Moment Lyapunov exponents of the Parametrical Hill

The Lyapunov exponent and moment Lyapunov exponents of Hill\' s equation with frequency and damping coefficient fluctuated by correlated wideband random processes are studied in this paper. The method of stochastic averaging, both the first-order and the second-order, is applied. The averaged Itô differential equation governing the pth norm is established and the pth moment Lyapunov exponents and Lyapunov exponent are then obtained. This method is applied to the study of the almost-sure and the moment stability of the stationary solution of the thin simply supported beam subjected to time-varying axial compressions and damping which are small intensity correlated stochastic excitations. The validity of the approximate results is checked by the numerical Monte Carlo simulation method for this stochastic system.