Stochastic stability of non-gyroscopic viscoelastic systems

In this paper the dynamic stability of non-gyroscopic viscoelastic systems under multiple parametric excitations is investigated. The largest Lyapunov exponent as an indicator of the almost-sure asymptotic stability of the system is obtained by applying the stochastic averaging method together with Khasminskii's technique. The integral term arising from the viscoelastic effect is averaged by making use of Larianov's method. As an application, the flexural-torsional instability of a deep rectangular viscoelastic beam under stochastically fluctuating central load and end moments applied simultaneously is investigated. Both cases of follower and non-follower central fluctuating load are included in this analysis. (C) 2003 Elsevier Ltd. All rights reserved.