Nonlinear Vibration Systems with Two Parallel Random Excitations

Abstract

Systems of nonlinear vibration differential equations are investigated where the non-linearities are given by polynomials of any degree. The random excitations are induced by two parallel processes. These random excitations of an often applied type are expressed by linear functionals of weakly correlated processes with correlation length $ϵ$. The moments of the solutions and their first and second derivatives are expanded with respect to $ϵ$ where all terms up to order ${ϵ}^2$ are included. Approximations of the correlation functions are given explicitely. Only the quadratic and cubic non-linearities have an influence on the correlation functions in this approximation order.