asymptotics of viscoelastic materials with nonlinear density and memory effects abstract this paper is concerned with the nonlinear viscoelastic equation t u t t u t t u u 0 s u t s d s f u h suitable to modeling extensional vibrations of thin rods with nonlinear material density t u t u and presence of memory effects this class of equations was studied by many authors but well posedness in the whole admissible range 0 4 and for f growing up to the critical exponent were established only recently the existence of global attractors was proved in presence of an additional viscous or frictional damping in the present work we show that the sole weak dissipation given by the memory term is enough to ensure existence and optimal regularity of the global attractor a for 4 and critical nonlinearity f

long time behavior of a quasilinear viscoelastic equation with past history abstract this paper is concerned with a class of quasilinear wave equations with memory u t u t t u u t t t t s u s d s u t f u h 0 which was considered by several authors with 0 since 2001 existing results are mainly devoted to global existence energy decay existence with small data and blow up of solutions however uniqueness seems to be an open problem and existence of attractors was no yet considered the objective of the present paper is to provide some results on the well posedness and long time behavior to this equation in a more general setting which includes past history that is by taking in the memory term

on pairs of matrices generating matrix rings and their presentations abstract let m n z be the ring of n by n matrices with integral entries and n 2 this paper studies the set g n z of pairs a b m n z 2 generating m n z as a ring we use several presentations of m n z with generators x i 1 n e i 1 i and y e 11 to obtain the following consequences 1 let k 1 the following rings have presentations with 2 generators and finitely many relations a j 1 k m m j q for any m 1 m k 2 b j 1 k m n j z where n 1 n k 2 and the same n i is repeated no more than three times 2 let d be a commutative domain of sufficiently large characteristic over which every finitely generated projective module is free we use 4 relations for x and y to describe all representations of the ring m n d into m m d for m n 3 we obtain information about the asymptotic density of g n f in m n f 2 over different fields and over the integers

optimum approximation for residual stiffness in linear system identification a new method of system identification uti 1 i zes projector m atrix theory and the moorepenrose generalized inverse to derive an analytical stiffness matrix which when combined with the analytical mass matrix will more closely p redict modal test results weighting matrices a re used to enforce connectivity and make weighted corrections to the original analytical stiffness matrix a simple and straightforward mathematical formulation is obtained the method is compared and contrasted with other methods found in the literature and a simple numerical example is presented

rounding errors of partial derivatives of simple eigenvalues of the quadratic eigenvalue problem in this paper we derive rounding errors of partial derivatives of a simple eigenvalue of the quadratic eigenvalue problem dependent on several parameters we prove a series of lemmas and finally get theorems of rounding errors of both nonsymmetric and symmetric qeps examples are given to show the validity of our theorems and numerical results show that our rounding error is a very good upper bound estimation of the relative error of the eigenvalue

sensitivity analysis of non conservative eigensystems an expression for the derivatives of eigenvalues and eigenvectors of non conservative systems is presented contrary to previous methods that use state space form 2n space to consider damping proposed method solves the eigenpair derivatives of damped system explicitly the computation size of n order is maintained and the eigenpair derivatives are obtained simultaneously from one equation so that it is efficient in cpu time and storage capacity moreover this method can be extended to asymmetric non conservative damped systems although additional problems are generated contrary to the eigenpair sensitivity methods of symmetric systems in asymmetric case an algebraic method for the eigenpair derivatives can be obtained through similar procedure the proposed expression is derived by combining the differentiations of the eigenvalue problem and normalization condition into one linear algebraic equation the numerical stability is proved by showing non singularity of the proposed equation and the efficiency of the derived expression is illustrated by considering a cantilever beam with lumped dampers and a whirling beam

