不完全连续三层微梁谐振器中热弹性阻尼研究  

Thermoelastic Damping in Three⁃Layer Microbeams with Incomplete Continuous Structure

作　　者：冶志翔 左万里 刘璇 YE Zhixiang;ZUO Wanli;LIU Xuan(School of Mechanical Engineering and Mechanics,Ningbo University,Ningbo Zhejiang 315211,China;School of Computer and Data Engineering,Ningbo Tech University,Ningbo Zhejiang 315100,China)

机构地区：[1]宁波大学机械工程与力学学院,浙江宁波315211 [2]浙大宁波理工学院计算机与数据工程学院,浙江宁波315100

出　　处：《传感技术学报》2023年第6期849-859,共11页Chinese Journal of Sensors and Actuators

基　　金：国家自然科学基金项目(51705261);浙江省教育厅一般科研项目(Y202248861)。

摘　　要：基于Euler-Bernoulli梁理论和二维傅里叶热传导定律,针对两端固定约束边界条件,通过截面分割法得到不完全连续三层微梁的固有频率,利用格林函数法求解波动温度场分布函数。然后利用能量法,建立了热弹性阻尼(Thermoelastic damping,TED)解析模型。通过ANSYS有限元数值解与MATLAB解析解对比,验证了所建模型的正确性。结果表明:(1)TED中厚度方向的收敛速度远大于长度方向收敛速度,TED对厚度方向上的热传递更为敏感;(2)在此结构基层开槽处两端无限接近时,可以简化为完全连续微梁结构模型;(3)若微梁长恒定不变,随着开槽长度的增加,TED呈减小趋势;(4)通过基层的开槽,此结构微梁的最大弹性势能以及热能损失都会降低;(5)在基层中进行刻蚀开槽时,槽的长度与厚度的比值应取较大值。Based on the Euler⁃Bernoulli beam vibration theory and the two⁃dimensional Fourier heat conduction theory,for the fixed constraint at both ends,the natural frequency of three⁃layer microbeams with incomplete continuous structure is calculated through the section segmentation approach,and Green function method is used to solve the distribution function of fluctuating temperature field.Finally,the thermoelastic damping is solved by using energy method.The model is verified by comparing the finite element numerical solution of ANSYS with the analytical solution of MATLAB.The results show that:①The convergence rate in the thickness direction of TED is much faster than that in the length direction.②When the two ends of the groove at the base of this structure are infinitely close,it can be simplified as a fully continuous microbeam structure model.③With the increase of the length of the slot,TED will decrease.④By grooving the base course,the loss of heat energy is much greater than the maximum elastic potential energy.⑤When etching and grooving the base course,the ratio of the slot length to thickness shall be large.

关 键 词：热弹性阻尼 开槽结构 热弹性耦合振动 微谐振器 品质因数 

分 类 号：TM38[电气工程—电机]