analytical part and a residual component capturing the corresponding singular behavior the analytical parts of the ring and point load green s functions are expressible in terms of the elliptic integrals and algebraic functions respectively the residual integrals which are regular can be evaluated by numerical contour integration to obtain correct results one must note and take into account the existence of multiple poles along the formal path of the inversion integrals the details of which are discussed in the paper to highlight the various aspects of the physical problem a set of illustrative numerical results is included

validation of the variational asymptotic beam sectional analysis the computer program vabs variational asymptotic beam section analysis uses the variational asymptotic method to split a three dimensional nonlinear elasticity problem into a twodimensional linear cross sectional analysis and a one dimensional nonlinear beam problem this is accomplished by taking advantage of certain small parameters inherent to beam like structures vabs is able to calculate the one dimensional cross sectional stiffness constants with transverse shear and vlasov refinements for initially twisted and curved beams with arbitrary geometry and material properties several validation cases are presented first an elliptic bar is modeled with transverse shear refinement using the variational asymptotic method and the solution is shown to be identical to that obtained from the theory of elasticity the shear center locations calculated by vabs for various cross sections agree well with those obtained from common engineering analyses comparisons with other composite beam theories prove that it is unnecessary to introduce ad hoc kinematic assumptions to build an accurate beam model for numerical validation values of the one dimensional variables are extracted from an abaqus model and compared with results from a one dimensional beam analysis using cross sectional constants from vabs furthermore point wise three dimensional stress and strain fields are recovered using vabs and the correlation with the three dimensional results from abaqus is excellent finally classical theory is shown to be insufficient for general purpose beam modeling appropriate refined theories are recommended for some classes of problems

hereditarily hypercyclic operators abstract we show that a continuous linear operator t on a frechet space satisfies the so called hypercyclicity criterion if and only if it is hereditarily hypercyclic and if and only if the direct sum t t is hypercyclic in particular hypercyclic operators with either a dense generalized kernel or a dense set of periodic points i e chaotic in the sense of r l devaney 1989 an introduction to chaotic dynamical systems addison wesley reading ma must satisfy the criterion finally we provide a characterization of those weighted shifts t that are hereditarily hyper cyclic with respect to a given sequence n k of positive integers as well as conditions under which t and t n k k 1 share the same set of hypercyclic vectors

discrete approximations and fixed set iterations in banach spaces we study autonomous differential inclusions with right hand sides satisfying a one sided lipschitz osl condition in banach spaces with uniformly convex duals we first show that the solution set is closed and obtain estimates for euler type discrete approximations we then use these results to derive an analogue of the exponential formula for the reachable set as well as results regarding the existence and approximation of a strongly invariant attractor in the case of a negative osl constant as a by product conditions for controllability of the reverse time system are obtained

singular perturbations in infinite dimensional control systems in this paper we consider a singularly perturbed control system involving differential inclusions in banach spaces with slow and fast solutions using the averaging approach we obtain sufficient conditions for the hausdorff convergence of the set of slow solutions in the supremum norm we present applications of the theorem to prove convergence of the fast solutions in terms of invariant measures and convergence of equi lipschitz solutions

energy flow models from finite element analysis computationally efficient methods are described by which the results of a finite element analysis of a system may be post processed to form energy flow models yielding time and perhaps frequency average subsystem energies as well as input and dissipated powers the methods are particularly efficient for excitation which is spatially distributed or broadband e g rain on the roof or if the frequency average response is required first a method based on a global finite element analysis is presented this involves a global modal decomposition and a reordering of the subsequent numerical calculations the properties of the distribution of the excitation and the system s mass and stiffness lead to subsystem force distribution mass distribution and stiffness distribution matrices the response is given by a sum of terms involving the interaction of a pair of global modes the contribution of each pair depending on the appropriate elements of the distribution matrices frequency averaging is performed by separating the resulting frequency dependent terms and integrating in most practical cases this integration can be done analytically next an alternative method involving component mode synthesis is described in this individual finite element analyses are performed for each subsystem using here the fixed interface method these are then assembled to perform a global modal analysis with the order of the model being much reduced the consequent results are then post processed in the same way finally a system comprising three coupled plates is presented as a numerical example