derivatives of complex eigenvectors using nelson s method 6shyy w an adaptive grid method for navier stokes flow computation applied mathematics and computation vol 21 no 3 1987 pp 201 219 7jeng y n andliou s c modi edmultipleone dimensional adaptive grid method numerical heat transfer part b vol 15 no 2 1989 pp 241 247 8jeng y n and lee z s revisit to the modi ed muliple onedimensional adaptive grid method numerical heat transfer part b vol 29 no 3 1996 pp 305 323 9bockelie m j and smith r e an adaptive grid method for computing the high speed 3d viscous flow about a re entry vehicle aiaa paper 92 2685 june 1992 10yee h c and harten a implicit tvd schemes for hyperbolic conservation laws in curvilinear coordinates aiaa journal vol 25 no 2 1987 pp 266 274 11jeng y n and liou y c adaptive grid generation by elliptic equations with grid control at all of the boundaries numerical heat transfer part b vol 23 no 2 1993 pp 135 151

natural frequency and mode shape sensitivities of damped systems part ii multiple natural frequencies abstract an efficient algorithm with proven numerical stability is derived for computation of eigenvalue and eigenvector derivatives of damped vibratory systems with multiple eigenvalues in the proposed method adjacent eigenvectors and orthonormal condition are used to compose an algebraic equation whose order is n m n m where n is the number of co ordinates and m the number of multiplicity of a multiple natural frequency the mode shape derivatives of the damped systems can be obtained by solving the algebraic equation the method can be consistently applied to both structural systems with structural design parameters and mechanical systems with lumped design parameters as an example of a structural system to demonstrate the theory of the proposed methods and its possibilities in the case of multiple eigenvalues the finite element model of the cantilever beam is considered and also a 5 dof mechanical system in the case of a non proportionally damped system the design parameter of the cantilever beam is its height and that of the 5 dof mechanical system is a spring

frictional versus viscoelastic damping in a semilinear wave equation in this article we show exponential and polynomial decay rates for the partially viscoelastic nonlinear wave equation subject to a nonlinear and localized frictional damping the equation that models this problem is given by begin eqnarray u tt kappa 0 delta u int 0 t mbox div a x g t s nabla u s ds f u b x h u t 0 mbox in omega times bbb r quad end eqnarray where a b are nonnegative functions a in c 1 overline omega b in l infty omega satisfying the assumption begin eqnarray a x b x geq delta 0 quad forall x in omega end eqnarray and f and h are power like functions we observe that the assumption 0 2 gives us a wide assortment of possibilities from which to choose the functions a x and b x and the most interesting case occurs when one has simultaneous and complementary damping mechanisms taking this point of view into account a distinctive feature of our paper is exactly to consider different and localized damping mechanisms acting in the domain but not necessarily strategically localized dissipations as considered in the prior literature

asymptotic stability and energy decay rates for solutions of the wave equation with memory in a star shaped domain we study the asymptotic stability and give the energy decay rates for solutions of the wave equation with boundary dissipation of the memory type

henrici s transformation and its application to the computation of derivatives of eigensystems in this paper we examine the application of henrici s transformation to a sequence of vectors generated by a simultaneous iteration method for computing the partial derivatives of eigenvalues and eigenvectors of parameter dependent matrices numerical results support our theoretical analysis and indicate that henrici s method compares favorably with other vector sequence transformation methods

stiffness matrix adjustment using mode data a procedure is introduced that uses in addition to mode data structural connectivity information to optimally adjust deficient stiffness matrices the adjustments performed are such that the percentage change to each stiffness coefficient is minimized the physical configuration of the analytical model is preserved and the adjusted model will exactly reproduce the modes used in the identification the theoretical development is presented and the procedure is demonstrated by numerical simulation of a test problem

existence and uniform decay rates of solutions to a degenerate system with memory conditions at the boundary in this article we study the degenerate system r 1 r 2 0 subject to memory conditions on the boundary given email protected 1 x u t email protected email protected u v email protected 0 r 2 x v t email protected a u v email protected 0 email protected 0 email protected 0 tg 1 t s email protected email protected s email protected 1x 0 email protected 0 email protected 0 tg 2 t s email protected email protected s email protected 1x 0 u 0 v 0 u 0 v 0 r 1u t 0 r 2v t 0 r 1u 1 r 2v 1 email protected where w is a bounded region in r n whose boundary is partitioned into disjoint sets c 0 c 1 we prove that the dissipations given by the memory terms are strong enough to guarantee exponential or polynomial decay provided the relaxation functions also decay exponentially or polynomially and with the same rate of decay

