黏弹性基体中挠曲电Timoshenko纳米梁振动特性分析

以黏弹性基体中的Timoshenko纳米梁为研究对象,综合考虑非局部效应、压电效应和挠曲电效应的影响,基于哈密顿原理建立了系统的振动控制方程和相应的边界条件,给出了两端简支边界条件下挠曲电纳米梁控制方程的求解方法,系统地研究了非局部参数、挠曲电系数以及黏弹性基体对挠曲电纳米梁振动特性的影响规律。结果表明:横向挠曲电系数能显著增加挠曲电纳米梁的结构刚度,而非局部效应和切向挠曲电系数则会降低系统的结构刚度。此外,通过研究黏弹性基体的影响规律,可得到挠曲电纳米梁不再发生往复振动时对应的黏弹性基体临界阻尼系数。相关研究结果可为挠曲电纳米梁在俘能器中的推广应用提供理论基础。

Vibration characteristics analysis of flexoelectric Timoshenko nano-beam in viscoelastic medium

Based on the Hamiltonian principle and taking nonlocal effect, piezoelectric effect and flexoelectric effect into consideration, the vibration governing equation and boundary conditions of the Timoshenko nano-beam in the viscoelastic medium were established, and the method of solving the governing equation of flexoelectric nano-beam with simply supported boundary conditions was adopted. The effects of nonlocal parameters, flexoelectric effect and viscoelastic medium on the vibration characteristics of the flexoelectric nano-beam were systematically studied. The results show that the transverse flexoelectric coefficient can significantly increase the structural stiffness of the flexoelectric nano-beam, while the nonlocal parameters and the tangential flexoelectric coefficient can reduce the structural stiffness of the system. In addition, the critical damping coefficient of the viscoelastic medium, in which the flexoelectric nanobeam no longer reciprocating vibration, can be obtained by studying the effects of viscoelastic medium. Research results can provide a theoretical basis for the extension and application of flexoelectric nano-beam in energy harvester.