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Updated: Jan 26, 2026

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Three-to-One Internal Resonance in MEMS Arch Resonators
1School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an 710129, China. wangze0127@mail.nwpu.edu.cn.
This study explores the nonlinear dynamics of microelectromechanical systems (MEMS) arches under combined AC/DC loading and internal resonance. Findings reveal energy transfer between modes and complex behaviors like Hopf bifurcations.
Area of Science:
- Nonlinear Dynamics
- Microelectromechanical Systems (MEMS)
Background:
- MEMS arches are susceptible to complex dynamic behaviors under external forces.
- Internal resonance can significantly alter system responses.
Purpose of the Study:
- Investigate the nonlinear dynamics of a MEMS arch.
- Analyze the effects of AC/DC loading and three-to-one internal resonance.
- Characterize energy transfer and bifurcations.
Main Methods:
- Method of multiple scales applied to the governing equation.
- Galerkin scheme for reduced-order model (ROM) derivation.
- Analysis of modulation equations for equilibrium and stability.
Main Results:
- Obtained a reduced-order model describing amplitude and phase modulation.
- Identified energy transfer between the first and third modes due to internal resonance.
- Observed rich dynamic behaviors including Hopf bifurcations and quasiperiodic motions.
Conclusions:
- Internal resonance facilitates energy exchange in MEMS arches.
- MEMS arch dynamics exhibit complex phenomena under combined loading conditions.
- The study provides insights into MEMS arch nonlinear behavior for design and control.
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