Subharmonic response of a single-degree-of-freedom nonlinear vibroimpact system to a randomly disordered periodic excitation

The subharmonic resonant response of a 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 asymptotic averaging over the period for slowly varying random processes. The averaged equations are solved exactly and algebraic equation of the amplitude of the response is obtained in the case without random disorder. A perturbation-based moment closure scheme is proposed and an iterative calculation equation for the mean square response amplitude is derived in the case with random disorder. The effects of damping, nonlinear intensity, detuning, 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 or large nonlinear stiffness, and when intensity of the random disorder increase, the steady-state solution may change from a limit cycle to a diffused limit cycle, and even change to a chaos one.