Control of a Forced Impacting Hertzian Contact Oscillator Near Sub- and Superharmonic Resonances of Order 2

Abstract

The effect of a fast harmonic base displacement and of a fast periodically time varying stiffness on vibroimpact dynamics of a forced single-sided Hertzian contact oscillator is investigated analytically and numerically near sub- and superharmonic resonances of order 2. The study is carried out using averaging procedure over the fast dynamic and applying a perturbation analysis on the slow dynamic. The results show that a fast harmonic base displacement shifts the location of jumps, triggering the vibroimpact response, toward lower frequencies, while a fast periodically time-varying stiffness shifts the jumps toward higher frequencies. This result has been confirmed numerically for both sub- and superharmonic resonances of order 2. It is also demonstrated that the shift toward higher frequencies produced by a fast harmonic parametric stiffness is larger than that induced by a fast base displacement.