linear damping models for structural vibration abstract linear damping models for structural vibration are examined first the familiar dissipation matrix model then the general linear model in both cases an approximation of small damping is used to obtain simple expressions for damped natural frequencies complex mode shapes and transfer functions results for transfer functions can be expressed in the form of very direct extensions of the familiar expression for the undamped case this allows a detailed discussion of the implications of the various damping models for the interpretation of measured transfer functions especially in the context of experimental modal analysis in the case of a dissipation matrix model it would be possible in principle to determine all the model parameters from measurements in the case of the general model however there is a fundamental ambiguity which prevents full determination of the model from measurements on a single structure

frequency domain analysis of exponentially damped linear systems abstract in this paper frequency domain analysis of linear exponentially damped systems subjected to arbitrary initial conditions is studied the standard discrete fourier transform dft procedure combined with fast fourier transform fft algorithms is applied to compute dynamic responses after transforming the original motion equations subjected to non zero initial conditions into new ones with completely null initial conditions by using the pseudo force approach a multi degree of freedom mdof system and a continuum system with exponential damping are considered as the illustrative problems the accuracy of the proposed method is evaluated by comparing the results with those obtained from simulink based on the state space method

antiperiodic boundary value problem for first order impulsive ordinary differential equations this paper discusses the antiperiodic boundary value problem for first order impulsive ordinary differential equations we establish several existence results by using the leray schauder alternative the lower and upper solution method and the monotone iterative technique

stability of viscous shock waves associated with a system of nonstrictly hyperbolic conservations laws we introduce a simple model of two conservation laws which is strictly hyperbolic except for a degenerate parabolic line in the state space besides classical shock waves it also exhibits overcompressive marginal overcompressive and marginal undercompressive shock waves our purpose is to study the behavior of the corresponding viscous waves in particular the manner in which these waves are stable there are several basic differences between classical shock waves and other types of shock waves a perturbation of an overcompressive shock wave gives rise to a new wave monotone marginal overcompressive waves behave distinctly from the nonmonotone ones analytical techniques used in our study include characteristic energy and weighted energy methods and nonlinear superposition through time invariants although we carry out our analysis for a simple model the general phenomena would hold for overcompressive waves which occur in other physical models

variational methods to the second order impulsive differential equation with dirichlet boundary value problem in this paper we study the existence of solutions for a class of second order impulsive differential equation by using the critical point theorem of y jabri and an even functional theorem we give some new criteria to guarantee that the impulsive differential equation has at least one solution infinitely many solutions under the assumption that a nonlinear term satisfies sublinear superlinear asymptotically linear respectively some recent results are extended and conditions of assumptions are simplified finally some examples are presented to illustrate our main results

a new class of volterra differential equations for which the solutions are globally asymptotically stable on etudie le systeme de lotka volterra i u i e i j 1 m p ij u j u i 0 0 0 t ou p p ij est une matrice reelle mxm et ou i 1 2 m les constantes e i sont choisies de telle maniere qu un point stationnaire q q i existe dans le premier quadrant

a quasilinearization method for p laplacian equations with a nonlinear boundary condition abstract in this work we consider a nonlinear elliptic problem with a nonlinear boundary condition assuming the existence of an ordered couple of a subsolution and a supersolution we develop a quasilinearization method in order to construct an iterative scheme that converges to a solution

a global formalism for nonlinear waves in conservation laws we introduce a unifying framework for treating all of the fundamental waves occurring in general systems ofn conservation laws fundamental waves are represented as pairs of states statisfying the rankine hugoniot conditions after trivial solutions have been eliminated by means of a blow up procedure these pairs form an n 1 dimensional manifold the fundamental wave manifold there is a distinguishedn dimensional submanifold of containing a single one dimensonal foliation that represents the rarefaction curves for all families similarly there is a foliation of itself that represent shock curves we identify othern dimensional submanifolds of that are naturally interpreted as boundaries of regions of admissible shock waves these submanifolds also have one dimensional foliations which represent curves of composite waves this geometric framework promises to simplify greatly the study of the stability and bifurcation properties

on a general model for damping when a structure exhibits a damped dynamic behavior that does not conform to the classical and well known viscous or hysteretic models a more general approach must be sought several questions may then be raised like i in which theoretical background should one base the investigation or ii can one apply common modal analysis tools to solve the problem recent works have shown that some types of materials and therefore structures demand a more rigorous behavior description and that it seems possible to address the problem by means of the theory of fractional derivatives leading to a model in terms of general damping parameters such an approach reveals itself somewhat complicated to implement in practice and some simplifications are necessary the authors discuss the use of a generalized damping concept for modeling the dynamic behavior of linear systems and show how this concept allows for a clearer interpretation and explanation of the behavior displayed by the common viscous and hysteretic models

