The moment Lyapunov exponent of a Timoshenko beam under bounded noise excitation

The moment Lyapunov exponents and the Lyapunov exponent of a two-dimensional system under bounded noise excitation are studied in this paper. The method regular perturbation is applied to obtain the small noise expansion of the pth moment Lyapunov exponent and the Lyapunov exponent. The results are applied to the study of the almost-sure and moment stability of the stationary solutions of the elastic beam subjected to the stochastic axial load. The boundaries of the almost-sure and moment stability of the elastic beam as the function of the damping coefficient and characteristics of the stochastic force are obtained.