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.
Keywords
stochastics, viscoelasticity, nonlinear oscillations,
stability, simulation, top Lyapunov exponents, random
stationary processes
