Influence of randomly varying damping coefficient on the dynamic stability of continuous systems

A method for the determination of sufficient conditions for the almost sure asymptotic stability of some continuous systems, when the damping coefficient is random time-dependent function is studied. In this case, the probabilistic property of the derivative process of the damping coefficient is taken into account. The problem is solved by means Liapunov direct method, and tested on a simply supported elastic beam, compressed by time-dependent stochastic axial force. Regions of almost sure asymptotic stability as functions of the constant part of viscous damping coefficient and magnitude of an axial force are given.