isospectral vibrating systems part 1 the spectral method as tudy is made of inverse problems forn n systems of the form l m 2 d k t his paper concerns the determination of systems in an equivalence class def ined by afi xed 2n 2n admissible jordan matrix i e a class of isospectral systems constructive methods are obtained for complex or real systems with no symmetry constraints it is also shown how isospectral families of complex hermitian matrices can be formed the case of real symmetric matrices is more difficult some partial solutions are obtained but in this case the theory remains incomplete examples are given 2 005 elsevier inc all rights reserved

uniform attractors for a non autonomous viscoelastic equation with a past history abstract this paper investigates the existence of uniform attractors for a non autonomous viscoelastic equation with a past history in a bounded domain r n n 1 by establishing the uniformly asymptotic compactness of the semi process generated by the global solutions our results improve those results by araujo et al 2013

global attractor for plate equation with nonlinear damping abstract in this paper we study the long time behavior of plate equation with nonlinear damping and critical nonlinearity we prove the existence of a global attractor in the space h 0 2 l 2

partial derivatives of the eigen triplet of the quadratic eigenvalue problem depending on several parameters this paper concerns the partial derivatives of the eigen triplet of the quadratic matrix polynomial q p l email protected 2m p email protected p k p where m p c p k p c n x n are complex analytic matrix valued functions email protected c m is a complex parameter vector first the analyticity theorem for simple eigenvalues and the corresponding eigenvectors is given second a new method is proposed to compute partial derivatives of the eigen triplet the derivatives of the eigen triplet can be obtained by solving algebraic linear equations of order n 1 where it only requires the information of the eigen triplet whose partial derivatives are to be computed and what is more important the condition numbers of the coefficient matrices are better than those of the nonsingular coefficient matrices arisen in the bordered matrix method 1 and nelson s method 5 numerical tests show the feasibility and efficiency of the new method the results are better or at least comparable with current methods

upper semicontinuity of pullback attractors for nonclassical diffusion equations our aim in this paper is to study the long time behavior in terms of upper semicontinuous property of pullback attractors of nonclassical diffusion equations with nonautonomous perturbation specifically we prove that under some proper assumptions the pullback attractor ae t t r of eq 1 and the global attractor a of eq 1 with e 0 satisfy lime 0 distx ae t a 0 for any t r

upper semicontinuity of pullback attractors for a non autonomous viscoelastic equation this paper is concerned with upper semicontinuity of pullback attractors for a non autonomous viscoelastic equation with a past history with a nonautonomous perturbation in particular under some proper assumptions we prove that the pullback attractor a e t t r of eq 1 1 with e 0 and the global attractor a of eq 1 1 with e 0 satisfy lim e 0 dist x a e t a 0 for any email protected r

spectral decomposition of real symmetric quadratic λ matrices and its applications spectral decomposition provides a canonical representation of an operator over a vector space in terms of its eigenvalues and eigenfunctions the canonical form often facilitates discussions which otherwise would be complicated and involved spectral decomposition is of fundamental importance in many applications the well known glr theory generalizes the classical result of eigendecomposition to matrix polynomials of higher degrees but its development is based on complex numbers this paper modifies the glr theory for the special application to real symmetric quadratic matrix polynomials q a mx2 cx k m nonsingular subject to the specific restriction that all matrices in the representation be realvalued it is shown that the existence of the real spectral decomposition can be characterized through the notion of real standard pair which in turn can be constructed from the spectral data applications to a variety of challenging inverse problems are discussed

inverse dynamic design technique for model correction and optimization the inverse dynamic design technique presented herein tunes a structural model to achieve a prespecified frequency response at certain critical points of the structure the technique can correct structural models based on vibration response test data and also can optimize structural design the technique works by partitioning the second order matrix equations of motion into assigned and auxiliary degrees of freedom and then performs a parameter optimization to assign new frequency response data to the model design variable linking symbolic or sparse matrix solutions and closed form gradients are used to streamline the computations the technique still requires a large amount of computation and thus is most applicable to small or moderate size dynamic models such as coarse mesh prototype models or models with repeated geometry or symmetry two small order example problems illustrate the technique the first example completely corrects the stiffness matrix of a corrupted analytical model using simulated measured exact frequency response data the second example flattens the first resonance peak of a truss structure by assigning a specified partial frequency response to the model