numerical study for the three dimensional rayleigh taylor instability through the tvd ac scheme and parallel computation the rayleigh taylor instability is a gravity driven instability of a contact surface between fluids of different densities the growth of this instability is sensitive to numerical or physical mass diffusion for this reason high resolution of the contact discontinuity is particularly important in this paper we address this problem using a second order tvd finite difference scheme with artificial compression we describe our numerical simulations of the 3d rayleigh taylor instability using this scheme the numerical solutions are compared to a the exact 2d solution in the linear regime and b numerical solutions using the tvd scheme and the front tracking method the computational program is used to study the evolution of a single bubble and 3d bubble merger i e the nonlinear evolution of a single mode and the process of nonlinear mode mode interaction

on the impulse response precursor of an ideal linear hysteretic damper the model of the ideal linear hysteretic damper has been shown to possess a non causal impulse response precursor however the relevant characteristics of the impulse response precursor its extremum monotonicity and asymptotic property were not well comprehended in the literature in this paper an impulse response precursor expression was derived it was observed that the impulse response precursor achieves its only extremum which is negative at the origin the impulse response precursor monotonically increases from this extremum to zero while time retraces to the negative infinity the asymptotic rate of impulse response precursor approaching zero is o 1 t the non causal size gets stronger as the loss factor increases numerical computation also shows that the non causal extremum is even deeper than the first trough of the causal portion of the impulse response when the loss factor is greater than 0 77

crises sudden changes in chaotic attractors and transient chaos abstract the occurrence of sudden qualitative changes of chaotic dynamics as a parameter is varied is discussed and illustrated it is shown that such changes may result from the collision of an unstable periodic orbit and a coexisting chaotic attractor we call such collisions crises phenomena associated with crises include sudden changes in the size of chaotic attractors sudden appearances of chaotic attractors a possible route to chaos and sudden destructions of chaotic attractors and their basins this paper presents examples illustrating that crisis events are prevalent in many circumstances and systems and that just past a crisis certain characteristic statistical behavior whose type depends on the type of crisis occurs in particular the phenomenon of chaotic transients is investigated the examples discussed illustrate crises in progressively higher dimension and include the one dimensional quadratic map the two dimensional henon map systems of ordinary differential equations in three dimensions and a three dimensional map in the case of our study of the three dimensional map a new route to chaos is proposed which is possible only in invertible maps or flows of dimension at least three or four respectively based on the examples presented the following conjecture is proposed almost all sudden changes in the size of chaotic attractors and almost all sudden destruction or creations of chaotic attractors and their basins are due to crises

first order impulsive ordinary differential equations with anti periodic and nonlinear boundary conditions the monotone iterative technique is a powerful method that have been used to approximate the extremal solutions of several problems 1 2 on the other hand impulsive differential equations are a basic tool to study some problems of biology medicine engineering and physics 3 in this paper we deal with the following nonlinear boundary value problem for first order differential equation with impulses at fixed points

monotone method for first order functional differential equations we study periodic boundary value problems relative to a general class of first order functional differential equations for this class of problems we develop the monotone iterative technique our formulation is very general including delay differential equations functional differential equations with maxima and integro differential equations but the case where the operator defining the functional dependence is not necessarily lipschitzian is also considered

fractional calculus a different approach to the analysis of viscoelastically damped structures fractional calculus is used to construct stress strain relationships for viscoelastic materials these relationships are used in the finite element analysis of viscoelastically damped structures and closed form solutions to the equations of motion are found the attractive feature of this approach is that very few empirical parameters are required to model the viscoelastic material and calculate the response of the structure for general loading conditions

isoparametric functions on riemannian manifolds i on etablit les proprietes de base des fonctions transnormales et on demontre le lemme du tube on demontre que soit m une variete de riemann lisse complete connexe et f une fonction transnormale sur m alors a les varietes focales de f sont des sous varietes lisses de m b chaque ensemble de niveau regulier de f est un tube sur d autres des varietes focales

identification of linear non viscous damping with different kernel functions in the time domain abstract the non viscous damping model considers the complete velocity history via a convolution over the kernel functions in this paper a procedure is proposed for identifying a damping model involving different kernel functions in the time domain the method uses responses calculated by the generic time domain integration with the known mass matrix and the stiffness matrix the relaxation parameter in the kernel function is identified through a summation of the error function and the damping coefficient matrix is identified via the linear least squares method two examples show that reasonable estimates could be obtained by the proposed method

monotone iterative technique for periodic boundary value problems with causal operators abstract in this paper we develop the monotone iterative technique for periodic boundary value problems with causal operators

an accurate low mach scheme for a compressible two fluid model applied to free surface flows classical approximate riemann solvers are known to be too much dissipative in the low mach number regime for this reason since the mach number in liquids is generally very small usual upwind schemes may provide inaccurate solutions when applied to the simulation of two phase flows in this paper to circumvent this difficulty while keeping a compressible model for the description of both gas and liquid an original accurate low mach scheme is introduced and theoretically studied extending some ideas already used for the gas dynamics system the proposed scheme is based on a centred formulation for the pressure gradient term in the momentum equation and on the introduction of a stabilising term proportional to the pressure difference between two neighbouring cells the scheme stability is ensured and theoretically proved under a convective cfl like condition by using a semi implicit time discretisation algorithm finally the correct asymptotic behaviour of the scheme in the limit of small mach numbers is assessed on several academic test cases