existence of hypercyclic operators on topological vector spaces the present paper introduces a very simple but very useful notion of the so called quasi extension ofl1 operators and proves that a large class of topological vector spaces admit continuous hypercyclic operators in particular it answers in the affirmative a question of s rolewicz posed in 1969 whether or not every infinite dimensional separable banach space admits a continuous hypercyclic operator

methods for overcoming breakdown problems in the unsymmetric lanczos reduction method the unsymmetric lanczos reduction ulr method is developed to solve the finite element based solution to the contaminant transport problem the method sometimes suffers from breakdown when at some step division by a pivot which is zero or near zero causes numerical instability in this paper the maximum pivot new start vector method is developed to overcome such breakdowns by constructing a new starting vector with the possible maximum pivot some cases of instability cannot be remedied by this approach pathological breakdowns and the switch method is developed to complete the solution by changing the algorithm to an arnoldi reduction approach investigation of some two dimensional examples and field problems illustrates the efficiency of the methods and substantial time savings over other existing solution methods 1998 john wiley sons ltd

discrete approximations relaxation and optimization of one sided lipschitzian differential inclusions in hilbert spaces we study discrete approximations of nonconvex differential inclusions in hilbert spaces and dynamic optimization optimal control problems involving such differential inclusions and their discrete approximations the underlying feature of the problems under consideration is a modified one sided lipschitz condition imposed on the right hand side i e on the velocity sets of the differential inclusion which is a significant improvement of the conventional lipschitz continuity our main attention is paid to establishing efficient conditions that ensure the strong approximation in the w1 p norm as p 1 of feasible trajectories for the one sided lipschitzian differential inclusions under consideration by those for their discrete approximations and also the strong convergence of optimal solutions to the corresponding dynamic optimization problems under discrete approximations to proceed with the latter issue we derive a new extension of the bogolyubov type relaxation density theorem to the case of differential inclusions satisfying the modified one sided lipschitzian condition all the results obtained are new not only in the infinite dimensional hilbert space framework but also in finite dimensional spaces

exact finite elements for wave propagation in range independent fluid solid media abstract a finite element technique fem is proposed for solving the two point ordinary differential equation ode boundary value problem for the wavefield in a layered horizontally homogeneous fluid solid medium at fixed horizontal wavenumber k the medium may consist of an arbitrary mixture of fluid and solid layers bounded at both ends by homogeneous half spaces in homogeneous layers the fem basis functions are chosen to be exact local solutions of the governing source free ode s and in a medium composed of homogeneous layers only the overall solution at fixed horizontal wavenumber k is exact without subdivision of the layers in layers with non constant material parameters standard second order accurate linear elements are used the fem stiffness matrix is symmetric with dimension and bandwidth essentially half of those obtained with a parallel shooting global matrix technique the stiffness matrix remains bounded and well conditioned as the lengths of exact elements grow and it can in general be decomposed into triangular factors without scaling or pivoting which contributes significantly to computational efficiency the use of the finite element technique for wavefield synthesis by hankel transform integration or by normal mode expansion is discussed in both cases general purpose numerical quadrature and zero finding techniques can be used if proper care is taken of the poles of the stiffness matrix in the complex k plane a pole free dispersion function efficiently computable from the fem stiffness matrix is derived a simple but useful general result in the theory of non linear eigenvalue problems for matrices is pointed out and used for computing the excitation coefficients of the modes of the discretized system the usefulness of the method is illustrated by presenting numerical results from a computationally intensive application example

structural dynamics analysis using an unsymmetric block lanczos algorithm this paper describes the way in which an unsymmetric block lanczos algorithm can be employed for approximate eigensolutions or dynamic response solutions for large systems having arbitrary damping and or repeated or closely spaced eigenvalues to reduce a square unsymmetric matrix which may have repeated eigenvalues to block tridiagonal form an unsymmetric block lanczos algorithm is developed right and left lanczos vectors generated by the reduction process are employed to define the reduced order model based on a discrete analytical model of general linear time invariant dynamic systems a special type of starting vector is also introduced which automatically includes the static displacement this reduced order model is employed to compute approximate eigenvalues vectors and dynamic responses of the original system to verify the proposed algorithm examples of an 8 dof beam rotor system are provided for eigensolutions and dynamic responses due to step and random external forces these examples showed promising results indicating that the proposed algorithm is worthy of further study

