Problems of the stability of elastic and viscoelastic systems under action of random loads, first of all of columns, subjected to the longitudinal force which is a stochastic stationary process, were considered by many authors. A sufficiently thorough survey of these works is contained in monograph [1]. The greatest number of results were obtained for that case, when the stationary process is supposed as a Gaussian white noise. If parametric forces are stationary wide-band processes then the solution of the stability problem becomes significantly more complicated. In such a case mainly sufficient conditions of the almost sure stability were obtained. It should be underlined that the estimation of stability boundaries, which are obtained with help of these criterions usually rather rough. If mentioned processes are arbitrary enough then for the solution of the stability problem more correct results, from the point of view of stability boundaries, can be obtained with help of a method of the statistical simulation of stochastic functions in a combination with computational methods for the solution of the problem.The present work is devoted to the investigation of the stability of elastic and viscoelastic systems, excited by random stationary parametric loads in the form of colored noises. Further the simulation routine is based on the Runge-Kutta method of the fourth order. For such a case a scheme of the simulation of the white noise is very important. Concrete versions of this simulation will be considered on examples below. The principal purpose of the present work is the investigation of the stability of system with respect to statistical moments. Since the closed system of equations for the moments of the displacements y_j(t) in the case of colored noise could not be obtained, the method ofstatistical data processing is applied. The estimation of moments for the instant t_n can beobtained as a result of statistical average of values , derived from the solution of equations,describing the behavior of the considered system, for the enough large number of realizations. Using the procedure, suggested in the work [1], the estimation of the top Liapunov exponent can be obtained. The fulfilled calculations allow to estimate the influence of different characteristics (of random stationary loads, of viscous properties of the material) on top Liapunov exponents and consequently on the stability with respect to statistical moments of the different order.
展开▼
