Generalized parametric resonance Academic Article uri icon

abstract

  • We consider the dynamic response of systems subjected to principal parametric resonant excitation in which the full potential, including nonlinearities, is modulated in a time-periodic manner. This work was motivated by the model of Rhoads et al. [J. Sound Vibration, 296 (2006), pp. 797--829], which was used to describe an interesting bifurcation structure that was experimentally observed in a micro-electro-mechanical system. The goal of the present investigation is to more fully explore this class of systems, described by a generalized nonlinear Mathieu equation, and ascertain general features of their response. The method of averaging is used to derive equations governing the slowly varying amplitude and phase for parametrically excited systems with weak nonlinearity, small damping, and near resonant excitation, allowing for a detailed analysis of the system steady-state response. Results for a general class of models are presented first, followed by details for two examples: (i) generalized parametric ...

publication date

  • January 1, 2016