<p>This study analyzed the coupled vibration of a MEMS resonator actuated by the electrodes of unequal lengths. The three-to-one internal resonance between the first and second modes is considered. The incremental harmonic balance (IHB) method was used to solve the governing equation. The stability and bifurcations of the equilibrium solutions for given parameters were determined by the multivariable Floquet theory. The research shows that the there-to-one internal resonance leads to the complex response, including jumping phenomenon, saddle-node bifurcation, and Hopf-bifurcation. Moreover, the numerical simulation is quantitatively given to illustrate the complex response caused by three-to-one internal resonance. The results of numerical simulation are consistent with those of IHB method.</p>

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Three-to-one internal resonance of MEMS resonator with electrodes of unequal lengths based on incremental harmonic balance method

  • Wang Ze,
  • Liang Jintao,
  • Yang Xuexia

摘要

This study analyzed the coupled vibration of a MEMS resonator actuated by the electrodes of unequal lengths. The three-to-one internal resonance between the first and second modes is considered. The incremental harmonic balance (IHB) method was used to solve the governing equation. The stability and bifurcations of the equilibrium solutions for given parameters were determined by the multivariable Floquet theory. The research shows that the there-to-one internal resonance leads to the complex response, including jumping phenomenon, saddle-node bifurcation, and Hopf-bifurcation. Moreover, the numerical simulation is quantitatively given to illustrate the complex response caused by three-to-one internal resonance. The results of numerical simulation are consistent with those of IHB method.