non local finite element analysis of damped beams non local viscoelastic beam models are used to analyse the dynamics of beams with different boundary conditions using the finite element method unlike local damping models the internal force of the non local model is obtained as weighted average of state variables over a spatial domain via convolution integrals with spatial kernel functions that depend on a distance measure in the finite element analysis the interpolating shape functions of the element displacement field are identical to those of standard two node beam elements however for non local damping nodes remote from the element do have an effect on the energy expressions and hence on the damping matrix the expressions of these direct and cross damping matrices may be obtained explicitly for some common spatial kernel functions and euler bernoulli beam theory alternatively numerical integration may be applied to obtain solutions examples are given where the eigenvalues are compared to the exact solution for a pinned pinned beam to demonstrate the convergence of the finite element method the results for beams with other boundary conditions are used to demonstrate the versatility of the finite element technique 2007 elsevier ltd all rights reserved

a topological characterization of the ω limit sets for analytic flows on the plane the sphere and the projective plane in this paper the limit sets for analytic and polynomial differential equations on the plane are characterized up to homeomorphisms the analogous problem is solved in full detail for analytic flows on the sphere and the projective plane we also explain how to carry on the same program for analytic flows defined on open subsets of these surfaces

attractors and symmetries of vector fields the inverse problem abstract the inverse problem of constructing dynamical systems x with a prescribed compact attracting set k r n and non trivial dynamics on it is solved the boundaries of the attracting basins corresponding to different connected components of k and the relationship between the symmetries of k x and are also studied

cubically convergent methods for selecting the regularization parameters in linear inverse problems we present three cubically convergent methods for choosing the regularization parameters in linear inverse problems the detailed algorithms are given and the convergence rates are estimated our basic tools are tikhonov regularization and morozov s discrepancy principle we prove that in comparison with the standard newton method the computational costs for our cubically convergent methods are nearly the same but the number of iteration steps is even less numerical experiments for an elliptic boundary value problem illustrate the efficiency of the proposed algorithms

generalized quasilinearization method for mixed boundary value problems a generalized quasilinearization method for a nonlinear mixed bvp is developed and a sequence of approximate solutions converging monotonically and quadratically to a solution of the given problem is presented

existence and multiplicity of solutions for some dirichlet problems with impulsive effects abstract in this paper we consider the existence and multiplicity of solutions for some dirichlet impulsive problems and some existence and multiplicity results are obtained the solutions are sought by means of lax milgram theorem and some critical theorems

global attractivity of positive periodic solutions for an impulsive delay periodic model of respiratory dynamics in this paper we shall consider the following nonlinear impulsive delay differential equation x t v t x t xn t m n xn t m t a e t 0 t tk x tk 1 1 bk x tk k 1 2 where m and n are positive integers v t and t are positive periodic continuous functions with period 0 in the nondelay case m 0 we show that the above equation has a unique positive periodic solution x t which is globally asymptotically stable in the delay case we present sufficient conditions for the global attractivity of x t our results imply that under the appropriate periodic impulsive perturbations the impulsive delay equation shown above preserves the original periodic property of the nonimpulsive delay equation in particular our work extends and improves some known results

supersensitivity due to uncertain boundary conditions summary we study the viscous burgers equation subject to perturbations on the boundary conditions two kinds of perturbations are considered deterministic and random for deterministic perturbations we show that small perturbations can result in o 1 changes in the location of the transition layer for random perturbations we solve the stochastic burgers equation using different approaches first we employ the jacobi polynomial chaos which is a subset of the generalized polynomial chaos for stochastic modeling converged numerical results are reported up to seven significant digits and we observe similar stochastic supersensitivity for the mean location of the transition layer subsequently we employ up to fourth order perturbation expansions we show that even with small random inputs the resolution of the perturbation method is relatively poor due to the larger stochastic responses in the output two types of distributions are considered uniform distribution and a truncated gaussian distribution with no tails various solution statistics including the spatial evolution of probability density function at steady state are studied copyright 2004 john wiley sons ltd

on the global structure of invariant regions of flows with asymptotically stable attractors several authors have pointed out the usefulness of shape theory which was introduced by k borsuk in 1968 as a tool in the study of dynamical systems in particular bogatyi and gutsu 4 garay 10 gunther and segal 11 hastings 12 robbin and salamon 16 rogers 17 and tezer 24 have obtained interesting results in dynamical systems using shape theoretical techniques one of the authors of the present article has given another connection between shape and topological dynamics 20 based on the approach to shape developed in 18 and 19 see also 21 for applications of shape theory to the study of uniform attractors most of the mentioned papers study properties of flows although 16 and 24 are devoted to discrete dynamical systems in particular a shape conley index is constructed in 16 for discrete dynamical systems and some shape theoretical ideas are used in 24 to study properties of topological conjugacy of shifts and homotopical shift equivalence for maps of polyhedra in the papers 4 10 11 12 20 21 some topological properties of the attractors of flows are studied for instance hastings established in 12 a higher dimensional poincare bendixson theorem proving the existence of attractors of certain flows in the interior of submanifolds of the euclidean space and comparing the shape of the attractor with that of the manifold other properties studied in the above papers are related to strong cellularity of the global attractors 10 and polyhedral shape of asymptotically stable compacta 4 11 20 a remarkable fact proved by

