Dynamic stability of axially loaded columns subjected to stochastic excitations.

Abstract

This paper deals with Lyapunov-type analysis of the dynamic stability of a linear elastic column subjected to an axial stochastic load. Within the past decade, the interest in stability of stochastic systems of differen tial equations has rapidly increased, as indicated by the large number of papers on the subject. The intent of this paper is to provide sufficient conditions on the absolute value of the excitation applied to the column problem in order to insure mean-square global stability. Although this problem has been investigated by several authors by considering the concept of almost sure stability, the bounds provided are related to only the mean value of the absolute value of the excitation, or, at best, the standard deviation of a Gaussian process with zero mean. In the present paper, we are able to relate the required bounds, for mean-square global stability, to the mean and variances of the excitation. The bounds are applicable for any general continuous random process. The sufficient bounds are obtained by using a Lyapunov type of approach, introduced by Bertram and Sarachik and extended here for stability in the mean-square sense.