Subharmonic response of a single-degree-of-freedom nonlinear vibroimpact system to a narrow-band excitation

The subharmonic response of single-degree-of-freedom nonlinear vibroimpact oscillator with a one-sided barrier to narrow-band random excitation is investigated. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, or velocity jumps, thereby permitting the applications of random averaging method. The averaged equations are solved exactly and the algebra equation of the amplitude of the response is obtained in the case without random perturbation. A perturbation-based moment closure scheme is proposed and an iterative calculation equation for the mean square response amplitude is derived for the case with random perturbation. The effects of damping, nonlinear intensity, detuning, bandwidth, and magnitudes of random excitations are analyzed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the peak amplitudes may be strongly reduced at large detuning, and when the intensity of the random excitation increases, the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle, even to a chaotic one.