the numerical study of the nonlinear dynamics of a light axially moving string abstract the vibration characteristics of a light axially moving band are investigated by a numerical study in the subcritical and supercritical speed ranges equations of motion for the geometrically nonlinear axially moving string are formulated using hamilton s principle and discretized by the finite element method the periodic nonlinear problem for the string is solved by the fourier galerkin newton fgn method the nonlinear dynamic behaviour of an axially moving band is examined through the dependences between the fundamental frequency axial velocity and vibration amplitude resulting from nonlinear free vibration in general the behaviour of the nonlinear axially moving string is similar to that of a nonlinear beam the most notable differences being the fact that the string does not undergo bifurcation from a straight configuration to curved equilibrium states in a supercritical transport speed regime nor does the equilibrium state remain straight

mean square power series solution of random linear differential equations this paper deals with the construction of random power series solutions of linear differential equations containing uncertainty through the diffusion coefficient the source term as well as the initial condition under appropriate hypotheses on the data we establish that the constructed random power series solution is mean square convergent in a certain interval whose length depends on the mean square norm of the random variable coefficient also the main statistical functions of the approximating stochastic process solution generated by truncation of the exact power series solution are given finally we apply the proposed technique to several illustrative examples

numerical solution ofmatrix differential models using cubic matrix splines this paper deals with the construction of approximate solution of first order matrixlinear differential equations using matrix cubic splines an estimation of the approximation error an algorithm for its implementation and some illustrative examples are included

efficient computation of the sound fields above a layered porous ground an efficient computation of sound fields due to a monopole source placed above a porous layer is presented this paper examines an improved scheme whereby the steepest descent path is selected for the numerical evaluation of the sommerfeld integral along the steepest descent path a standard gaussian hermite quadrature can be used to calculate the sound fields effectively the suggested numerical scheme is accurate at all frequencies except in the very near field the proposed method is more numerically efficient than other computational schemes especially at long ranges and high source frequencies

computing continuous numerical solutions of matrix differential equations abstract in this paper we construct analytical approximate solutions of initial value problems for the matrix differential equation x t a t x t x t b t l t with twice continuously differentiable functions a t b t and l t continuous we determine in terms of the data the existence interval of the problem given an admissible error e we construct an approximate solution whose error is smaller than e uniformly in all the domain

a hybrid bie ffp scheme for predicting barrier efficiency outdoors to assess the acoustical performance of noise screens in the presence of an arbitrary sound speed profile a numerical scheme based on a combination of the boundary integral and fast field program methods is developed the green s function required in the boundary integral is evaluated by a fast field formulation the procedure is validated by comparing its predictions with other numerical results for simple cases and with measurements for indoor model experiments simulating downward refracting conditions it is predicted that the performance of a noise screen placed 50 m from the source is reduced considerably by moderate downwind conditions

random hermite differential equations mean square power series solutions and statistical properties abstract this paper deals with the construction of random power series solution of second order linear differential equations of hermite containing uncertainty through its coefficients and initial conditions under appropriate hypotheses on the data we establish that the constructed random power series solution is mean square convergent we provide conditions in order to obtain random polynomial solutions and as a consequence random hermite polynomial are introduced also the main statistical functions of the approximate stochastic process solution generated by truncation of the exact power series solution are given finally we apply the proposed technique to several illustrative examples comparing the numerical results with respect to those provided by other available approaches including monte carlo simulation

a frequency domain based numeric analytical method for non linear dynamical systems abstract in this paper a multiharmonic balancing technique is used to develop certain algorithms to determine periodic orbits of non liner dynamical systems with external parametric and self excitations essentially in this method the non linear differential equations are transformed into a set of non linear algebraic equations in terms of the fourier coefficients of the periodic solutions which are solved by using the newton raphson technique the method is developed such that both fast fourier transform and discrete fourier transform algorithms can be used it is capable of treating all types of non linearities and higher dimensional systems the stability of periodic orbits is investigated by obtaining the monodromy matrix a path following algorithm based on the predictor corrector method is also presented to enable the bifurcation analysis the prediction is done with a cubic extrapolation technique with an arc length incrementation while the correction is done with the use of the least square minimisation technique the under determined system of equations is solved by singular value decomposition the suitability of the method is demonstrated by obtaining the bifurcational behaviour of rolling contact vibrations modelled by hertz contact law

