Spectral response of asymmetrical random oscillators

An analytical procedure to estimate the power spectral density (PSD) response of a weakly damped oscillator with a nonlinear asymmetrical restoring force under external stochastic wide-band excitation is presented. An equivalent linear system with random parameters is derived, from which the PSD is deduced. The use of corrective terms yields an approximation of the PSD in the region of the second and third harmonic resonant frequencies (as well as at higher harmonics). In the same way, the PSD of the reaction force is also reported. The method is applied to an impact oscillator with asymmetrical clearances and asymmetrical elastic stops.