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Nonlinear Coupled Vibration of Electrically Actuated Arch with Flexible Supports

机译：带柔性支撑的电动拱的非线性耦合振动

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摘要

The nonlinear coupled vibration of an electrically actuated arch microbeam has attracted wide attention. In this paper, we studied the nonlinear dynamics of an electrically actuated arch microbeam with flexible supports. The two-to-one internal resonance between the first and second modes is considered. The multiple scales method is used to solve the governing equation. Four first-order ordinary differential equation describing the modulation of the amplitudes and phase angles were obtained. The equilibrium solution and its stability are determined. In the case of the primary resonance of the first mode, stable periodic motions and modulated motions are determined. The double-jumping phenomenon may occur. In the case of the primary resonance of the second mode, single-mode and two-mode solutions are possible. Moreover, double-jumping, hysteresis, and saturation phenomena were found. In addition, the approximate analytical results are supported by the numerical results.
机译：电驱动弓形微束的非线性耦合振动已引起广泛关注。在本文中，我们研究了具有柔性支撑的电动拱微梁的非线性动力学。考虑第一和第二模式之间的一对一内部共振。多尺度方法用于求解控制方程。获得了四个描述振幅和相位角调制的一阶常微分方程。确定平衡溶液及其稳定性。在第一模式的初级共振的情况下，确定稳定的周期性运动和调制运动。可能会出现双跳现象。在第二模式的初级共振的情况下，单模式和双模式解决方案是可能的。此外，还发现了双跳，磁滞和饱和现象。此外，数值结果支持了近似分析结果。

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