large amplitude vibrations of parabolic cables the non linear equations of motion for the coupled transverse vertical vibrations of parabolic cables are presented approximate solutions are developed by using the method of multiple scales solutions and numerical results are obtained and discussed for some special cases

a hybrid pseudo force laplace transform method for non linear transient response of a suspended cable a hybrid numerical scheme involving the combination of the laplace transform technique and the pseudo force method is proposed to analyze the non linear transient response of a suspended cable subjected to arbitrary dynamic loading a theoretical model of the cable with multi degree of freedom is first obtained through discretization of the partial differential equations by finite difference approximation the non linear governing equations take into account the effects of quadratic and cubic geometric non linearities the proposed method deals with the non linear effects as pseudo forces and then establishes an iterative solution scheme in the alternating laplace time domain by means of fast numerical laplace transform this method eschews a time stepping process and therefore is computationally efficient it also readily deals with the viscoelastic damping with frequency dependent model parameters and the hysteresis damping in terms of complex stiffness models numerical examples are presented to evaluate the dynamic responses of suspended cables under a concentrated sinusoidal force and a distributed random excitation and to identify the non linear response properties by comparison with the linear vibration the validity and accuracy of the proposed method is also verified by comparing the results with those obtained by using the direct time integration

controllability on principal fibre bundles with compact structure group abstract in this paper we consider the controllability problem for systems defined on principal fibre bundles in which the set of associated vector fields is invariant under the action of the structure group and projects down on to a set of vector fields on the base space it is shown that if the system is accessible and the structure group is compact then the system is controllable if and only if the system is controllable when projected onto the base space the connection between these systems and systems admitting symmetries generated by free and proper group actions is described and various examples are given relating to systems on homogeneous spaces

complete elastic characterization of viscoelastic materials by dynamic measurements of the complex bulk and young s moduli as a function of temperature and hydrostatic pressure abstract two independent systems to measure the dynamic complex young s and bulk moduli of viscoelastic materials as a function of temperature and hydrostatic pressure are described in the young s modulus system a bar shaped sample is adhered to a piezoelectric shaker and mounted vertically inside an air filled pressure vessel data are obtained using both the traditional resonant approach and a wave speed technique in the bulk modulus system the compressibility of a sample of arbitrary shape immersed in castor oil and placed inside a pressure chamber is measured data can be obtained at frequencies typically ranging from 50 hz to 5 khz at temperatures comprised between 2 and 50 c and under hydrostatic pressures ranging from 0 to 2 mpa young s or 6 5 mpa bulk typical data obtained with both systems are presented and it is shown how these data can be combined to completely characterize the elasticity of the material under investigation in particular they can be used to obtain experimental values of the complex poisson s ratio whose accurate measurement is otherwise quite challenging to perform directly as an example the magnitude and loss tangent of poisson s ratio are presented for a nearly incompressible rubber

tables of green s functions for the theory of beam vibrations with general intermediate appendages abstract the paper deals with the construction and tabulation of green s functions in a form suitable for use in determining natural frequencies and mode shapes of beams with intermediate attachments and of various boundary conditions the beam may have rotational and linear elastic attachments as well as rotational and linear attached inertias example computations are illustrated

the poisson s loss factor of solid viscoelastic materials the complex poisson s ratio plays an important role in characterizing the linear dynamic behaviour of solid materials and occurs in a number of equations used for acoustical and vibration calculus the ratio of the imaginary part to the real part of complex poisson s ratio is referred to as poisson s loss factor the magnitude of the poisson s loss factor is investigated in this paper for homogeneous isotropic linear solid viscoelastic materials with positive poisson s ratio the relation of the poisson s loss factor to the material damping is determined it is shown that the magnitude of the poisson s loss factor is approximately proportional to the difference between the shear and bulk loss factors and is a rational fractional function of the dynamic poisson s ratio in addition relationships are developed which enable one to determine the approximate magnitude of the poisson s loss factor from knowledge only of the shear loss factor and the dynamic poisson s ratio it is shown that the poisson s loss factor is smaller than the shear loss factor usually by one order of magnitude at least moreover it is pointed out that the poisson s loss factor of a high loss and a low loss material may be about the same experimental data on two rubbers and a hard plastic are presented to verify the theoretical conclusions

