Response Analysis of Nonlinear Free Vibration of Parallel-Plate MEMS Actuators: An Analytical Approximate Method
Response Analysis of Nonlinear Free Vibration of Parallel-Plate MEMS Actuators: An Analytical Approximate Method
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DOI：
10.1007/s42417-020-00204-7
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发表时间：
2020-03
影响因子：
2.7
通讯作者：
Yongping Yu;Lihui Chen;Zhigang Wang;Guojiang Liu
中科院分区：
文献类型：
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作者：
Yongping Yu;Lihui Chen;Zhigang Wang;Guojiang Liu
目的研究静电驱动微机械系统的非线性自由振动。方法采用无阻尼弹簧-质量模型和动力学运动方程对平行板微静电执行器进行运动分析。利用Galerkin法和耦合的Galerkin法和牛顿法，构造了上述问题的一阶解析近似周期解和周期解。此外，还得到了二阶和三阶解析近似解。结果在本工作中，讨论了已知的静态和动态Pull-in参数。随着动态吸引点的增加，相轨迹变为非周期轨迹。得到并比较了不同物理参数下微静电作动器的周期、相轨迹和随时间变化的位移的近似解和“精确”解。结论对于不同幅值的大范围非线性振动，解析近似解不仅是一种显式表达式，而且具有良好的精度。
PurposeIn this work, nonlinear free vibration of electrostatically actuated micromechanical system has been investigated. These nonlinear solutions are analytically derived.MethodsAn undamped spring-mass model and dynamic equation of motion are employed for the parallel-plate microelectrostatic actuator. The first analytical approximate period and periodic solution of the mentioned problems are constructed with the help of Galerkin’s method and coupling of Galerkin’s with Newton’s method. In addition, the second and third analytical approximate solutions are also derived. The “exact” solutions are obtained from direct integration.ResultsIn this work, the well-known static and dynamic pull-in parameters are discussed. Phase trajectory becomes non-periodic with the dynamic pull-in point. The approximate and “exact” solutions of period, phase trajectory, and time-dependent displacement of microelectrostatic actuators at various physical parameters are obtained and compared.ConclusionsIt is found that the analytical approximate solutions are not only an explicit expression but also have excellent precision for a wide range of nonlinear vibration with different amplitudes.