dual algorithms for fast calculation of the fourier bessel transform this paper presents a new procedure for the fast calculation of the fourier bessel transform the computation is performed in a dual mode and involves two matched algorithms the first of which provides the lower order components while the second yields intermediate and higher order samples of the transform the first algorithm is based on the fourier selection summation fss method derived in a previous study while the second relies on the bessel function large argument asymptotic expansion it is shown that the dual procedure constructed along these lines requires a computation time which is about four times that needed by a single n point fast fourier transform

effect of smoothing piecewise linear oscillators on their stability predictions the effects of smoothing non smooth function on estimation of dynamical stability of the periodic response determined in the frequency domain are considered in this paper for that purpose a simple single degree of freedom system with piecewise linear force displacement relationship subjected to a harmonic force excitation is analyzed stability of the periodic response obtained in the frequency domain by the incremental harmonic balance method is determined by using the floquet liapounov theorem results obtained are verified in the time domain by the method of piecing the exact solutions and runge kutta integration routine

acoustic scattering by an inhomogeneous layer on a rigid plate the problem of scattering of time harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in r 2 is considered the density is assumed to be unity in the media within the layer the sound speed is assumed to be an arbitrary bounded measurable function the problem is modelled by the reduced wave equation with variable wavenumber in the layer and a neumann condition on the plate to formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced a generalization of the rayleigh expansion condition for diffraction gratings with the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate under additional assumptions on the wavenumber in the layer uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established general results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data

upper and lower eigenvalue summation bounds of the lyapunov matrix differential equation and the application in a class time varying nonlinear system in this paper we first show a class relation between the eigenvalue of functional matrix derivative and the derivative of function matrix eigenvalue applying the relation we transform the time v

the harmonic balance method for bifurcation analysis of large scale nonlinear mechanical systems abstract the harmonic balance hb method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems the objective of this paper is to exploit the method for bifurcation analysis i e for the detection and tracking of bifurcations of nonlinear systems to this end an algorithm that combines the computation of the floquet exponents with bordering techniques is developed a new procedure for the tracking of neimark sacker bifurcations that exploits the properties of eigenvalue derivatives is also proposed the hb method is demonstrated using numerical experiments of a spacecraft structure that possesses a nonlinear vibration isolation device

accurate fft based hankel transforms for predictions of outdoor sound propagation without modification the fft based hankel transform that is used in the fast field program developed for applications in underwater acoustics is not sufficiently accurate for predictions of outdoor sound propagation near to finite impedance boundaries numerical problems arise from singularities in the integrand and from representation of an infinite integral by a finite sum modifications to the basic algorithm are proposed to improve its accuracy these modifications include integration below the real axis subtraction of an analytic function and addition of terms to represent the difference between the finite sum and the sum to infinity predictions of the modified algorithm of propagation in a calm isothermal atmosphere from a point source near to a boundary are compared both with those of the unmodified algorithm and with exact solutions or analytic approximations

random matrix difference models arising in long term medical drug strategies abstract this paper deals with the construction of random discrete solutions of coupled linear difference equations incorporating uncertainty into both the initial condition and the source term first sufficient conditions in order to guarantee mean square stability of the solution are provided then the main statistical functions such as mean and covariance of the discrete solution stochastic process are given finally illustrative examples of potential interest in long time medical drug strategies are shown

solving initial and two point boundary value linear random differential equations a mean square approach abstract this paper deals with the construction of mean square real valued solutions to both initial and boundary value problems of linear differential equations whose coefficients are assumed to be stochastic processes and initial and boundary conditions are random variables a key result to conduct our study is the extension of the leibniz integral rule to the random framework taking advantage of the so called random fourth calculus exact expressions for the main statistical functions average and variance associated to the solutions to both problems are also provided illustrative examples computing the average and standard deviation are included

