Some Exact Solutions in the Theory of Nonlinear Random Oscillations

This paper develops the exact steady-state solutions for the response of a class on nonlinear oscillators to stochastic excitation. The techniques are applied to two problems, (1) the steady-state response of a self-excited oscillator, with multiple limit cycles, under white noise excitation, and (2) the response of a nonlinear oscillator under both additive and multiplicative stochastic excitation.