几何非线性条件下微纳米梁型谐振器的非线性支撑损失  

Nonlinear support loss in micro/nano beam resonators induced by geometric nonlinearity

作　　者：马程中 王检耀 史柯文 孔子文 杨伟东 陈思宇 国凤林 Chengzhong Ma;Jianyao Wang;Kewen Shi;Ziwen Kong;Weidong Yang;Siyu Chen;Fenglin Guo(School of Naval Architecture,Ocean and Civil Engineering(State Key Laboratory of Ocean Engineering),Shanghai Jiao Tong University,Shanghai,200240,China;School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai,200092,China;Department of Engineering Mechanics,Tsinghua University,Beijing,100084,China)

机构地区：[1]School of Naval Architecture,Ocean and Civil Engineering(State Key Laboratory of Ocean Engineering),Shanghai Jiao Tong University,Shanghai,200240,China [2]School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai,200092,China [3]Department of Engineering Mechanics,Tsinghua University,Beijing,100084,China

出　　处：《Acta Mechanica Sinica》2024年第3期165-175,共11页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos.12102222 and 11272206).

摘　　要：作为微纳米机械谐振器主要的能量耗散源之一,支撑损失主要采用未考虑中面拉伸效应的线性理论进行研究.然而该理论却无法适用于大挠度非线性振动状态谐振器的支撑损失.为此,我们研究了考虑几何非线性和轴向预拉力的两端固支微梁谐振器处于面内弯曲振动模式时的支撑损失,旨在准确模拟大挠度振动下高性能谐振器的支撑损失.本文不仅考虑了支撑结构与谐振器连接区域受中面拉伸产生的正应力作用而引起的支撑损失,也考虑了受剪应力作用而引起的支撑损失,并且理论结果与有限元模拟以及文献中实验结果一致.另外,本文还研究了轴向预拉力对谐振器非线性振动特性的影响,并讨论了谐振器的振幅、长高比以及轴向预拉力对支撑损失的影响.理论结果表明,相比于线性振动状态下谐振器的支撑损失,由谐振器大变形振动产生的中面拉伸效应会引起更大的支撑损失,并且会随非线性振幅的增大而增大.本文提出的非线性支撑损失模型有望对评估非线性振动谐振器的支撑损失以及阐明支撑损失随非线性振幅增大的现象提供理论指导.Support loss,as one of the main energy dissipation sources in micro/nano mechanical resonators,is generally evaluated by linear theories without considering mid-plane stretching.Predictions of support loss based on linear elastic theory cannot be applied to resonators working in nonlinear regime with large vibration amplitude.In this regard,we investigate the support loss of a doubly clamped micro/nano beam resonator in in-plane flexural vibration in this study,with both geometric nonlinearity and axial pre-tension considered,aiming to accurately model the support loss for high-performance resonators under large-deflection vibration.The expression of support loss is derived,with both the normal stress induced by the mid-plane stretching and shear stress distributed in the attachment region of the support taken into account.The analytical model proposed in this work is validated by finite element simulations and the experimental data of previous studies.Furthermore,the influence of the axial pre-tension on nonlinear vibration properties and that of the vibration amplitude on the support loss are probed.The effects of the axial pre-tension and the aspect ratio on the support loss are also analyzed.The analytical results demonstrate that the mid-plane stretching effect due to geometric nonlinearity leads to larger support loss,and the support loss increases with vibration amplitude.Hopefully,the nonlinear model of support loss developed in this work may provide guidelines to evaluate the support loss and elucidate the phenomenon of the support loss increasing with vibration amplitude.

关 键 词：Support loss Micro/nano beam resonator Geometric nonlinearity Axial pre-tension 

分 类 号：TN751[电子电信—电路与系统]