universal attractor in h4 for the nonlinear one dimensional compressible navier stokes equations abstract this paper is concerned with the regularity exponential stability of solutions and existence of universal attractor in h 4 for a nonlinear one dimensional compressible navier stokes equations describing a motion of heat conductive viscous real gas in a bounded domain 0 1 some new ideas and more delicated estimates are introduced to prove these results

global attractor for a model of extensible beam with nonlinear damping and source terms abstract this paper is concerned with the existence of a global attractor for the nonlinear beam equation with nonlinear damping and source terms u t t 2 u m u 2 d x u f u g u t h in r where is a bounded domain of r n m is a nonnegative real function and h l 2 the nonlinearities f u and g u t are essentially u u u u and u t r u t respectively with r 0 and this kind of problem models vibrations of extensible beams and plates

a new iterative method for many eigenpair partial derivatives abstract a new iterative method is proposed for computing partial derivatives of many eigenpairs this method simultaneously computes a few eigenpair partial derivatives for each origin shift partial derivatives of eigenpairs whose eigenvalues are closest to the origin shift can be computed hence this method may be used for partial derivatives of all eigenpairs convergence of the proposed method is established finally numerical experiments are given to show the effectiveness of the proposed method

davidson method for eigenpairs and their derivatives introduction e igenpair derivatives with respect to system parameters are widely used in many fields such as model updating 1 damage detection 2 and structural optimization 3 the computation of eigenvalue derivatives is simple and straightforward however calculation of eigenvector derivatives is much more complicated at present methods for calculating eigenvector derivatives mainly include the finite difference method 4 modal method 5 6 nelson method 7 etc the nelson method yields an accurate solution of eigenpair derivative and the method was widely accepted using lanczos vectors ojalvo and zhang8 developed a method for computation of eigenvector derivatives however this method failed in some cases because it neglected the derivatives of lanczos vectors based on the lanczos method yuan et al 9 present a procedure for synchrocalculation of eigenpairs and their derivatives the davidson method see ref 10 is an efficient way to compute the extreme eigenvalues and their corresponding eigenvectors of a large sparse and symmetric matrix compared with the lanczos method the davidson method is usually more efficient because it applies preconditioning techniques in solving eigenvalue problems based on the davidson method this note proposes a new method for simultaneously calculating the eigenpairs and their derivatives of the symmetric matrices when the proposed method is used the system

global existence and uniform decay for a nonlinear viscoelastic equation with damping abstract in this paper we investigate a nonlinear viscoelastic equation with linear damping global existence of weak solutions and the uniform decay estimates for the energy have been established

generators of maximal orders let r be the ring of algebraic integers in a number field k and let be a maximal order in a finite dimensional semisimple k algebra b building on our previous work 3 we compute the smallest number of algebra generators of considered as an r algebra this reproves and vastly extends the results of p a b pleasants who considered the case when b is a number field in order to achieve our goal we obtain several results about counting generators of algebras which have finitely many elements these results should be of independent interest

uniform attractor for non autonomous hyperbolic equation with critical exponent abstract in this paper we study the uniform attractor for semilinear wave equation with mixed differential quotient terms and critical nonlinearity we prove the existence of the uniform attractor in h 0 1 l 2

an efficient algebraic method for computing eigensolution sensitivity of asymmetric damped systems in this paper an efficient algebraic method for the computation of eigensolution derivatives of asymmetric damped systems with distinct eigenvalues is presented by introducing an additional and new normalization condition we construct two extended systems of linear equations with nonsingular coefficient matrices which are transpose to each other we can compute the derivatives of the eigenvalues and their associated right and left eigenvectors by solving the two systems respectively in this way the cpu computation time and the storage space are considerably reduced finally a numerical example is included to demonstrate the validity of the proposed method