the dimension of chaotic attractors dimension is perhaps the most basic property of an attractor in this paper we discuss a variety of different definitions of dimension compute their values for a typical example and review previous work on the dimension of chaotic attractors the relevant definitions of dimension are of two general types those that depend only on metric properties and those that depend on the frequency with which a typical trajectory visits different regions of the attractor both our example and the previous work that we review support the conclusion that all of the frequency dependent dimensions take on the same value which we call the dimension of the natural measure and all of the metric dimensions take on a common value which we call the fractal dimension furthermore the dimension of the natural measure is typically equal to the lyapunov dimension which is defined in terms of lyapunov numbers and thus is usually far easier to calculate than any other definition because it is computable and more physically relevant we feel that the dimension of the natural measure is more important than the fractal dimension

anti periodic boundary value problems for first order impulsive functional differential equations this paper considers existence of solutions for a class of first order functional differential equation with anti periodic boundary value conditions we introduce new concept of lower and upper solutions which is quite different from the former one and we present that monotone iterative technique coupled with lower and upper solutions is still valid

existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti periodic boundary conditions this paper describes the method of quasilinearization for first order nonlinear impulsive functional differential equations with anti periodic boundary conditions a monotone iterative technique coupled with lower and upper solutions is employed to obtain sequences of approximate solutions converging monotonically and quadratically to the unique solution of the problem at hand 2007 elsevier ltd all rights reserved

calculation of eigensolution derivatives for nonviscously damped systems using nelson s method a method to calculate the derivatives of the eigenvalues and eigenvectors of multiple degree of freedom damped linear dynamic systems with respect to arbitrary design parameters is presented in contrast to the traditional viscous damping model a more general nonviscous damping model is considered the nonviscous damping model is such that the damping forces depend on the past history of velocities via convolution integrals over given kernel functions because of the general nature of the damping eigensolutions are generally complex valued and eigenvectors do not satisfy the classical orthogonality relationship the proposed method to calculate the eigenvector derivative depends only on the eigenvector concerned numerical examples are provided to illustrate the derived results nomenclature c j constant associated with the derivative of u j d s dynamic stiffness matrix d j constant associated with the derivative of v j g s laplace transform of g t g t nonviscous damping matrix k stiffness matrix l laplace transform of m mass matrix m total number of eigenvectors n number of degrees of freedom of the system n number of relaxation parameters p design parameter rank rank of a matrix s laplace domain parameter u j jth eigenvector t displacement vector v j jth adjoint left eigenvector x j vector associated with the derivative of u j yj vector associated with the derivative of v j j normalization constant for the jth eigenvector j jth eigenvalue k relaxation parameters subscripts t matrix transpose derivative with respect to s

improved approximate methods for calculating frequency response function matrix and response of mdof systems with viscoelastic hereditary terms as we know it is difficult and unnecessary to obtain all the eigenpairs of a large scaled viscoelastic nonviscous or hysteretic damping systems which means that the mode truncation scheme is generally used and the mode truncated error is therefore introduced this study is aimed at eliminating the influence of the unavailable modes on the dynamic response of mdof systems with viscoelastic hereditary terms the energy dissipation terms of the system depend on the past history of motion via convolution integrals over some kernel functions therefore the system is a nonviscously damped system which has been considered as the most generalized damping model within the scope of a linear mechanical analysis to approximate frequency response function frf matrix and response without using the unavailable modes we suggest two methods which attempt to approximate the influence of the unavailable modes in terms of the lower modes and system matrices by using the first one or two terms of neumann expansion of the contribution of the unavailable modes in contrast with the frf matrix approximated in terms of the first two terms of neumann expansion these procedures cannot be extended to further high order terms since all of them will be affected by the frequency dependent variation of damping matrix from previous terms finally an example is shown that the two presented methods can make the mode truncated error reduce and may be used to approximate the influence of nonviscous modes contributed to frf matrix due to the fact that the nonviscous modes are difficult to be obtained accurately even if a small scaled model is used for some eigensolution methods

systems of first order impulsive functional differential equations with deviating arguments and nonlinear boundary conditions abstract this paper is concerned with the existence of solutions for systems of first order impulsive functional differential equations with deviating arguments and nonlinear boundary conditions by establishing new comparison results and applying the monotone iterative technique we obtain the sufficient conditions for the existence of extremal system of solutions

