一类厚度误差影响下单边微谐振器模态耦合动力学研究  

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

作　　者：冯晶晶[1,2] 王冲 郝淑英[1,2] 胡文华[1,2] 吴梦玉 FENG Jingjing;WANG Chong;HAO Shuying;HU Wenhua;WU Mengyu(Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control,Tianjin University of Technology,Tianjin 300384,China;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：《振动与冲击》2022年第21期325-332,341,共9页Journal of Vibration and Shock

基　　金：国家自然基金(12072233,12072234,12002236);天津市自然科学基金(20JCYBJC00510)。

摘　　要：通过表面加工技术制造的微谐振器不可避免的存在加工误差,该文章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,更大程度地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。Micro-resonators manufactured by surface processing technology inevitably have machining errors.Here,section parameters used to describe changes of upper and lower surfaces of micro-beam were introduced,and based on Euler-Bernoulli beam model,modal coupled vibration of micro-beam resonators under thickness form error was studied.The corresponding nonlinear coupled equations were deduced by using Galerkin discretization and the multi-scale method,and critical thresholds to cause coupled vibrations under different cross-section parameter errors were obtained.The theoretical solution to frequency-response curve was numerically verified.It was shown that modal coupling can effectively suppress midpoint displacement of micro-beam;decrease in section parameters can promote modal coupling within the system,suppress midpoint displacement of micro-beam to a larger extent,and broaden frequency-response bandwidth of the system;modal coupled resonances of the system under different section parameters analyzed in the study can have potential application value for improving stability and rated voltage of micro-resonator system.

关 键 词：微谐振器 截面参数 多尺度法 模态耦合振动 

分 类 号：O322[理学—一般力学与力学基础] V263.6[理学—力学]