a multistep transversal linearization mtl method in non linear dynamics through a magnus characterization a new form of a multi step transversal linearization mtl method is developed and numerically explored in this study for a numeric analytical integration of non linear dynamical systems under deterministic excitations as with other transversal linearization methods the present version also requires that the linearized solution manifold transversally intersects the non linear solution manifold at a chosen set of points or cross section in the state space however a major point of departure of the present method is that it has the flexibility of treating non linear damping and stiffness terms of the original system as damping and stiffness terms in the transversally linearized system even though these linearized terms become explicit functions of time from this perspective the present development is closely related to the popular practice of tangent space linearization adopted in finite element fe based solutions of non linear problems in structural dynamics the only difference is that the mtl method would require construction of transversal system matrices in lieu of the tangent system matrices needed within an fe framework the resulting time varying linearized system matrix is then treated as a lie element using magnus characterization w magnus on the exponential solution of differential equations for a linear operator commun pure appl math vii 1954 649 673 and the associated fundamental solution matrix fsm is obtained through repeated lie bracket operations or nested commutators an advantage of this approach is that the underlying exponential transformation could preserve certain intrinsic structural properties of the solution of the non linear problem yet another advantage of the transversal linearization lies in the non unique representation of the linearized vector field an aspect that has been specifically exploited in this study to enhance the spectral stability of the proposed family of methods and thus contain the temporal propagation of local errors a simple analysis of the formal orders of accuracy is provided within a finite dimensional framework only a limited numerical exploration of the method is presently provided for a couple of popularly known non linear oscillators viz a hardening duffing oscillator which has a non linear stiffness term and the van der pol oscillator which is self excited and has a non linear damping term

random analytic solution of coupled differential models with uncertain initial condition and source term this paper deals with the construction of random power series solution of vector initial value problems containing uncertainty in both initial condition and source term under appropriate hypothesis on the data we prove that the random series solution constructed by a random frobenius method is convergent in the mean square sense also the main statistical functions of the approximating stochastic process solution generated by truncation of the exact series solution are given finally we apply the proposed technique to several illustrative examples

analytic numerical approximating processes of diffusion equation with data uncertainty this paper deals with the construction of approximating processes for solving mixed problems related to the diffusion equation where the initial condition is assumed to be a stochastic process and the diffusion coefficient is a random variable expectation and standard deviation of the approximation processes are given

a semi analytical locally transversal linearization method for non linear dynamical systems an numeric analytical implicit and local linearization methodology called the locally transversal linearization ltl is developed in the present paper for analyses and simulations of non linear oscillators the ltl principle is based on deriving the locally linearized equations in such a way that the tangent space of the linearized equations transversally intersects that of the given non linear dynamical system at that particular point in the state space where the solution vector is sought for purposes of numerical implementation two different numerical schemes namely ltl 1 and ltl 2 schemes based on the ltl methodology are presented both ltl 1 and ltl 2 procedures finally reduce the given set of non linear ordinary differential equations odes to a set of transcendental algebraic equations valid over a short interval of time or over a short segment of the evolving trajectories as projected on the phase space while in the ltl 1 scheme the desired solution vector at a forward time point enters the linearized differential equations as an unknown parameter in the ltl 2 scheme a set of unknown residues enters the linearized system as parameters a limited set of examples involving a few well known single degree of freedom sdof non linear oscillators indicate that the ltl methodology is capable of accurately predicting many complicated non linear response patterns including limit cycles quasi periodic orbits and even strange attractors copyright 2001 john wiley sons ltd

construction and computation of variable coefficient sylvester differential problems abstract in this paper initial value problems for sylvester differential equations x t a t x t x t b t f t with analytic matrix coefficients are considered first an exact series solution of the problem is obtained given a bounded domain and an admissible error a finite analytic numerical series solution is constructed so that the error with respect to the exact series solution is uniformly upper bounded by in an iterative procedure for the construction of the approximate solutions is included

ground effect analysis surface wave and layer potential representations abstract this paper presents two kinds of analytical exact expressions of the sound field reflected by a plane boundary as obtained by using either surface wave or layer potentials representations both solutions are first expressed as a sum of integrals which have a form suitable for numerical computation then these integrals are expanded into convergent series which provide analytical approximations of the solution numerical techniques are proposed for computing a the surface wave representation and b the approximation deduced from the layer potentials representation this approximation and the classical one sum of the surface wave and the first two terms of the asymptotic series are compared with the exact solution several examples show that the approximate formulas established here are valid on a range much wider than the validity domain of the classical ones

random airy type differential equations mean square exact and numerical solutions this paper deals with the construction of power series solutions of random airy type differential equations containing uncertainty through the coefficients as well as the initial conditions under appropriate hypotheses on the data we establish that the constructed random power series solution is mean square convergent over the whole real line in addition the main statistical functions such as the mean and the variance of the approximate solution stochastic process generated by truncation of the exact power series solution are given finally we apply the proposed technique to several illustrative examples which show substantial speed up and improvement in accuracy compared to other approaches such as monte carlo simulations