periodic solutions for semi linear evolution inclusions in this paper we study the periodic problem for semi linear evolution inclusion using techniques from multivalued analysis and fixed point theorems we establish existence theorems under the one sided lipschitz condition first we prove existence theorems for nonconvex and convex problem second we look for extremal periodic solutions and prove the relaxation theorem

numerical modeling of acoustic emission in laminated tensile test specimens abstract acoustic emission from transverse matrix cracks and fiber fracture in typical laminated tensile test specimens is modeled the acoustic sources are described as time dependent displacement discontinuities which subsequently are translated to volume forces the transient waves are computed using a finite element model of the specimen s cross section the finite element modeling leads to a system of differential equations in the axial coordinate and time the differential equations are solved using fourier transforms and eigenmode superposition followed by inversion of the transforms through residue calculus and fft computed time histories for matrix cracking and fiber fracture are presented the highest frequency content in these signals corresponds typically to 300 khz a method to measure the average matrix crack propagation velocity is suggested

frequency division method for ae source characterization this paper describes a new algorithm based on a frequency division method by which a solution to the inverse source problem of acoustic emission can be obtained the algorithm is applicable to cases in which the acoustic emission signal can be expressed as a bilinear equation involving weighted green s functions or its spatial derivatives convolved with a common source time function through division of the detected signals in the frequency domain the common source time function is eliminated and the ratios of the weighting constants can be recovered by solving a set of linear equations using these recovered ratios the source time function can be found from the signal at any receiver point application of this algorithm is made to process the signals simulating the formation of a microcrack in an elastic plate modeled with a second order moment tensor dynamic information about the source is recovered by processing the signals at two receiver points if four receivers are used the second order tensor can be recovered at each frequency of the recorded signals additional information about the source can be extracted by diagonalizing and rotating the recovered moment tensor the effect of noise on the inversion scheme is also considered

on asymptotically correct linear laminated plate theory abstract the focus of this paper is the development of asymptotically correct theories for laminated plates the material properties of which vary through the thickness and for which each lamina is orthotropic this work is based on the variational asymptotical method a mathematical technique by which the three dimensional analysis of plate deformation can be split into two separate analyses a one dimensional through the thickness analysis and a two dimensional plate analysis the through the thickness analysis includes elastic constants for use in the plate theory and approximate closed form recovering relations for all three dimensional field variables expressed in terms of plate variables in general the specific type of plate theory that results from this procedure is determined by the procedure itself however in this paper only reissner like plate theories are considered often called first order shear deformation theories this paper makes three main contributions first it is shown that construction of an asymptotically correct reissner like theory for laminated plates of the type considered is not possible in general second a new point of view on the variational asymptotical method is presented leading to an optimization procedure that permits a derived theory to be as close to asymptotical correctness as possible third numerical results from such an optimum reissner like theory are presented these results include comparisons of plate displacement as well as of three dimensional field variables and are the best of all extant reissner like theories indeed they even surpass results from theories that carry many more generalized displacement variables

structural optimization with frequency constraints by genetic algorithm using wavelet radial basis function neural network abstract in this study a combination of genetic algorithm ga and neural networks nn is proposed to find the optimal weight of structures subject to multiple natural frequency constraints the optimization is carried out by an evolutionary algorithm using discrete design variables the evolutionary algorithm employed in this investigation is virtual sub population vsp method to reduce the computational time of optimization process the natural frequencies of structures are evaluated using properly trained radial basis function rbf and wavelet radial basis function wrbf neural networks in the wrbf neural network the activation function of hidden layer neurons is substituted with a type of wavelet functions in this new network the position and dilation of the wavelet are fixed and only the weights are optimized the numerical results demonstrate the robustness and high performance of the suggested methods for structural optimization with frequency constraints it is found that the best results are obtained by vsp method using wrbf network

fixed set iterations for relaxed lipschitz multimaps abstract a dynamical system described by an autonomous differential inclusion with a right hand side satisfying a relaxed lipschitz condition as well as its euler approximations are studied we investigate the asymptotic properties of the solutions and of the attainable sets it is shown that the system has a strongly flow invariant set or a fixed set that is a set such that each trajectory starting from it does not leave it this set is also an attractor i e it attracts the continuous and the discrete euler trajectories as the time tends to infinity we give estimates of the rate of attraction an algorithm for approximating the fixed set by the attainable sets of the discrete system is also presented

