基于非局部理论的黏弹性基体中压电纳米梁热-机电振动特性  

Thermo-electro-mechanical vibration analysis of piezoelectric nanobeams embedded in viscoelastic medium based on nonlocal elasticity theory

作　　者：张大鹏[1] 雷勇军[1] ZHANG Dapeng;LEI Yongjun(College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China)

机构地区：[1]国防科技大学空天科学学院,湖南长沙410073

出　　处：《国防科技大学学报》2020年第6期142-149,共8页Journal of National University of Defense Technology

基　　金：国家自然科学基金资助项目(11902348);湖南省自然科学基金资助项目(2020JJ5650)。

摘　　要：基于非局部Euler梁理论和Hamilton原理建立黏弹性基体中压电纳米梁的热-机电振动特性分析模型。综合考虑非局部效应、压电效应、温度场、电场等复杂因素影响,推导出黏弹性基体中压电纳米梁振动特性分析的振动控制方程,并利用分布参数传递函数方法求解出一般边界条件下压电纳米梁的固有频率及相应振型。以锆钛酸铅压电陶瓷-4材料制成的某压电纳米梁为例,给出了四种典型边界条件下该压电纳米梁的前四阶固有频率,并系统分析了非局部效应、外部电压、温度载荷、黏弹性基体等因素对压电纳米梁热-机电振动特性的影响规律。分析结果表明:所建立的振动特性分析模型及其求解方法在分析黏弹性基体中压电纳米梁的热-机电振动特性问题中准确有效。Based on the nonlocal elasticity theory and Hamilton′s principle,the model for thermo-electro-mechanical vibration analysis was developed for a piezoelectric nanobeam embedded in viscoelastic medium.Governing equations of motion and boundary conditions for vibration analysis were derived where thermo-electro-mechanical loadings,viscoelastic foundation,nonlocal effect and piezoelectric effect were considered simultaneously.The transfer function method was employed to obtain the natural frequencies in closed form for the nanobeam with various boundary conditions.A detailed parametric study was also carried out for the effects of nonlocal parameter,boundary conditions and viscoelastic foundation on the vibration of nanobeams.The study demonstrates the accuracy and the efficiency of the developed model for vibration analysis of a complicated multi-physics system comprising nonlocal piezoelectric nanobeams,viscoelastic foundation and thermo-electro-mechanical loadings.

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

分 类 号：O343[理学—固体力学]