加工误差影响下微谐振器的非线性分析  

Nonlinear analysis of microresonators under the influence of processing errors

作　　者：赵懿炜 王冲 冯晶晶[1,2] ZHAO Yiwei;WANG Chong;FENG Jingjing(Tianjin Key Laboratory for Advanced Mechanical System Design and Intelligent Control,Tianjin University of Technology,Tianjin 300384,China 2.National Demonstration Center for Experimental Mechanical and Electrical Engineering Education,Tianjin University of Technology,Tianjin 300384,China)

机构地区：[1]天津理工大学天津市先进机电系统设计与智能控制重点实验室,天津300384 [2]天津理工大学机电工程国家级实验教学示范中心,天津300384

出　　处：《天津理工大学学报》2025年第1期23-28,共6页Journal of Tianjin University of Technology

基　　金：国家自然科学基金(12072233,12072234);天津市自然科学基金(20JCYBJC00510)。

摘　　要：微梁在加工过程中,由于加工精度的限制以及偏置的加工方法,导致其形状发生变形,出现浅拱形态。这种加工误差存在的方式可归结为微梁厚度方向上的变形和初始变形,将影响微谐振器的非线性特性。文中同时考虑微谐振器模型的初始变形与厚度形态误差,研究其对系统动态频率响应的影响。应用达朗贝尔原理建立了微梁的数学模型。通过伽辽金法对模型进行降价,并使用多尺度法以及Runge-Kutta法分析了系统的软硬特性。通过分析截面系数、初始上升系数和直流电压之间的变化关系,使系统实现线性振动,从而为谐振器性能的提升提供理论依据。During the machining process of the microbeam,the limitations of the machining accuracy and the biased machining method lead to the deformation of its shape and the appearance of a shallow arch morphology.This machining error exists in the way that can be attributed to the deformation in the thickness direction of the microbeam and the initial deformation which will affect the nonlinear characteristics of the microresonator.In this paper,both the initial deformation and thickness morphology errors of the microresonator model are considered to investigate their effects on the dynamic frequency response of the system.A mathematical model of the microbeam is constructed using D′Alembert′s principle,and the model is downscaled by the Galliakin method,and the soft and stiff characteristics of the system are analyzed using the multiscale method as well as the Runge-Kutta method.The system is made to achieve linear vibration by analyzing the variation relationship between the cross-sectional coefficient,the initial rise coefficient and the DC voltage,thus providing a theoretical basis for the improvement of the resonator performance.

关 键 词：初始变形 厚度误差 微谐振器 多尺度法 RUNGE-KUTTA法 

分 类 号：TH122[机械工程—机械设计及理论]