powerful fe approaches for pochhammer s dispersion modelling simple and very effective finite element approaches for modelling of the dispersion of torsional longitudinal and flexural waves propagated in infinite and elastic cylindrical bars pochhammer s problem and hollow cylinders are presented the approaches allow one to model given problems without using infinite elements and their usage is demonstrated by using dispersion curves shapes of waves and tables of phase velocities comparison of finite element solutions solved in one task from small sized models with exact solutions shows an excellent agreement the maximum relative differences among the 20 lowest fem and analytical phase velocities was less than 0 000015 the approaches and results hold also for cylinders with finite lengths simply supported on both ends copyright 2003 john wiley sons ltd

guidelines and recommendations to construct theories for metallic and composite plates this work has evaluated the refinement of some classical theories such as the kirchhoff and reissner mindlin theories adding generalized displacement variables up to fourth order to the taylor type expansion in the thickness plate direction isotropic orthotropic and laminated plates have been analyzed varying the thickness ratio orthotropic ratio and stacking sequence of the layout higher order theories have been implemented according to the compact scheme known as the carrera unified formulation the results have been restricted to simply supported orthotropic plates subjected to harmonic distributions of transverse pressure for which closed form solutions are available for a given plate problem isotropic orthotropic or laminated the effectiveness of each employed generalized displacement variable has been established comparing the error obtained accounting for and removing the variable in the plate governing equations a number of theories have therefore been constructed imposing a given error with respect to the available best results guidelines and recommendations that are focused on the proper selection of the displacement variables that have to be retained in refined plate theories are then furnished it has been found that the terms that have to be used according to a given error vary from problem to problem but they also vary when the variable that has to be evaluated displacement stress components is changed diagrams errors in terms of geometrical and orthotopic ratios and graphical schemes have been built to establish the appropriate theories with respect to the data of the problem under consideration

a look ahead lanczos algorithm for unsymmetric matrices abstract the two sided lanczos algorithm is known to suffer from serious breakdowns these occur when the associated moment matrix does not permit triangular factorization we modify the algorithm slightly so that it corresponds to using a 2 x 2 pivot in triangular factorization whenever a 1 x 1 pivot would be dangerous the incidence of breakdown is greatly reduced the price paid is that the tridiagonal matrix produced by the algorithm now has bumps whenever a 2 x 2 pivot is used author

a recursive approach for the finite element computation of waveguides abstract the finite element computation of structures such as waveguides can lead to heavy computations when the length of the structure is large compared to the wavelength such waveguides can in fact be seen as one dimensional periodic structures in this paper a simple recursive method is presented to compute the global dynamic stiffness matrix of finite periodic structures this allows to get frequency response functions with a small amount of computations examples are presented to show that the computing time is of order log 2 n where n is the number of periods of the waveguide

propagating waves and end modes in pretwisted beams abstract a method is presented for studying propagating waves and end modes in a uniformly pretwisted beam the variationally derived equations of motion are based on three dimensional elasticity and finite element modelling of the cross section this discretization procedure accommodates arbitrarily shaped cross sections of inhomogeneous anisotropic material properties that follow the pretwist rotation rate an harmonic solution form in both timetand axial co ordinate is introduced i e exp i k t resulting in a two parameter algebraic eigensystem by specifying the axial wavenumberk the eigenproblem permits real frequencies of propagating modes to be determined by specifying real frequency both real and complex axial wavenumbers can be extracted where real values pertain to propagating modes and the complex ones to edge vibrations or end modes due to pretwist the effect of extension torsion and flexural are coupled examples of homogeneous isotropic beams with rectangular and square cross sections are given to illustrate the method of analysis and the physical behavior

the usage of standard finite element codes for computation of dispersion relations in materials with periodic microstructure a method with which standard finite element programs can be used to compute dispersion relations in periodic composites is proposed the method is applied to two composite microstructures a two phase laminate and a fiber composite the dispersion relations computed for the laminate are compared with a known analytical solution and the agreement is very good the dispersion relations computed for the fibrous composite are compared with an existing approximate model and experimental results from the literature the agreement between the approximate model the experiments and the computations is very good in the wave guide case and satisfactory for the wave reflect case

