Almost sure stability of dynamical systems under combined harmonic and stochastic excitations

Abstract

The almost sure asymptotic stability and the associated sample behavior of mechanical and structural systems under combined harmonic and stochastic excitations are examined. The method of extended stochastic averaging developed by the author is used to obtain a lower-dimensional Markov processes for multi-degree-of-freedom structures subjected to both harmonic and stochastic excitations, provided that the intensities of these excitations are small. The approach in this paper formulated for the study of almost sure asymptotic stability is based on the well-developed concept of Lyapunov exponents. The largest Lyapunov exponent is obtained explicitly by using the lower-dimensional approximate Itô equations. The results from this analysis are applied to study the almost sure asymptotic stability of uncoupled flapping motion of rotor blades in forward flight under the effect of atmospheric turbulence.