一类厚度误差影响下单边微谐振器模态耦合动力学研究

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (21) : 325-332.

论文

冯晶晶1,2，王冲1,2，郝淑英1,2，胡文华1,2，吴梦玉1,2

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Modal coupled dynamics of unilateral micro-resonator under influence of thickness error

FENG Jingjing1,2, WANG Chong1,2, HAO Shuying1,2, HU Wenhua1,2, WU Mengyu1,2

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文章历史 +

摘要

通过表面加工技术制造的微谐振器不可避免地存在加工误差，本文引入了用于描述微梁上下表面变化的截面参数，并基于欧拉伯努利梁模型，研究了厚度形态误差下微梁谐振器模态间的耦合振动。应用Galerkin离散和多尺度方法获得了相应的非线性耦合方程，得到了不同截面参数误差下产生耦合振动的临界阈值，对频率响应曲线理论解进行了数值验证，表明了模态耦合可以有效地抑制微梁中点位移；同时截面参数的减小会促进系统内部的模态耦合，更大程度的抑制了微梁中点位移并且拓宽了系统的频率响应带宽。该研究中所分析的不同截面参数下系统模态耦合共振问题对于提升微谐振器系统稳定性和额定电压均具有潜在的应用价值。
关键词：微谐振器；截面参数；多尺度法；模态耦合振动

Abstract

Microresonators manufactured by surface processing technology inevitably have processing errors, this article introduces the section parameters used to describe the changes in the upper and lower surfaces of the microbeam, based on the Euler Bernoulli beam model, the coupling vibration between the modes of the microbeam resonator under the thickness shape error is studied. The corresponding nonlinear coupling equations are obtained by Galerkin discretization and multiscale method, and the critical thresholds of coupling vibration under different section parameters are obtained. The coincidence between the theoretical solution and the numerical solution of the frequency response curve verifies that the modal coupling can effectively suppress the midpoint displacement of the micro beam; the reduction of the section parameters will promote the modal coupling within the system, restrain the midpoint displacement of the microbeam to a greater extent, and broaden the frequency response bandwidth of the system. The modal coupling resonance under different section parameters analyzed in this study has potential application value for improving the stability and rated voltage of microresonator system.
Key words: microresonator; section parameters; multiscale method; modal coupling vibration

导出引用

冯晶晶1,2，王冲1,2，郝淑英1,2，胡文华1,2，吴梦玉1,2. 一类厚度误差影响下单边微谐振器模态耦合动力学研究[J]. 振动与冲击, 2022, 41(21): 325-332

FENG Jingjing1,2, WANG Chong1,2, HAO Shuying1,2, HU Wenhua1,2, WU Mengyu1,2. Modal coupled dynamics of unilateral micro-resonator under influence of thickness error[J]. Journal of Vibration and Shock, 2022, 41(21): 325-332

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