Levinson矩形微板谐振器热弹性阻尼解析解  

Analytical solution of thermoelastic damping in Levinson micro rectangular plate resonators

作　　者：李世荣 刘荣桂[1] 武永 LI Shi-rong;LIU Rong-gui;WU Yong(Department of Civil Engineering,Nantong Institute of Technology,Nantong 226002,China;School of Civil Science and Engineering,Yangzhou University,Yangzhou 225127,China)

机构地区：[1]南通理工学院建筑工程学院,江苏南通226002 [2]扬州大学建筑科学与工程学院,江苏扬州225127

出　　处：《振动工程学报》2021年第5期1009-1019,共11页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(11672260);江苏省科技服务平台培育项目(XQPT202102)。

摘　　要：基于Levinson高阶剪切板理论,给出了四边简支微板谐振器热弹性耦合自由振动的复频率以及板内变温场的精确解析解;由复频率法给出了表征微板热弹性阻尼的逆品质因子;通过数值结果分析了Levinson微板的热弹性阻尼随几何尺寸和振动模态变化的规律,并与一阶剪切变形理论和经典板理论的预测结果进行了比较,分析了剪切变形对热弹性阻尼的影响程度。数值结果表明,对于中厚板和厚板谐振器,经典板理论预测的热弹性阻尼值明显大于剪切变形板理论的预测值。这是由于经典板理论忽略了横向剪切变形,从而过高地估计了微板的抗弯刚度。另外,在四边简支条件下,还给出了Mindlin微板和Levinson微板热弹性阻尼预测值之间的比较。结果表明,Levinson高阶剪切变形理论能够更好地预测厚板谐振器的热弹性阻尼。这是因为Levinson理论下的位移场能够精确满足上下表面应力为零的条件,温度场包含了厚度方向坐标的高阶项。Based on Levinson’s higher-order shear deformation plate theory,accurate analytical solutions for the complex natural frequency and the field of temperature change of a simply supported rectangular micro plate resonator in thermoelastic coupled free vibration are obtained.Furthermore,inverse quality factor representing the TED is extracted by using the complex frequency approach.Numerical results are presented to show the variation regulation of the TED versus the aspect ratio of the micro Levinson plate in different vibration modes.By comparing the values of TED based on the Levinson plate theory with those based on both Mindlin and Kirchhoff plate theories,the level of effect of shearing deformation on the TED is analyzed.The numerical results show that for the moderate thick and thick plate resonators the values of TED evaluated by the classical plate theory are obviously greater than that by shearing strained plate theory.It is because that the classical plate theory ignores the transvers shear deformation and over estimates the rigidity of the structure.In addition,the comparison between the predicted values of TED of Mindlin and Levinson microplates with four simply supported edges is given.As a result,Levinson higher-order shear deformation plate theory can better predict the TED of the thick microplate,because the displacement field of Levinson plate theory can accurately satisfy the stress-free conditions at the upper and lower surface and the temperature field contains the higher order term of the through-thickness coordinate.

关 键 词：热弹耦合振动 Levinson板理论 复频率 热弹性阻尼 解析解 

分 类 号：O343.6[理学—固体力学]