the lanczos biorthogonalization algorithm and other oblique projection methods for solving large unsymmetric systems many powerful methods for solving systems of equations can be regarded as projection methods most of the projection methods known for solving linear systems are orthogonal projection methods but little attention has been given to the class of nonorthogonal or oblique projection methods which is particularly attractive for large nonsymmetric systems the purpose of the paper is to present some methods in the general setting of oblique projection methods and to give some theoretical results some experiments comparing the various algorithms are reported

hypercyclicity and chaotic left multiplication mappings on operator spaces let x be a separable infinite dimensional banach space and b x b e the algebra of all bounded linear operators on x for any t b x define a left multiplication mapping lt b x b x b ylt v tv v b x we give a hypercyclicity criterion on b x and in addition if x is a banach space with a symmetric basis we give a similar criterion on its dual space x we also investigate the connections between hypercyclic and chaotic behavior of lt on b x and that of t on x and prove that t is chaotic in the sense of devaney if and only if the left multiplication operator lt is chaotic

dynamic condensation in a damped system through rational selection of primary degrees of freedom abstract various system reduction methods have been proposed to calculate eigenvalues and eigenvectors with computational efficiency in the case of system condensation the method of selecting proper primary degrees of freedom pdofs is crucial because they are closely related to the accuracy and reliability of eigensystem prediction in a reduced system although reasonable selection methods for pdofs have been proposed for undamped systems these methods cannot be directly extended to damped systems we propose a pdof selection method for a damped system the proposed method is based on the ratio of dof wise energy distributions in order to estimate the energy distribution of the structure ritz vectors are obtained using a two sided lanczos algorithm energy distribution matrices are calculated from the obtained ritz vectors then degrees of freedom dofs corresponding to the lowest rayleigh quotients are selected as the pdofs the efficiency and reliability of the proposed method are demonstrated using numerical examples

on the power input to point loaded hysteretically damped structures abstract the power input to point loaded hysteretically damped one and two dimensional structures is investigated both uniform and periodic structures are considered and in each case the input power is expressed in terms of the solutions of the damped dispersion relation in the case of a one dimensional periodic structure for example it is found that the input power is directly proportional to the rate of change of the phase constant with frequency an established approximate formula states that the power input to a structure is independent of damping and proportional to the modal density by considering the specific cases of a beam on multiple supports and a cylindrical shell it is shown here that the damping can significantly affect the input power

finite element computation of dispersion properties of thin walled waveguides abstract a method is presented for the numerical computation of the wavenumbers and associated modes of the cross section of thin walled waveguides the method is based on finite element techniques a thin shell type finite element of the cross section is developed by using the virtual work formulation for one dimensional propagation the case of a waveguide the set of equations of motion evaluated by finite element discretization is then transformed into a simple eigenvalue problem involving a general real matrix two examples are analyzed by the finite element method developed the circular cylindrical shell straight thin walled pipe and the thin walled beam of i shaped cross section the so called i profile results obtained by the finite element method by donnell s shell theory and by using simple euler bernoulli beam theory are compared

dynamic stiffness for structures with distributed deterministic or random loads abstract the dynamic stiffness method applies mainly to excitations of harmonic nodal forces for distributed loads modal analysis is generally required in the case of a clamped clamped beam the modal decomposition of a uniformly distributed load by the eigenbeam functions inherits slow convergence because the finite loads at the beam ends cannot be represented efficiently by the zero deflection and zero slope of the clamped clamped beam functions the computed reactions at the supports do not converge at all the problem is eliminated in this paper by using the finite element interpolation functions for the distributed load if the distributed load is adequately represented explicit exact solutions are found otherwise the residual load is expanded in the modal space as the residual modal force is much smaller and agrees well with the clamped clamped conditions fast convergence is achieved by means of the principle of superposition a structure with members having distributed loads can be analyzed by two systems one is associated with the individual members having distributed loads and the other is associated with resulting equivalent nodal forces the required frequency functions are given for all possible cases the results presented are exact if the load is interpolated adequately by finite element shape functions both deterministic and random loads are considered closed form solutions are obtained for the first time

