Equivalent Nonlinear System Method for Stochastically Excited and Dissipated Integrable Hamiltonian Systems

Abstract

An equivalent nonlinear system method is proposed to obtain the approximate probability density for the stationary response of multi-degree-of-freedom integrable Hamiltonian systems with linear and (or) nonlinear dampings and subject to external and (or) parametric excitations of Gaussian white noises. The equivalent nonlinear systems are obtained on the basis of one of the following three criteria: least mean-squared difference in damping forces, dissipation energy balancing, or least mean-squared difference in dissipation energies. Two examples are given to illustrate the application and validity of the method and the differences in the three equivalence criteria. The method is also extended to a more general class of systems which include the stochastically excited and dissipated integrable Hamiltonian systems as special cases.