基于偶应力压电理论的双层矩形微板静态特性分析  

Static analysis of bilayered rectangular micro-plate based on couple stress piezoelectric theory

作　　者：许瑞发 张荣敏 周莎莎 李安庆 XU Ruifa;ZHANG Rongmin;ZHOU Shasha;LI Anqing(School of Mechanical Engineering,Qilu University of Technology(Shandong Academy of Sciences),Jinan 250353,China;Shandong Institute of Mechanical Design and Research,Jinan 250031,China)

机构地区：[1]齐鲁工业大学(山东省科学院)机械工程学院,山东济南250353 [2]山东省机械设计研究院,山东济南250031

出　　处：《齐鲁工业大学学报》2023年第3期18-24,共7页Journal of Qilu University of Technology

基　　金：国家自然科学基金(12202220);山东省自然科学基金(ZR2022QA044);科教产融合试点工程项目(2022PX089);2022年大学生创新创业训练计划项目(项目名称:海洋器件防附着缓释材料药物微孔释放机制研究)。

摘　　要：基于偶应力压电理论发展了一个新的横观各向同性双层压电微板力学模型,根据变分原理推导了该模型的控制方程,并利用傅里叶级数法获得了数值解。基于该模型,分析了双层矩形微板的中心挠度与轴向应力等静态特性。结果表明,当无量纲相对厚度t大于1时,本模型的计算结果明显小于应变梯度理论的计算结果。当远离中性层时,轴向应变有增大趋势,而且轴向应力的分布呈现出分段式。本模型对压电微超声换能器的设计具有指导意义。This paper develops a new model of transversely isotropic piezoelectric bilayered micro-plate based on the couple stress piezoelectric theory.The governing equation is derived according to the variation principle.Numerical results are acquired by using the Fourier series method.Based on the new model,static deformation behaviors such as the size-dependent central deflection and the distribution of the axial stress are investigated.It is found that when the normalized relative thickness is greater than 1,the result of the present model is obviously smaller than the result of the strain gradient theory.Moreover,the axial strain is greater in the plane further from the neutral plane,and the distribution of the axial stress is segmented.The novel model is helpful to design the piezoelectric micromachined ultrasonic transducer.

关 键 词：双层微板 横观各向同性 压电效应 偶应力 

分 类 号：O343[理学—固体力学]