Nonlinear Coupled Vibration of Electrically Actuated Arch with Flexible Supports
Abstract
:1. Introduction
2. Problem Formulation
- The arch is shallow, i.e., ; hence, the parallel-plate assumption is valid;
- As the microbeam is slender, the Euler-Bernoulli beam theory is used, neglecting the effect of shear and rotary inertia;
- The simplest viscous damping model is adopted to model the dissipative mechanisms of the resonator;
- As the size of the structure is small, the size effects are considered.
3. The Method of Multiple Scales
3.1. Primary Resonance of the First Mode
3.2. Primary Resonance of the Second Mode
4. Numerical Results
4.1. Primary Resonance of the First Mode
4.2. Primary Resonance of the Second Mode
4.3. Numerical Verification
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Wang, Z.; Ren, J. Nonlinear Coupled Vibration of Electrically Actuated Arch with Flexible Supports. Micromachines 2019, 10, 729. https://doi.org/10.3390/mi10110729
Wang Z, Ren J. Nonlinear Coupled Vibration of Electrically Actuated Arch with Flexible Supports. Micromachines. 2019; 10(11):729. https://doi.org/10.3390/mi10110729
Chicago/Turabian StyleWang, Ze, and Jianting Ren. 2019. "Nonlinear Coupled Vibration of Electrically Actuated Arch with Flexible Supports" Micromachines 10, no. 11: 729. https://doi.org/10.3390/mi10110729