wave propagation in connected waveguides of varying cross section the spectral element method is extended to problems involving arbitrary non uniform waveguides by introducing an approximate tapered element the depth of the cross section is assumed to vary linearly thus allowing an arbitrary variation to be modelled as a collection of piece wise linear segments the frequency dependent stiffness relation is established using the displacement fields of the uniform deep waveguide both longitudinal and transverse as the ritz functions the element is verified by comparison with a 2 d finite element solution

suppression of time aliasing in the solution of the equations of motion of an impacted beam with partial constrained layer damping abstract signal processing issues encountered when an analytical spectrum is converted in the time domain with an inverse discrete fourier transform are investigated in the analytical model of the transient time response of an impacted beam with partial constrained layer damping pcld developed in ref d granger a ross effects of partial constrained viscoelastic layer damping parameters on the initial transient response of impacted cantilever beams experimental and numerical results journal of sound and vibration 321 1 2 2009 45 64 doi 10 1016 j jsv 2008 09 039 noncausal effects were observed for lightly damped structures as discussed in the present paper the noncausal effects were due to time aliasing occurring when continuous frequency spectra were discretized to suppress such errors the numerical laplace transform is introduced and applied to the previous model which was based on fourier transforms the equations of motion of the system and the viscoelastic properties of the core are formulated in the laplace domain a window is used in the laplace domain to avoid amplification of the gibbs oscillations that are caused by the truncation of the spectrum the new solution technique is compared to the previous method it is shown that noncausal effects appearing in the first milliseconds of time signals with the use of discrete fourier transforms are avoided with the laplace transform solution method numerical results are validated for transient responses using experimental impact force signals the results are in good agreement with experimental data

on the number of control sets on projective spaces the purpose of this paper is to provide an upper bound for the number of control sets for linear semigroups acting on a projective space rpd 1 these semigroups and control sets were studied by colonius and kliemann 1993 who proved that there are at most d control sets here we apply the results of san martin and tonelli 1995 about control sets for semigroups in semisimple lie groups and make a case by case analysis according to the transitive groups on rpd 1 which were classified by boothby and wilson 1975 1979 in order to improve that upper bound it turns out that in some cases there are at most d 2 or d 4 control sets

non linear galloping of sagged cables in 1 2 internal resonance the aeroelastic behaviour of a flexible elastic suspended cable driven by mean wind speed blowing perpendicularly to the cable s plane is investigated by applying the galerkin procedure to the partial differential equations of motion and using an in plane and an out of plane mode as shape functions a two d o f model is derived the discrete equations are coupled through quadratic and cubic terms arising both from geometric and aerodynamic effects the associated linear frequencies are assumed to be in an almost 1 2 ratio so that internal resonance occurs the multiple scale perturbation method is employed to obtain a set of three amplitude modulation equations whose coefficients depend on the mean wind speed which is assumed as control parameter two perturbative solutions are developed each based on a different assumption about the order of magnitude of the static displacements produced by steady state wind forces analytical results are then compared with direct numerical integrations of discrete non linear equations by performing a bifurcation analysis the existence of several equilibrium branches is proved the relative importance of geometric and aerodynamic non linearities is discussed through simplified models the influence on critical and postcritical behaviour of several parameters including geometrical cable parameters detuning and non symmetric flow effects is investigated the important role played by the steady state forces is highlighted

free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements this paper presents a formulation of an approximate spectral element for uniform and tapered rotating euler bernoulli beams the formulation takes into account the varying centrifugal force mass and bending stiffness the dynamic stiffness matrix is constructed using the weak form of the governing differential equation in the frequency domain where two different interpolating functions for the transverse displacement are used for the element formulation both free vibration and wave propagation analysis is performed using the formulated elements the studies show that the formulated element predicts results that compare well with the solution available in the literature at a fraction of the computational effort in addition for wave propagation analysis the element shows superior convergence

finite element analysis of a three dimensional underwater cable with time dependent length three dimensional underwater vibrations of a geometrically non linear cable with a weight at the lower end are investigated the length of the cable is time dependent a set of non linear time varying differential equations describing this system is derived by hamilton s principle and the variable domain finite element method the results of numerical simulation are presented for constant speed and sinusoidal axial motions of the cable the vibration responses of three initial conditions are shown the effects of initial displacements initial tensions due to gravity and the hydrodynamic forces on the non linear longitudinal and transverse amplitudes are presented finally some conclusions are drawn

