Oscillations and Stability of Viscoelastic Systems, Subjected to Random Stationary Loads

Abstract

In the present work the oscillations and the stability of elastic and viscoelastic systems, subjected to loads, randomly changing in time, are considered. These loads are assumed in the form of wide-band stationary processes. The stability of an equilibrium state or of an unperturbed motion with respect to perturbations of initial conditions is investigated. The relaxation kernel of the material is assumed degenerate. A numerical method for the analysis of the motion and stability of such systems is offered. It is based on the statistical simulation of random processes method corresponding to the variation of loads in time. With this aim the canonical expansions method is used. For each realization of the load the numerical solution of equations, describing the dynamic behavior of the system, is found. With the help of Liapunov exponents, which are calculated for these solutions, the decision about the stability of the system is made. The efficiency of the proposed method is illustrated by an example of a plate under the action of a random in-plane load under small or finite deflections. The proposed method allows to investigate oscillations and the stability of systems, excited by random stationary processes, which correlation function and probability distribution can be sufficiently arbitrary.