the bellman kalaba lakshmikantham quasilinearization method for neumann problems in this paper we develop a generalized quasilinearization method for a nonlinear neumann problem and obtain a sequence of approximate solutions converging monotonically and quadratically to a solution of the problem

finite element model updating with damping identification abstract most of finite element model updating techniques do not employ damping matrices and hence cannot be used for accurate prediction of complex frequency response functions frfs in this paper damped finite element model updating procedure is proposed and tested with the objective that the damped finite element updated model is able to predict the measured frfs accurately the proposed damped updating procedure is a two step procedure in the first step mass and stiffness matrices are updated using frf data and in the second step damping matrix is identified using updated mass and stiffness matrices that are obtained in the previous step the effectiveness of the proposed procedure is demonstrated by numerical examples as well as by actual experimental data firstly a study is performed using a numerical simulation based on fixed fixed beam structure with non proportional viscous damping model the numerical study is followed by case involving actual measured data for the case of f shaped test structure the results have shown that the proposed procedure can be used for accurate prediction of the complex frfs

classification of strange attractors by integers we show how to characterize a strange attractor by a set of integers these are extracted from the chaotic time series data by first reconstructing the low period orbits and then determining the template or knot holder which supports all periodic orbits embedded in the strange attractor and the strange attractor itself the template is identified by a set of integers which therefore characterize the strange attractor this identification is explicitly demonstrated for the pirogon using a relatively small data set 5000 points

a galerkin method for distributed systems with non local damping in this paper a non local damping model including time and spatial hysteresis effects is used for the dynamic analysis of structures consisting of euler bernoulli beams and kirchoff plates unlike ordinary local damping models the damping force in a non local model is obtained as a weighted average of the velocity field over the spatial domain determined by a kernel function based on distance measures the resulting equation of motion for the beam or plate structures is an integro partial differential equation rather than the partial differential equation obtained for a local damping model approximate solutions for the complex eigenvalues and modes with non local damping are obtained using the galerkin method numerical examples demonstrate the efficiency of the proposed method for beam and plate structures with simple boundary conditions for non local and non viscous damping models and different kernel functions

quantification of non viscous damping in discrete linear systems abstract the damping forces in a multiple degree of freedom engineering dynamic system may not be accurately described by the familiar viscous damping model the purpose of this paper is to develop indices to quantify the extent of any departures from this model in other words the amount of non viscosity of damping in discrete linear systems four indices are proposed two of these indices are based on the non viscous damping matrix of the system a third index is based on the residue matrices of the system transfer functions and the fourth is based on the measured complex modes of the system the performance of the proposed indices is examined by considering numerical examples

eliminating the modal truncation problem encountered in frequency responses of viscoelastic systems increasing the number of degrees of freedom used in finite element analysis for mechanical and structural systems with viscoelastic damping the need to consider the modal truncation problem of viscoelastic systems is more than ever before the higher modes may be unnecessary to obtain in dynamic analysis for engineering applications for viscoelastic systems the modal truncation problem may be more frequently encountered since the nonviscous modes are difficult or even impossible to be found accurately even if a small scaled problem is considered for some eigensolution methods this study aims at eliminating the influence of the higher modes on the frequency responses of viscoelastically damped systems a method is presented by making the equilibrium equations of motion into a subspace equation spanned in terms of the columns of a projection basis obtained by considering the use of the contribution of the lower modes and the first two terms of the neumann expansion of the contribution of the unavailable modes finally three example studies are provided to illustrate the effectiveness of the derived results it is shown that the proposed method can reduce the modal truncation error significantly

a quasilinearization method for elliptic problems with a nonlinear boundary condition abstract we study a nonlinear elliptic second order problem with a nonlinear boundary condition assuming the existence of an ordered couple of a supersolution and a subsolution we develop a quasilinearization method in order to construct an iterative scheme that converges to a solution furthermore under an extra assumption we prove that the convergence is quadratic

vibration analysis of beams with non local foundations using the finite element method in this paper a non local viscoelastic foundation model is proposed and used to analyse the dynamics of beams with different boundary conditions using the finite element method unlike local foundation models the reaction of the non local model is obtained as a weighted average of state variables over a spatial domain via convolution integrals with spatial kernel functions that depend on a distance measure in the finite element analysis the interpolating shape functions of the element displacement field are identical to those of standard two node beam elements however for non local elasticity or damping nodes remote from the element do have an effect on the energy expressions and hence the damping and stiffness matrices the expressions of these direct and cross matrices for stiffness and damping may be obtained explicitly for some common spatial kernel functions alternatively numerical integration may be applied to obtain solutions numerical results for eigenvalues and associated eigenmodes of euler bernoulli beams are presented and compared where possible with results in literature using exact solutions and galerkin approximations the examples demonstrate that the finite element technique is efficient for the dynamic analysis of beams with non local viscoelastic foundations copyright 2007 john wiley sons ltd

