High-order subharmonic parametric resonance of nonlinearly coupled micromechanical oscillators |
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Authors: | J Zhu C Q Ru A Mioduchowski |
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Institution: | (1) Department of Mechanical Engineering, University of Alberta, Edmonton, T6G 2G8, Canada |
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Abstract: | 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. |
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Keywords: | 62 30 +d Mechanical and elastic waves vibrations 63 22 +m Phonons or vibrational states in low-dimensional structures and nanoscale materials |
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