a robust transfer matrix formulation for the ultrasonic response of multilayered absorbing media an improved version of the transfer matrix approach is presented for ultrasonic wave interaction in multilayered media generalized expressions are obtained for reflection and transmission coefficients in either fluid or solid half space and problems associated with numerical stability are solved efficiently the formulation is applicable to longitudinal and shear input waves alike at arbitrary incidence angles and for any sequence of solid or fluid layers also allowance is made for viscoelastic behavior by means of relaxation functions in the laplace transform domain finally the response to arbitrary incident pulse shapes and beam profiles is described through application of two dimensional numerical laplace inversion

a multiscale coupling method for the modeling of dynamics of solids with application to brittle cracks we present a multiscale model for numerical simulations of dynamics of crystalline solids the method combines the continuum nonlinear elasto dynamics model which models the stress waves and physical loading conditions and molecular dynamics model which provides the nonlinear constitutive relation and resolves the atomic structures near local defects the coupling of the two models is achieved based on a general framework for multiscale modeling the heterogeneous multiscale method hmm we derive an explicit coupling condition at the atomistic continuum interface application to the dynamics of brittle cracks under various loading conditions is presented as test examples

a bridging domain method for coupling continua with molecular dynamics abstract a bridging domain method for coupling continuum models with molecular models is described in this method the continuum and molecular domains are overlapped in a bridging subdomain where the hamiltonian is taken to be a linear combination of the continuum and molecular hamiltonians we enforce the compatibility in the bridging domain by lagrange multipliers or by the augmented lagrangian method an explicit algorithm for dynamic solutions is developed results show that this multiscale method can avoid spurious wave reflections at the molecular continuum interface without any additional filtering procedures even for problems with significant nonlinearities the method is also shown to naturally handle the coupling of the continuum energy equation with the molecular subdomain a multiple time step algorithm is also developed within this framework

a matrix methodology for spectral analysis of wave propagation in multiple connected timoshenko beams the dynamics of the timoshenko beam is recast such that the description requires information only at the end points this is then presented in the form of a dynamic stiffness relation suitable for assembling as is done analogously for conventional finite elements the analysis gives the exact frequency dependent response for the timoshenko beam irrespective of the length of the element the frequency domain response is converted to the time domain response using the fast fourier algorithm fft examples of its use in wave propagation studies are given

computation of eigenvalues in proportionally damped viscoelastic structures based on the fixed point iteration abstract linear viscoelastic structures are characterized by dissipative forces that depend on the history of the velocity response via hereditary damping functions the free motion equation leads to a nonlinear eigenvalue problem characterized by a frequency dependent damping matrix in the present paper a novel and efficient numerical method for the computation of the eigenvalues of linear and proportional or lightly non proportional viscoelastic structures is developed the central idea is the construction of two complex valued functions of a complex variable whose fixed points are precisely the eigenvalues this important property allows the use of these functions in a fixed point iterative scheme with help of some results in fixed point theory necessary conditions for global and local convergence are provided it is demonstrated that the speed of convergence is linear and directly depends on the level of induced damping in addition under certain conditions the recursive method can also be used for the calculation of non viscous real eigenvalues in order to validate the mathematical results two numerical examples are analyzed one for single degree of freedom systems and another for multiple ones

non linear oscillations of a four degree of freedom model of a suspended cable under multiple internal resonance conditions abstract a four degree of freedom model able to capture the main phenomena which are likely to occur in the non planar finite dynamics of an elastic suspended cable subjected to external forcings and support motions is developed from the continuum equations it contains two in plane and two out of plane components one symmetric and one antisymmetric an order two multiple time scales solution is obtained for the case of primary external resonance and three simultaneous internal resonances cable at crossover frequency possible classes of steady state planar non planar unimodal multimodal regular motions of the system are identified and their linearized stability analysis is performed some results are presented to highlight the role played by key perturbations on the onset of various classes the rich behaviour of the system and the influence of some control parameters on the response