analysis of the critical velocity of a load moving on a beam supported by a finite depth foundation abstract a detailed analysis of the critical velocity of a uniformly moving load is carried out in this paper it is assumed that the load is traversing an infinite beam supported by a finite depth foundation under plane strain condition the problem is solved analytically in the fourier domain respecting two formulations of the interface condition the critical velocity is determined as the velocity under which the undamped beam deflection tends to infinity i e by identifying double poles in the fourier image of the beam deflection situated on the real fourier variable axis results obtained are compared with the previously published results of this author where simplifying assumptions were imposed on the shear contribution of the foundation based on the results an addition to the previous formula for critical velocity estimate is proposed it is confirmed that there are several critical velocities but the lowest one which is the dominating one smoothly changes from the classical value to the lowest wave velocity of propagation in the foundation according to the mass ratio defined as the square root of the fraction of the foundation mass to the beam mass particular situations where the first double pole cannot be formed in this model are discussed in detail in such cases a significant increase of deflection is observed in the vicinity of the expected location defining thus a pseudo critical velocity attention is paid to the cases where there are two or more very close critical velocities which causes an increased risk for practical applications in addition several options of damping are compared

identification of damping part 1 viscous damping abstract characterization of damping forces in a vibrating structure has long been an active area of research in structural dynamics the most common approach is to use viscous damping where the instantaneous generalized velocities are the only relevant state variables that affect damping forces however viscous damping is by no means the only damping model within the scope of linear analysis any model which makes the energy dissipation functional non negative is a possible candidate for a valid damping model this paper and its companion see pp 63 88 of this issue are devoted to developing methodologies for identification of such general damping models responsible for energy dissipation in a vibrating structure this paper considers identification of viscous damping under circumstances when the actual damping model in the structure is non viscous a method is presented to obtain a full non proportional viscous damping matrix from complex modes and complex natural frequencies it is assumed that the damping is small so that a first order perturbation method is applicable the proposed method and several related issues are discussed by considering numerical examples based on a linear array of damped spring mass oscillators it is shown that the method can predict the spatial location of damping with good accuracy and also give some indication of the correct mechanism of damping

comments on nonlinear vibration of viscoelastic beams described using fractional order derivatives abstract this discussion seeks to address some of the inconsistencies and concerns regarding fractional derivatives when applied to vibration analysis of viscoelastically damped beams 1 detailed numerical assessments of the major fractional derivatives of concern have been carried out with their relationships numerically examined numerical results have shown that two of the key equations of 1 are mathematically inappropriate and their applications could lead to serious modelling errors a simplified yet representative nonlinear system with fractional viscoelastic damping and cubic stiffness nonlinearity is used to illustrate the existence of periodic steady state solutions as well as amplitude frequency characteristics of such fractional nonlinear systems

eigenvalues of linear viscoelastic systems the calculation of eigenvalues of single and multiple degree of freedom linear viscoelastic systems is considered the assumed viscoelastic forces depend on the past history of motion via convolution integrals over exponentially decaying kernel functions current methods to solve this type of problem normally use the state space approach involving additional internal variables such approaches often increase the size of the eigenvalue problem to be solved and can become computationally expensive for large systems here an approximate non state space based approach is proposed for this type of problem the proposed approximations are based on certain physical assumptions which simplify the underlying characteristic equation to be solved closed form approximate expressions of the complex and real eigenvalues of the system are derived these approximate expressions are obtained as functions of the elastic eigenvalues only this enables one to approximately calculate the eigenvalues of complex viscoelastic systems by simple post processing of the elastic undamped eigenvalues representative numerical examples are given to verify the accuracy of the derived expressions

on the quantification of damping model uncertainty abstract the characterization of uncertainty in the damping forces in a vibrating structure is of significant interest in structural dynamics the most common approach is to use a viscous damping matrix with uncertain coefficients the viscous damping is not the only damping model within the scope of linear analysis any model which makes the energy dissipation functional non negative is a possible candidate for a valid damping model there are many functional forms which can be used as damping models in this paper two approaches are proposed to quantify such model form uncertainty associated with the use of the viscous damping model not only the model parameters the first approach is based on an ensemble of equivalent damping functions and the second approach is based on the random matrix theory the results obtained from the two methods are compared using numerical examples it was observed that the random matrix theory can be used to quantify damping model uncertainty in some cases

the monotone iterative technique for impulsive hybrid set valued integro differential equations abstract we develop the monotone method for impulsive hybrid set integro differential equations in all its generality some interesting observations are presented

some applications of hausdorff dimension inequalities for ordinary differential equations upper bounds are obtained for the hausdorff dimension of compact invariant sets of ordinary differential equations which are periodic in the independent variable from these are derived sufficient conditions for dissipative analytic n dimensional periodic differential equations to have only a finite number of periodic solutions for autonomous equations the same conditions ensure that each bounded semi orbit converges to a critical point these results yield some information about the lorenz equation and the forced duffing equation