asymptotic theory for static behavior of elastic anisotropic i beams abstract end effects for prismatic anisotropic beams with thin walled open cross sections are analyzed by the variational asymptotic method the decay rates for disturbances at the ends of prismatic beams are evaluated and the most influential end disturbances are incorporated into a refined beam theory thus the foundations of vlasovs theory as well as restrictions on its applicability are obtained from the variational asymptotic point of view vlasovs theory is proved to be asymptotically correct for isotropic i beams the asymptotically correct generalization of vlasovs theory for static behavior of anisotropic beams is presented in light of this development various published generalizations of vlasovs theory for thin walled anisotropic beams are discussed comparisons with a numerical 3 d analysis are provided showing that the present approach gives the closest agreement of all published theories the procedure can be applied to any thin walled beam with open cross sections

polynomial level set method for polynomial system reachable set estimation in this paper we present a polynomial level set method for advecting a semi algebraic set for polynomial systems this method uses the sub level representation of sets the problem of flowing these sets under the advection map of a dynamical system is converted to a semi definite program which is then used to compute the coefficients of the polynomials the method presented in this paper does not require either the sets being positively invariant or star shaped hence the proposed algorithm can describe the behavior of system states both inside and outside the domain of attraction and can also be used to describe more complex shapes of sets we further address the related problems of constraining the degree of the polynomials various numerical examples are presented to show the effectiveness of advection approach

spectral finite element analysis of the vibration of straight fluid filled pipes with flanges spectral finite element analysis of the vibration of straight fluid filled pipes with flanges

application of the spectral finite element method to turbulent boundary layer induced vibration of plates the spectral finite element method and equally the dynamic stiffness method use exponential functions as basis functions thus it is possible to find exact solutions to the homogeneous equations of motion for simple rod beam plate and shell structures normally this restricts the analysis to elements where the excitation is at the element ends this study removes the restriction for distributed excitation that in particular has an exponential spatial dependence by the inclusion of the particular solution in the set of basis functions these elementary solutions in turn build up the solution for an arbitrary homogeneous random excitation a numerical implementation for the vibration of a plate excited by a turbulent boundary layer flow is presented the results compare favourably with results from conventional modal analysis

transient elastic wave analysis of 3 d large scale cavities by fast multipole bem using implicit runge kutta convolution quadrature abstract existing boundary element methods bems have been proven to be efficient numerical techniques particularly in modeling wave propagation problems but still remain limitations in solving large scale problems the main disadvantages may be caused by several problems including high cost and large amount of computer memory for the computation a time domain bem in which a collocation method is used for the time discretization also shows numerical instability for small cfl courant friedrichs lewy number in this work we propose a new three dimensional 3 d approach for solving transient elastic wave propagation problems of large scale spherical and spheroidal cavities by the convolution quadrature bem accelerated by fast multipole method fmm using an implicit runge kutta scheme in abbreviation we name it as irk based cq fmbem two special techniques pertaining to the fmm including the scaling of modified spherical bessel functions and the truncation method are used to enhance the efficiency and stability of our proposed method this approach is found to be particularly suitable for 3 d large scale problems as its high accuracy stability of time marching process and computational efficiency these properties are subsequently illustrated through numerical examples dealing with large scale wave problems of 3 d single spherical and spheroidal cavities and multiple equally and irregularly spherical cavities the accuracy of the present formulation is verified by comparing the obtained results with available reference solutions in the literature some numerical aspects of time increments sizes and topological shapes of cavities and their influences on the deformations and the waveforms are investigated also detailed investigation of the computational efficiency of our proposed method such as cpu time required memory etc is presented all the implementation tasks are carried out using the tokyo tech supercomputer which is called tsubame 2 5 42

