High-order subharmonic parametric resonance of multiple nonlinearly coupled micromechanical nonlinear oscillators

• DOI: 10.1007/s00707-009-0242-8
• Publication Date: 2009-10-12T03:41:17Z
• Authors: J. Zhu; C. Q. Ru; A. Mioduchowski
• Keywords: Parametric oscillator; Nonlinear resonance; Multiple-scale analysis; Harmonic balance; Subharmonic function

High-order subharmonic parametric resonance of coupled microbeams is studied based on a model of multiple nonlinearly coupled micromechanical nonlinear oscillators. Of particular interest are the effects of nonlinear coupling between adjacent oscillators and elastic nonlinearity of individual oscillators. First, we analyze parametric resonance of a nonlinearly coupled nonlinear oscillator, and conduct instability analysis of steady-state solutions. Then we study parametric resonance of three nonlinearly coupled nonlinear oscillators. It is found that the nonlinear coupling between adjacent oscillators leads to the appearance of high-order subharmonic parametric resonance which, to the best of our knowledge, has received little attention in previous related works. In the present analysis, the effects of elastic nonlinearity of individual oscillators, damping and some loading parameters (such as dc and ac voltages) on high-order subharmonics are also examined in detail. Our results suggest that the range of excitation frequency for parametric resonance of coupled oscillators can be much larger than what the previous studies predicted, due to the appearance of high-order subharmonic parametric resonance. These results are believed to offer new and interesting insights into the ongoing research on nonlinear dynamics of coupled microbeams or nanobeams in MEMS or NEMS.