High-order subharmonic parametric resonance of nonlinearly coupled micromechanical oscillators
Department of Mechanical Engineering, University of Alberta, Edmonton, T6G 2G8, Canada
Corresponding author: a firstname.lastname@example.org
Published online: 22 September 2007
This paper studies parametric resonance of coupled micromechanical oscillators under periodically varying nonlinear coupling forces. Different from most of previous related works in which the periodically varying coupling forces between adjacent oscillators are linearized, our work focuses on new physical phenomena caused by the periodically varying nonlinear coupling. Harmonic balance method (HBM) combined with Newton iteration method is employed to find steady-state periodic solutions. Similar to linearly coupled oscillators studied previously, the present model predicts superharmonic parametric resonance and the lower-order subharmonic parametric resonance. On the other hand, the present analysis shows that periodically varying nonlinear coupling considered in the present model does lead to the appearance of high-order subharmonic parametric resonance when the external excitation frequency is a multiple or nearly a multiple (≥3) of one of the natural frequencies of the oscillator system. This remarkable new phenomenon does not appear in the linearly coupled micromechanical oscillators studied previously, and makes the range of exciting resonance frequencies expanded to infinity. In addition, the effect of a linear damping on parametric resonance is studied in detail, and the conditions for the occurrence of the high-order subharmonics with a linear damping are discussed.
PACS: 62.30.+d – Mechanical and elastic waves; vibrations / 63.22.+m – Phonons or vibrational states in low-dimensional structures and nanoscale materials
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007