closed form solutions for frequency equation and mode shapes of elastically supported euler bernoulli beams abstract this paper is concerned with the problem of free vibration of an euler bernoulli beam supported with an arbitrary number of translational springs of different constant stiffnesses the natural frequencies and mode shapes are calculated by means of the green s function method seven different boundary conditions are considered at both ends of the beam fixed pinned sliding free translational spring rotational spring and combined translational rotational spring each boundary condition on one end is combined with all other boundary conditions on the other yielding a total of 49 possible cases it has been shown in this paper that a green s function for any set of boundary conditions can be represented as a linear combination of function coefficients calculated for homogeneous boundary conditions and also a new form of the general solution is formulated using this principle green s functions are calculated and tabulated for each of the 49 possible cases which in essence closes the question of analytical solutions for this particular kind of problem using green s functions the tabulated solutions were used as the starting point in the derivation of the general formulae and to provide a new insight into the underlying mathematical structure of the solutions formulated with green s functions this can be of practical interest to the end user who wishes to implement them in computer code the validity of the obtained solutions is demonstrated with examples whose solutions are compared to the results in the published literature and to the results obtained with fem

a generalized complex eigenvector method for dynamic analysis of heterogeneous viscoelastic structures a generalized complex eigenvector method which can be used to a linear dynamic analysis of viscoelastic structures is described here dynamic analysis is understood as transient analysis and frequency response analysis the generalized complex eigenvector method is based on nite element discretization of structure approximation of viscoelastic properties by di erential operators and mode superposition technique coe cients of di erential operator are de ned from the condition of best coincidence of complex characteristic of viscoelastic material and complex characteristic of di erential operator in preset frequency range advantage of this method is that it allows to take into account the real changes of the viscoelastic property in frequency range also the generalized complex eigenvector method permit to describe a viscoelastic properties by two functions complex young s modulus complex poisson s ratio the method is veri ed with the help of comparing with solutions obtained by complex modulus method an in uence of viscoelastic poisson s ratio on transient and frequency responses of structure is demonstrated copyright 2001 john wiley sons ltd

vibration confinement in a general beam structure during harmonic excitations abstract in the present paper the green s function is utilized to provide a simple exact and direct analytical method for analysis of a beam structure of generic boundary conditions with attached springs and or finite masses the aim is to confine the vibration in a certain part of the structure the beam equation is based on the timoshenko beam theory with corrections for shear deformation and rotary inertia effects in the analysis the beam is driven by a harmonic external excitation the attached springs are modeled as simple reactions that provide transverse forces to the beam while each added mass provides a transverse force in addition to a moment at its location these forces moments act as secondary forces moments that reduce the response caused by the external force numerical simulations are conducted to find the optimal masses and or springs that confine the vibration in a certain chosen region the results were compared to that obtained from euler bernoulli beam theory beams that are excited by a bi harmonic force as well as dual excitation forces are analyzed in addition the case when the beams are excited near resonances is discussed also a method is proposed to impose a node at any desired location along the structure

dynamic analysis of large displacement cable motion with experimental verification cables used in engineering applications may undergo large displacement motion when subjected to dynamic loads particularly for cables with relatively low tension as cables are much weaker in the out of plane motion than the in plane motion three dimensional dynamic analysis is often necessary even when the excitation contains only a small out of plane component this paper presents the dynamic analysis of three dimensional cable motion accounting for axial flexural and torsional deformations as well as geometric non linearity due to large displacements and rotations the comprehensive study covers analytical formulation numerical strategy based on an iterative finite difference scheme and experimental verification by means of shaking table tests a specific problem of cable motion due to support excitation is used to illustrate the asymmetry and sensitivity of the dynamic tension response associated with geometric non linearity of large displacement cable motion the shaking table tests validate the accuracy of the numerical results obtained for both two dimensional and three dimensional cases

