微型压电谐振器各向异性电-力-热耦合作用下的热弹性耗散模型

Piezoelectric micromechanical resonators are widely used in many application fields such as military, aerospace, communication, etc. Thermoelastic dissipation/damping (TED) has a significant effect on the performance of vacuum-operated micro-resonators because it determines the quality factor (Q) of the resonators. However, few researches have been performed on TED in piezoelectric resonators. The aim of this project is to develop analytical models for computing TED in microbeam and microplate piezoelectric resonators. This project includes the following parts: The heat conduction equation will be presented with multi-field coupling. Then, the temperature field will be given. The maximum strain energy stored in the structure and the work lost per cycle of oscillation will be calculated based on the constitutive equations for anisotropic materials. Applying the thermal-energy approach, analytical models for TED in microbeam and microplate piezoelectric resonators will be developed. The analytical models will be verified by comparing their results with the results computed by finite element method and the experimental results. Based on the analytical models, the effects of the boundary conditions, the electric field and the equilibrium temperature on TED will be explored. Our results can be used to optimize the design of microbeam and microplate piezoelectric resonators and gain useful insight into a fundamental mechanism of dissipation.

压电微机械谐振器在军事、宇航、通信等领域有着广阔的市场和应用前景。热弹性阻尼（TED）对真空封装微机械谐振器中的品质因数（Q）具有重要的影响。然而，关于压电谐振器中热弹性阻尼机理的研究还很有限。本项目拟以微梁、微板结构压电谐振器为研究对象，探究其中的热弹性能量耗散机理。具体研究包括：建立压电微机械谐振器中电-力-热多场耦合时的温度场控制方程，求解谐振结构中的温度场分布函数。根据所得温度场分布函数和各向异性材料的本构方程，求解出最大储存弹性势能和单位周期中损失的能量。利用能量法，建立压电微梁、微板结构中的热弹性阻尼解析模型。通过与有限元数值模型计算结果与实验测量值的比较，验证解析模型的正确性。依据所建立的解析模型，分析约束条件、激振电场及环境温度等对热弹性阻尼的影响。本项目的研究可以深化对各向异性压电微谐振器中热弹性能量耗散机理的认识，并可为合理设计微梁、微板结构压电谐振器提供理论支援。

压电微机械谐振器相较于传统硅微谐振器，具有驱动力大、能耗低、响应速度快、位移精度高等优点。本项目针对压电微梁谐振器，开展电-力-热耦合下的温度场研究，各向异性压电材料中热弹性阻尼机理研究。初步建立了横观各向同性压电微梁谐振器中，二维热传导条件下的热弹性阻尼模型。此外，项目申请人还进行了三层微板结构谐振器中热弹性阻尼模型研究；非傅立叶热传导下，微梁中热弹性阻尼研究；双层微梁中热弹性阻尼研究；三层微梁中热弹性能量分布研究。上述研究工作的主要结论如下：.（1）各向异性压电谐振器中的热弹性阻尼与梁的振型有关；随着外接电场电压的增加，热弹性阻尼会降低。.（2）当两层材料临界频率相距较远，且两层材料对热弹性阻尼贡献相当时（其数值受到材料的Zener模量影响），热弹性阻尼频谱曲线会表现为两个阻尼峰。当两层材料频率相距较近时，阻尼热弹性阻尼频谱曲线仅为一个阻尼峰。.（3）三层微谐振结构中，中间层的能量耗散较小，且在一些特殊频率下，会出现负的能量耗散。进一步研究表示，单层结构或双层结构，在中间部分也会出负的能量耗散，其主要原因是波动温度场的非线性，导致局部的热应变从滞后变为了超前，从而使在其他部分消耗的能量在中间部分又释放出一些。.（4）热弹性阻尼频谱曲线的单峰、双峰以及多峰现象受双相位滞后比，梁的半径或厚度影响。值得注意的是，双相位滞后非傅立叶热传导会带来额外的双峰现象。