the generalized quasilinearization method for second order three point boundary value problems abstract in this paper we obtain the existence and uniqueness results for general second order three point boundary value problems by applying the method of upper and lower solutions together with leray schauder degree as well as obtaining monotone iteration schemes which converge quadratically to the unique solution of some specific second order three point boundary value problem by using the method of quasilinearization

anti periodic solutions of lienard equations with state dependent impulses abstract subject to a priori bounds lienard equations with state dependent impulsive forcing are shown to admit a unique absolutely continuous anti periodic solution with first derivative of bounded variation on finite intervals the point wise convergence of a sequence of iterates to the solution is obtained along with a bound for the rate of convergence the results are applied to josephson s and van der pol s equations

on monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations abstract in this paper we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions of first and second order periodic boundary value problems and periodic solutions of functional differential equations we obtain some new results relative to the lower solution and upper solution with

existence results for the p laplacian with nonlinear boundary conditions in this paper we study the existence of nontrivial solutions for the problem pu u p 2u in a bounded smooth domain rn with a nonlinear boundary condition given by u p 2 u f u on the boundary of the domain the proofs are based on variational and topological arguments

rapid convergence of the iterative technique for first order initial value problems in this paper we study the convergence of the approximate solutions of the first order problem u t f t w t u o u o we prove that if there exists kf u k k 1 and it is a continuous function then it is possible to construct two sequences of approximate solutions converging to a solution with rate of convergence of order k

symmetric state space method for a class of nonviscously damped systems multiple degree of freedom linear nonviscously damped systems are considered it is assumed that the nonviscousdampingforcesdependonthepasthistoryofvelocitiesviaconvolutionintegralsoverexponentiallydecaying kernel functions the traditional state space approach well known for viscously damped systems is extended to such nonviscously damped systems using a set of internal variables suitable numerical examples are provided to illustrate the proposed approach i introduction v iscousdampingisthemostcommonmodelforthemodeling of vibration damping in linear systems this model e rst introduced by rayleigh 1 assumes that the instantaneous generalized velocities are the only relevant variables that determine damping viscous damping models are used widely for their simplicity and mathematical convenience even though the behavior of real structural materials is at best poorly mimicked by simple viscous models forthisreason itiswellrecognizedthat ingeneral aphysically realistic model of damping will not be viscous damping models in whichthedissipativeforcesdependonanyquantityotherthantheinstantaneous generalized velocities are nonviscous damping models mathematically any causal model that makes the energy dissipation functional nonnegative is a possible candidate for a nonviscous damping model clearly a wide range of choice is possible either based on the physics of the problem or by selecting a model a priori and e tting its parameters from experiments here we will use a particular type of damping model that is not viscous and throughout the paper the terminology nonviscous damping will refer to this specie c model only possiblythemostgeneralwaytomodeldampingwithinthelinear range is to use nonviscous damping models that depend on the past history of motion via convolution integrals over kernel functions 2 the equations of motion of an n degree of freedom linear system with such damping can be expressed by

boundary value problem for first order impulsive functional integro differential equations this paper investigates extremal solutions of the boundary value problem for impulsive functional integro differential equations with nonlinear boundary conditions and deviating arguments in the presence of a lower solution u and an upper solution v with u v existence of extremal solutions is proved by establishing a new comparison principle and using the monotone iterative technique

nonlinear and stochastic phenomena the grand challenge for partial differential equations the major problems for partial differential equations are either nonlinear or stochastic or both considerable progress has occurred recently in these areas much of which has resulted from a striking interplay among theory computation and applications the nonlinear structures emphasized here are the nonlinear hyperbolic waves which occur in the solutions of nonlinear hyperbolic conservation laws and associated dissipative equations these equations are those most commonly used to model physical and chemical processes in continuum systems in one space dimension these nonlinear waves form traveling waves for which the methods of dynamical systems and bifurcation theory are very useful established points of view toward mathematical theories have been challenged by recent work e g uniqueness of solutions entropy conditions and elliptic regions in hyperbolic equations a type of geometry is defined in the state space of the conservation law by the nonlinear waves this geometry is generically sing

eigensolutions of nonviscously damped systems based on the fixed point iteration abstract in this paper nonviscous nonproportional symmetric vibrating structures are considered nonviscously damped systems present dissipative forces depending on the time history of the response via kernel hereditary functions solutions of the free motion equation leads to a nonlinear eigenvalue problem involving mass stiffness and damping matrices this latter as dependent on frequency viscous damping can be considered as a particular case involving damping forces as function of the instantaneous velocity of the degrees of freedom in this work a new numerical procedure to compute eigensolutions is proposed the method is based on the construction of certain recursive functions which under a iterative scheme allow to reach eigenvalues and eigenvectors simultaneously and avoiding computation of eigensensitivities eigenvalues can be read then as fixed points of those functions a deep analysis of the convergence is carried out focusing specially on relating the convergence conditions and error decay rate to the damping model features such as the nonproportionality and the viscoelasticity the method is validated using two 6 degrees of freedom numerical examples involving both nonviscous and viscous damping and a continuous system with a local nonviscous damper the convergence and the sequences behavior are in agreement with the results foreseen by the theory