space time numerical simulation and validation of analytical predictions for nonlinear forced dynamics of suspended cables abstract this paper presents space time numerical simulation and validation of analytical predictions for the finite amplitude forced dynamics of suspended cables the main goal is to complement analytical and numerical solutions accomplishing overall quantitative qualitative comparisons of nonlinear response characteristics by relying on an approximate kinematically non condensed planar modeling a simply supported horizontal cable subject to a primary external resonance and a 1 1 or 1 1 vs 2 1 internal resonance is analyzed to obtain analytical solution a second order multiple scales approach is applied to a complete eigenfunction based series of nonlinear ordinary differential equations of cable damped forced motion accounting for both quadratic cubic geometric nonlinearities and multiple modal contributions local scenarios of cable uncoupled coupled responses and associated stability are predicted based on chosen reduced order models as a cross checking tool numerical simulation of the associated nonlinear partial differential equations describing the dynamics of the actual infinite dimensional system is carried out using a finite difference technique employing a hybrid explicit implicit integration scheme based on system control parameters and initial conditions cable amplitude displacement and tension responses are numerically assessed thoroughly validating the analytically predicted solutions as regards the actual existence the meaningful role and the predominating internal resonance of coexisting competing dynamics some methodological aspects are noticed along with a discussion on the kinematically approximate versus exact as well as planar versus non planar cable modeling

effects of partial constrained viscoelastic layer damping parameters on the initial transient response of impacted cantilever beams experimental and numerical results the effects of partial constrained viscoelastic layer damping on the first milliseconds of the transient vibration of an impacted beam is studied using an analytical model the viscoelastic properties of the core are frequency dependent and the shear modulus is modelled using a prony series the equations of motion of the system are obtained using lagrange s equations the equations of motion are converted in the frequency domain using a fourier transform and they are solved for frequency displacements using the assumed modes method they are then converted back in the time domain using an inverse fourier transform the technique is validated for transient responses using experimental impact force signals the numerical results are in good agreement with experimental data four partial constrained viscoelastic layer damping parameters are studied the length the placement the viscoelastic layer thickness and the constraining layer thickness it turns out that the length of the partial constrained viscoelastic layer damping has the most important effect on the initial transient displacement while the viscoelastic layer thickness has little effect noncausal effects in the model are discussed and are mainly induced when the partial constrained viscoelastic layer damping treatment is poorly effective

matrix propagator method for layered porous media analytical expressions and stability criteria we fully expand the thomson haskell propagator matrix method to obtain closed form analytical expressions for the reflectivity and transmittivity of a horizontally stratified poroelastic biot type medium that is bounded from above and below by fluid half spaces stable and unstable regions of the propagator matrix method are determined by means of comparison with the inherently stable reflectivity method it was found that the stability is mainly determined by the imaginary part of the vertical wavenumber of the biot slow wave

the dynamic analysis of a suspended cable due to a moving load the dynamic behaviour of a saggy suspension cable under a moving load was investigated first of all the updated lagrangian formulation and the finite element method were used to derive the property matrices of a saggy suspension cable in order to define the discretized equations of motion then the jacobi method was applied to the determination of the natural frequencies and the mode shapes of the suspended cable the moving load induced dynamic responses of the saggy suspended cable were obtained by using the newmark direct integration method incorporated with the newton raphson iteration technique the influence of some pertinent factors such as speed of moving load ratio of axial rigidity to total cable weight ae 0mg0l and ratio of moving load mass to total cable mass is the key point of the dynamic analysis

the lyapunov spectrum of families of time varying matrices for l families of time varying matrices centered at an unperturbed matrix the lyapunov spectrum contains the floquet spectrum obtained by considering periodically varying piecewise constant matrices on the other hand it is contained in the morse spectrum of an associated flow on a vector bundle a closer analysis of the floquet spectrum based on geometric control theory in projective space and in particular on control sets is performed introducing a real parameter p 0 which indicates the size of the li perturbation we study when the floquet spectrum the morse spectrum and hence the lyapunov spectrum all coincide this holds if an inner pair condition is satisfied for all up to at most countably many p values

identification of complex moduli and poisson s ratio from measured strains on an impacted bar identification of complex moduli and poisson s ratio from measured strains on an impacted bar

