Abstract
Stochastic jump phenomena in the random responses of a Duffing oscillator subjected to the harmonic excitation with random perturbation are investigated. The stochastic jump phenomena correspond to the existence of multiple stationary responses, which differ in phase angle to the excitation. In our previous research, the product of complex wavelet transform of the response and the complex conjugate of that of the excitation has been proposed as the phase angle of each frequency. In this paper, we introduce several thresholds for the argument of this product to distinguish the state of the response. These thresholds are determined from the approximate frequency response function to harmonic excitation. Numerical examples show that there is the optimal threshold, and the optimal value can successfully classify the states of the response.
