基于非局部理论的黏弹性基体上压电纳米板热-机电振动特性研究  

Thermo-electro-mechanical vibration responses of piezoelectric nanoplates embedded in viscoelastic medium via nonlocal elasticity theory

作　　者：张大鹏[1] 雷勇军[1] 段静波 ZHANG Dapeng;LEI Yongjun;DUAN Jingbo(College of Aerospace Science and Engineering,National University of Defense Technology,Changsha 410073,China;Department of Engineering Mechanics,Shijiazhuang Tiedao University,Shijiazhuang 050043,China)

机构地区：[1]国防科技大学空天科学学院,长沙410073 [2]石家庄铁道大学工程力学系,石家庄050043

出　　处：《振动与冲击》2020年第20期32-41,共10页Journal of Vibration and Shock

基　　金：国家自然科学基金(11872372,11702325);国防科技大学科研计划(ZK17-02-06)。

摘　　要：基于非局部弹性理论研究黏弹性基体上压电纳米板的热-机电振动特性。综合考虑非局部效应、压电效应以及温度场、电场等因素影响,根据Kirchhoff板理论和Hamilton原理建立黏弹性基体上压电纳米板的热-机电振动特性分析模型,然后利用Galerkin条形传递函数方法进行求解,得到一般边界条件下压电纳米板固有频率的半解析解。通过与文献结果进行对比,验证所建分析模型与求解方法的有效性,并在此基础上系统分析非局部效应、边界条件、外电压、温度变化梯度等对压电纳米板振动特性的影响规律。结果表明,所建立的分析模型及其求解方法在分析黏弹性基体上压电纳米板的热-机电振动特性问题中准确有效。Thermo-electro-mechanical vibration of piezoelectric nanoplates embedded in viscoelastic medium was investigated via nonlocal elasticity theory.Considering nonlocal effect,piezoelectric effect,viscoelasticity of surrounding medium and thermo-electro-mechanical loadings simultaneously,governing equations of piezoelectric nanoplates were derived,and the natural frequencies were obtained by introducing the Galerkin strip distributed transfer function method.The developed model was validated by comparing the obtained results with those available in literature.The influences of nonlocal parameter,boundary conditions,external electric voltage and increment temperature were also examined in detail.The results demonstrate the efficiency of the developed model for thermo-electro-mechanical vibration analysis of piezoelectric nanoplates embedded in viscoelastic medium.

关 键 词：压电纳米板 黏弹性基体 振动特性 非局部弹性理论 传递函数方法 

分 类 号：O343[理学—固体力学]