perfectly matched layers for time harmonic elastodynamics of unbounded domains theory and finite element implementation abstract one approach to the numerical solution of a wave equation on an unbounded domain uses a bounded domain surrounded by an absorbing boundary or layer that absorbs waves propagating outwards from the bounded domain a perfectly matched layer pml is an unphysical absorbing layer model for linear wave equations that absorbs almost perfectly outgoing waves of all non tangential angles of incidence and of all non zero frequencies this paper develops the pml concept for time harmonic elastodynamics in cartesian coordinates utilising insights obtained with electromagnetics pmls and presents a novel displacement based symmetric finite element implementation of the pml for time harmonic plane strain or three dimensional motion the pml concept is illustrated through the example of a one dimensional rod on elastic foundation and through the anti plane motion of a two dimensional continuum the concept is explored in detail through analytical and numerical results from a pml model of the semi infinite rod on elastic foundation and through numerical results for the anti plane motion of a semi infinite layer on a rigid base numerical results are presented for the classical soil structure interaction problems of a rigid strip footing on a i half plane ii layer on a half plane and iii layer on a rigid base the analytical and numerical results obtained for these canonical problems demonstrate the high accuracy achievable by pml models even with small bounded domains

control sets of linear systems on semi simple lie groups abstract in this paper we study the main properties of control sets with nonempty interior of linear systems on semisimple lie groups we show that unlike the solvable case linear systems on semisimple lie groups may have more than one control set with nonempty interior and that they are contained in right translations of the one around the identity

recovery of elastic parameters of cellular materials by inversion of vibrational data abstract this investigation addresses the inverse problem of the retrieval of the macroscopic young s modulus and poisson ratio of light fluid saturated cellular materials from the measured resonance frequencies of their vibrational response the latter is shown to be generally nonlinear for all except very small excitations in order to remain in the linear regime and thus avoid ambiguities in the characterization of the material we employ lightweight piezoelectric transducers and sensors and a low noise amplifier for the acquisition of dynamic response data the cellular materials under investigation polyurethane melamine are shown to behave as isotropic equivalent homogeneous elastic solids with rayleigh damping equivalent to a rheological model having the same dependence of attenuation on frequency in the frequency band of interest our viscoelastic model is validated by comparing its predictions of the dynamic response of the specimens to the predictions of the more complete biot interaction model the computations with both of these models are carried out by means of 3d finite element fe codes for a variety of specimen shapes and sizes once the simpler viscoelastic model is validated it is then employed to compute the trial resonance frequencies which are the solutions of an eigenvalue problem associated with this model during the inversion process the cost function which is a measure of the discrepancy between the trial and measured resonance frequencies for a number of vibrational modes is constructed and then minimized by the levenberg marquardt optimization algorithm in order to recover the sought for moduli finally a discussion is presented concerning the influence of the size and shape of the specimens as well as the number of employed modes on the uniqueness and quality of the inversion

a spectral multiscale method for wave propagation analysis atomistic continuum coupled simulation in this paper we present a new multiscale method which is capable of coupling atomistic and continuum domains for high frequency wave propagation analysis the problem of non physical wave reflection which occurs due to the change in system description across the interface between two scales can be satisfactorily overcome by the proposed method we propose an efficient spectral domain decomposition of the total fine scale displacement along with a potent macroscale equation in the laplace domain to eliminate the spurious interfacial reflection we use laplace transform based spectral finite element method to model the macroscale which provides the optimum approximations for required dynamic responses of the outer atoms of the simulated microscale region very accurately this new method shows excellent agreement between the proposed multiscale model and the full molecular dynamics md results numerical experiments of wave propagation in a 1d harmonic lattice a 1d lattice with lennard jones potential a 2d square bravais lattice and a 2d triangular lattice with microcrack demonstrate the accuracy and the robustness of the method in addition under certain conditions this method can simulate complex dynamics of crystalline solids involving different spatial and or temporal scales with sufficient accuracy and efficiency c 2014 elsevier b v all rights reserved

molecular dynamics boundary conditions for regular crystal lattices we present a method for deriving molecular dynamics boundary conditions for use in multiple scale simulations that can be applied at a planar boundary for any solid that has a periodically repeating crystal lattice the method is based on a linearization in the vicinity of the boundary and utilizes a fourier and laplace transforms in space and time to eliminate the degrees of freedom associated with atoms outside the boundary this method is straightforward to implement numerically and thus can be automated for a general crystal lattice we show that this method reproduces the known kernel for a 1d linear chain and apply the approach to obtain the damping kernel matrices for two real crystal lattices the graphene and diamond structures of carbon