systems of differential equations that are competitive or cooperative v convergence in 3 dimensional systems abstract for 3 dimensional systems that are competitive or cooperative we present new criteria for existence of equilibria and cycles convergence of all trajectories global stability and structural stability a certain type of positive feedback loop is shown to be structurally stable

an application of variational method to second order impulsive differential equation on the half line abstract in this paper we study the multiplicity of solutions for second order impulsive differential equation with a parameter on the half line by using a variational method and a three critical points theorem we give some new criteria to guarantee that the impulsive problem has at least three classical solutions also an example is given in this paper to illustrate the main results

inverse problems for dynamical systems in this paper we consider the problem of reconstructing a structurally stable vector field from its global phase portrait or from certain local pieces of the phase portrait we show that for arbitrary finite sets of points and of simple closed curves we can construct a structurally stable system having the elements of those sets as its critical points and limit cycles and a prescribed topological type in a neighborhood of each of them given a global structurally stable phase portrait we can construct a structurally stable polynomial system which is topologically equivalent to it some of our results were originally announced in 28 1 the general theory of dynamical systems orginated in the study of solution curves for systems of ordinary differential equations in a phase space this qualitative theory had its first major development in the work of poincare on the topology of integral curves a typical problem is to give a geometric description of the solutions of a particular system or class of systems with emphasis on the location of special features such as critical points and periodic orbits an inverse problem then is the construction of a system of equations given geometric properties of the solutions which may be in the form of a picture of the flow a schematic diagram of phase space or a list of critical orbits defined analytically a method for solving such problems is potentially useful in building models in the various fields in which the theory of dynamical systems is now being applied it could provide a basic model to which statistical identification techniques 141 could then be applied there is also an intrinsic interest in methods for constructing polynomial systems of prescribed type which is related to the lack of any progress toward a solution of hilbert s sixteenth problem the recent appearance of a counterexample 27 to the petrovsky landis conjecture for quadratic systems leaves the problem completely open one of the earliest results of this kind was obtained by forster in 1938

conservation laws of mixed type describing three phase flow in porous media in this paper we examine the mathematical structure of a model for three phase incompressible flow in a porous medium we show that in the absence of diffusive forces the system of conservation laws describing the flow is not necessarily hyperbolic we present an example in which there is an elliptic region in saturation space for reasonable relative permeability data a linearized analysis shows that in nonhyperbolic regions solutions grow exponentially however the nonhyperbolic region if present will be of limited extent which inherently limits the exponential growth to examine these nonlinear effects we resort to fine grid numerical experiments with a suitably dissipative numerical method these experiments indicate that the solutions of riemann problems remain well behaved in spite of the presence of a linearly unstable elliptic region in saturation space in particular when initial states are outside the elliptic region the riemann problem solution appears to stay outside the region further

on the concept of attractor this note proposes a definition for the concept of attractor based on the probable asymptotic behavior of orbits the definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor

approximation of solutions for an initial and terminal value problem for the forced duffing equation with non viscous damping an algorithm to find explicit approximate solutions of an initial and terminal value problem for the forced duffing equation with non viscous damping is accomplished via a generalized quasilinearization method in fact we obtain a monotone sequence of approximate solutions converging uniformly and quadratically to a unique solution of the problem

damped lateral vibrations of straight and curved cables with no axial pre load abstract this paper presents a study of the lateral vibrations of straight and curved cables with no axial pre load for the computation of the vibration transmissibility we used finite elements based on the euler bernoulli theory the dissipation of energy was studied with viscous and structural damping models where the rayleigh coefficients and the frequency dependence of the loss factor were identified by using the equality between the measured and the computed natural frequencies the frequency dependence of the dynamic modulus of elasticity was estimated and used for all the studied types of cable the excitation was the result of moving the support in a direction perpendicular to the axis of the cable the mathematical model for the computation of the vibrations of the straight and curved cables was verified with experimental measurements in which the support excitation was achieved with an electrodynamic shaker and the amplitude force was measured at the fixed support with a dynamometer for the curved cable the mathematical model was verified for in plane and out off plane vibrations three straight cables of different lengths were analyzed for the dependence of the rayleigh coefficients on the length of the cables

on the modal analysis of non conservative linear systems this paper applies the results of classical eigenvalue theory to the analysis of a non conservative vibratory system general results are obtained for the response of a multiple degree of freedom system which is represented by a set of linear second order differential equations with constant coefficients for the case when the eigenvalues of the system are distinct these results confirm those obtained by 1 fawzy and bishop by a different method the latter results are restricted to distinct eigenvalues but the more general analysis presented here allows the case of multiple eigenvalues to be included the physical interpretation of complex normal co ordinate vectors is discussed and some simple numerical examples illustrate the results the approach described here lends itself to numerical computation using computer library programs for eigenvalue determination