Superharmonic Responses of an Oscillator with Impact
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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Superharmonic responses are characteristic of many nonlinear systems undergoing high intensity of excitation. Recent experimental investigation findings of energy harvesting involves nonlinear systems have observed superharmonic dynamics and phenomenological effects which yields superior electrical power relative to that achieved by the fundamental harmonic. Superharmonic response, indicated by dynamics occurring at integer fractions of the fundamental frequency, exhibits a behavior that the response frequency is several times of the frequency of the excitation. Particularly in an electrostatic power harvester, each oscillation is accompanied by power harvesting. Thus, the superharmonic response leads to doubling, tripling or even more times of the power harvesting cycles than that introduced by the fundamental harmonic which is the same as the forcing cycle. The most general mechanism of an electrostatic power harvester consists a variable capacitor which could be modeled as a bilinear stiffness oscillator with limiters or stoppers. In particular, we are interested in investigating the superharmonic responses of such models when forced at a frequency much lower than the resonance frequency of the oscillator and large amplitude responses when the forcing is "subcritical", i.e. the forcing amplitude is below the threshold to cause impact as predicted based on the linear theory. It is exemplified by previous investigations that the superharmonic responses at subcritical forcing amplitude are desirable responses of power harvesters when forced at a frequency well-below its resonance frequency. Although a large literature already exists on the studies of impact, it seems that additional experimental investigations focusing on low frequency responses are still warranted.