spectrally formulated wavelet finite element for wave propagation and impact force identification in connected 1 d waveguides in this paper a novel wavelet based spectral finite element is developed for studying elastic wave propagation in 1 d connected waveguides first the partial differential wave equation is converted to simultaneous ordinary differential equations odes using daubechies wavelet approximation in time these odes are then solved using finite element fe technique by deriving the exact interpolating function in the transformed domain spectral element captures the exact mass distribution and thus the system size required is very much smaller then conventional fe the localized nature of the compactly supported daubechies wavelet allows easy imposition of initial boundary values this circumvents several disadvantages of the conventional spectral element formulation using fast fourier transforms fft particularly in the study of transient dynamics the proposed method is used to study longitudinal and flexural wave propagation in rods beams and frame structures numerical experiments are performed to show the advantages over fft based spectral element methods the efficiency of the spectral formulation for impact force identification is also demonstrated

frequency dependences of complex moduli and complex poisson s ratio of real solid materials abstract the concept of a complex modulus of elasticity is a powerful and widely used tool for characterizing the linear dynamic elastic and damping properties of solid materials in the frequency domain it is shown in this paper that typical characters of frequency dependences of all complex moduli shear young s etc and complex poisson s ratios of real solid materials can be determined by transforming the causal and real relaxation and creep responses respectively from the time domain into the frequency domain even without having to specify the processes of relaxation and creep it is proved that all dynamic moduli monotonically increase and the dynamic poisson s ratio monotonically decreases with increasing frequency and all respective loss factors pass through at least one maximum these frequency dependences are generally valid for any real solid material regardless of the actual damping mechanisms some experimental results are presented and interpreted in the light of the theory the usefulness of theoretical predictions in materials engineering measurements of dynamic properties and in modelling dynamic behaviour is discussed

forward projection of transient sound pressure fields radiated by impacted plates using numerical laplace transform forward propagation of the transient sound pressure radiated by an impacted plate is presented it is shown that direct and inverse time domain discrete fourier transforms involved in fourier transform based near field acoustical holography nah lead to aliasing errors in the reconstructed time signals adding trailing zeros to the initial time signals is an inefficient way to reduce time aliasing errors hence the numerical laplace transform is introduced and a fourier transform based transient nah tnah approach is formulated an error measure is introduced to compare both nah and tnah with respect to the propagation distance and the location of the observation point in the projection plane the percentage of error with tnah is reduced by more than a factor of 10 without adding trailing zeros to the initial signals simulation results are validated experimentally using a free plexiglas plate impacted at its center

legendre and laguerre polynomial approach for modeling of wave propagation in layered magneto electro elastic media a numerical method to compute propagation constants and mode shapes of elastic waves in layered piezoelectric piezomagnetic composites potentially deposited on a substrate is described the basic feature of the method is the expansion of particle displacement stress fields electric and magnetic potentials in each layer on different polynomial bases legendre for a layer of finite thickness and laguerre for the semi infinite substrate the exponential convergence rate of the method for propagation of love waves is numerically verified the main advantage of the method is to directly determine complex wave numbers for a given frequency via a matricial eigenvalue problem in a way that no transcendental equation has to be solved results are presented and the method is discussed

higher order eigensensitivities based numerical method for the harmonic analysis of viscoelastically damped structures this paper presents an efficient numerical method for the harmonic analysis of viscoelastically damped structural systems characterized by a frequency dependent structural damping matrix making use of the complex mode superposition method departing from the undamped eigensolution the proposed numerical method updates the complex and frequency dependent eigenpair avoiding the solution of a complex eigenproblem for each computational frequency the complex eigenvalues and eigenvectors are updated within the desired tolerance by an adaptive step size control scheme using the first and higher order eigenderivatives the influence on the computation time of the considered number of eigenderivatives and the tolerance is discussed and the efficiency of the proposed numerical method for the harmonic analysis of viscoelastically damped large ordered structural systems is proved finally a practical application is presented where the harmonic response of a constrained layer damping cantilever beam subjected to a base motion is analyzed the complex and frequency dependent eigenvalues and eigenvectors are computed the modal contributions to the total response are determined and the total response is approximated by the complex mode superposition method finally the approximated response is validated with the exact one computed by the direct frequency method and with that experimentally measured copyright 2011 john wiley sons ltd

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