NONLINEARLY DAMPED SYSTEMS UNDER SIMULTANEOUS BROAD-BAND AND HARMONICEXCITATIONS

The probability distribution of the response of a nonlinearly damped s ystem subjected to both broad-band and harmonic excitations is investi gated. The broad-band excitation is additive, and the harmonic excitat ions can be either additive or multiplicative. The frequency of a harm onic excitation can be either near or far from a resonance frequency o f the system. The stochastic averaging method is applied to obtain the Ito type stochastic differential equations for an averaged system des cribed by a set of slowly varying variables, which are approximated as components of a Markov vector. Then, a procedure based on the concept of stationary potential is used to obtain the exact stationary probab ility density for a class of such averaged systems. For those systems not belonging to this class, approximate solutions are obtained using the method of weighted residuals. Application of the exact and approxi mate solution procedures are illustrated in two specific cases, and th e results are compared with those obtained from Monte Carlo simulation s.