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

a peano theorem for fuzzy differential equations with evolving membership grade abstract the peano theorem on the existence without possible uniqueness of solutions has been a perplexing problem in the theory of fuzzy differential equations the difficulty appears to be due to the standard use of the supremum metric defined by the supremum over the hausdorff metric between the level sets of the fuzzy sets another may have been the classical formulation of fuzzy differential equations in terms of the hukuhara derivative of the level sets here a peano theorem is established for fuzzy differential equations formulated in a recent paper by the authors by combining hullermeier s suggestion of defining fuzzy differential equations at each level set via differential inclusions with aubin s morphological equations which allow non local set evolution a major difference from previous publications is the use of the endograph metric end essentially the hausdorff metric between the endographs in r n 0 1 of fuzzy sets instead of the supremum metric another is that the membership grades of the fuzzy sets are also allowed to evolve under the fuzzy differential equations the result applies for a very general class of fuzzy sets without additional assumptions of fuzzy convexity compact supports or even normality

universal and chaotic multipliers on spaces of operators we use tensor product techniques to study universality hypercyclicity and chaos of multipliers defined on operator ideals and of multiplication operators on the space of all continuous and linear operators thus continuing the work of kit chan we also obtain the first examples of outer multipliers on a banach algebra which are chaotic in the sense of devaney and prove sufficient conditions for the existence of closed subspaces of universal vectors for operators between frechet spaces

periodic solutions for nonlinear differential inclusions with multivalued perturbations abstract in this paper the periodic solutions for nonlinear differential inclusion governed by convex subdifferential and different perturbations are studied it is firstly proved that the differential inclusion has unique periodic solution if the perturbation function is a single valued function then by schauder s fixed point theorem and kakutani s fixed point theorem we prove that the differential inclusion has at least a periodic solution when the perturbation function is an upper semicontinuous or lower semicontinuous multifunction moreover the existence of the extremal solution for the differential inclusion is also studied finally based on one sided lipschitz osl assumption we prove the related relaxation theorem

input power to waveguides calculated by a finite element method this paper considers the power injected into waveguide structures from forces that are concentrated along the waveguide but are otherwise arbitrary the motion of the structure is described by a set of coupled linear one dimensional wave equations these equations are in this work devised by the waveguide finite element method which is a versatile tool for describing wave motion in general structures that have uniform properties along one direction two separate procedures are derived the first is based on spatial and frequency averaging of a modal solution the second procedure is based on a spatial fourier transform which by nature assumes the waveguide to be infinite it is shown that in the limit of zero damping the two methods are identical subsequently input power to a stiffener in a railway car structure is calculated and compared with an in situ measurement showing a fair agreement

identification of a scatterer embedded in elastic heterogeneous media using dynamic xfem abstract a numerical approach for identifying a scatterer embedded in elastic heterogeneous media is described this scatterer may be a crack a void or an inclusion with properties that have detectable contrasts from those of the host medium the forward wave propagation problem is solved using the dynamic extended finite element method xfem which allows the boundary of the scatterer to be easily relocated over a stationary background mesh the inverse problem is cast as a minimization problem whereby the unknown shape parameters of the scatterer e g a line crack s center coordinates size and orientation are the updating parameters a gradient based method is utilized to solve the minimization problem in order to alleviate the potential manifestation of multiple solutions to the inverse problem various deployment patterns for multiple sensors are investigated and also a divide and conquer approach is adopted wherein a set of independent inversions using multiple initial guesses are carried out

elastic wave scattering around cavities in inhomogeneous continua by the bem this work examines elastic wave scattering around cavities embedded in a continuum with depth dependent shear modulus and under conditions of plane strain a restricted case of inhomogeneity is considered where the poisson ratio is fixed at 0 25 and where the density profile also varies but proportionally to the shear modulus for this specific case the wave speeds remain macroscopically constant and it becomes possible to recover the exact green functions by using an algebraic transformation method these functions are subsequently used as kernels in a standard 2d boundary element formulation defined in the laplace transform domain the final step involves an inverse laplace transformation whereby the transient behavior of cavities in the aforementioned inhomogeneous continuum can be recovered two basic examples are solved namely the circular cylindrical cavity under sudden internal explosion and under a pressure wave sweep in the latter case it is possible to investigate the effect that the angle of wave incidence has on the displacement and stress that develop along the cavity s perimeter given the fact that the shear modulus is changing along the vertical direction these examples serve to illustrate the present approach and to reveal some interesting differences that are observed in transient wave scattering phenomena between homogeneous and continuously inhomogeneous models where the latter models yield a more realistic representation of geological formations