Natural frequency analysis of laminated piezoelectric beams with arbitrary polarization directions  

作　　者：Zhi LI Cuiying FAN Mingkai GUO Guoshuai QIN Chunsheng LU Dongying LIU Minghao ZHAO 

机构地区：[1]School of Mechanics and Safety Engineering,Zhengzhou University,Zhengzhou,450001,China [2]School of Electromechanical Engineering,Henan University of Technology,Zhengzhou,450001,China [3]School of Civil and Mechanical Engineering,Curtin University,Perth,Western Australia,6845,Australia [4]School of Civil Engineering,Guangzhou University,Guangzhou,510006,China [5]Henan Province Industrial Science&Technology Institute for Anti-fatigue Manufacturing,Zhengzhou,450001,China [6]Henan Province Engineering Research Center of Anti-fatigue Manufacturing Technology,Zhengzhou,450001,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2024年第11期1949-1964,共16页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.12272353 and 12002316);the Key Scientific and Technological Research Projects in Henan Province of China(No.232102211075)。

摘　　要：Piezoelectric devices exhibit unique properties that vary with different vibration modes,closely influenced by their polarization direction.This paper presents an analysis on the free vibration of laminated piezoelectric beams with varying polarization directions,using a state-space-based differential quadrature method.First,based on the electro-elasticity theory,the state-space method is extended to anisotropic piezoelectric materials,establishing state-space equations for arbitrary polarized piezoelectric beams.A semi-analytical solution for the natural frequency is then obtained via the differential quadrature method.The study commences by examining the impact of a uniform polarization direction,and then proceeds to analyze six polarization schemes relevant to the current research and applications.Additionally,the effects of geometric dimensions and gradient index on the natural frequencies are explored.The numerical results demonstrate that varying the polarization direction can significantly influence the natural frequencies,offering distinct advantages for piezoelectric elements with different polarizations.This research provides both theoretical insights and numerical methods for the structural design of piezoelectric devices.

关 键 词：piezoelectric laminated beam free vibration arbitrary polarization state-space equation differential quadrature method natural frequency 

分 类 号：O32[理学—一般力学与力学基础] TB34[理学—力学]