Abstract
The response characteristics of the nonlinear oscillator to the harmonic excitation with the random perturbation and those to the narrow-band random excitation are compared. The Fokker-Planck equations governing the probability density functions of the responses to these two types of excitations are derived and solved by the finite difference method. The numerical examples for the Duffing oscillator are shown and compared with corresponding Monte Carlo simulation results. The relation between the jump phenomenon in the sample function of the displacement response and the multiple peak of the probability density function of the response is considered.
