Vol. 5, No. 2, 2010

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The simulation of stochastically excited viscoelastic systems and their stability

Vadim D. Potapov

Vol. 5 (2010), No. 2, 227–239

An efficient method for the analysis of nonlinear elastic and viscoelastic systems under the action of parametric forces in the form of Gaussian random stationary processes is suggested. The spectral densities of the input random stationary processes are assumed to be in the form of rational functions. The method is based on the simulation of stochastic processes and the numerical solution of differential equations, describing the motion of the system. Considering a sample of solutions, statistical characteristics of trajectories can be found. The effect of the parameters of the input random processes on the indicated statistical characteristics is investigated. Special attention is devoted to investigation of the stability of the unperturbed motion of elastic and viscoelastic systems. To analyze the stability of the unperturbed motion of the system the motion due to perturbations of the initial conditions is considered. The method of the stability investigation is based on the numerical solution of differential equations, describing the perturbed motion of the system, and the calculation of the top Lyapunov exponents. The method results in the estimation of the stability with respect to statistical moments of different orders. In some cases the superposition of a stochastic noise on the deterministic periodic excitation can have a stabilizing effect on the motion of elastic and viscoelastic systems.

stochastics, viscoelasticity, nonlinear oscillations, stability, simulation, top Lyapunov exponents, random stationary processes
Received: 3 December 2008
Revised: 22 June 2009
Accepted: 20 August 2009
Published: 30 August 2010
Vadim D. Potapov
Department of Structural Mechanics
Moscow State University of Means Communication
Obraztsov street, 15
Moscow 127994