Vibrational subharmonic and superharmonic resonances

Abstract

We investigate the response to the low-frequency of a bistable system perturbed by a low-frequency and a high-frequency excitation. The resonance induced by the high-frequency excitation or simply by a variation of a system parameter can occur at the frequency which is equal to, or smaller, or larger than the low-frequency excitation. Similarly to what happens with the subharmonic resonance and the superharmonic resonance phenomenon, we name the resonance that occur at these frequencies as vibrational subharmonic resonance and vibrational superharmonic resonance, respectively. While the traditional vibrational resonance reported in the literature appears in a continuous region in a three-dimensional surface, however the vibrational subharmonic resonance and the vibrational superharmonic resonance reported here occur only in some discrete regions. Here, we show the new results describing both the vibrational subharmonic resonance and the vibrational superharmonic resonance at a frequency which is not an integer multiple of the low-frequency. It is different from the nonlinear vibrational resonance reported in the former literatures, which only give the high-order vibrational resonance at frequencies that are multiple of the excitation frequency.