One-dimensional dynamic equations of a piezoelectric semiconductor beam with a rectangular cross section and their application in static and dynamic characteristic analysis  

作　　者：Peng LI Feng JIN Jianxun MA 

机构地区：[1]School of Human Settlements and Civil Engineering, Xi'an Jiaotong University [2]State Key Laboratory for Strength and Vibration of Mechanical Structures,Xi'an Jiaotong University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2018年第5期685-702,共18页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11672223,11402187,and 51178390);the China Postdoctoral Science Foundation(No.2014M560762);the Fundamental Research Funds for the Central Universities of China(No.xjj2015131)

摘　　要：Within the framework of continuum mechanics, the double power series ex- pansion technique is proposed, and a series of reduced one-dimensional （1D） equations for a piezoelectric semiconductor beam are obtained. These derived equations are universal, in which extension, flexure, and shear deformations are all included, and can be degen- erated to a number of special cases, e.g., extensional motion, coupled extensional and flexural motion with shear deformations, and elementary flexural motion without shear deformations. As a typical application, the extensional motion of a ZnO beam is analyzed sequentially. It is revealed that semi-conduction has a great effect on the performance of the piezoelectric semiconductor beam, including static deformations and dynamic be- haviors. A larger initial carrier density will evidently lead to a lower resonant frequency and a smaller displacement response, which is a little similar to the dissipative effect. Both the derived approximate equations and the corresponding qualitative analysis are general and widely applicable, which can clearly interpret the inner physical mechanism of the semiconductor in the piezoelectrics and provide theoretical guidance for further experimental design.Within the framework of continuum mechanics, the double power series ex- pansion technique is proposed, and a series of reduced one-dimensional （1D） equations for a piezoelectric semiconductor beam are obtained. These derived equations are universal, in which extension, flexure, and shear deformations are all included, and can be degen- erated to a number of special cases, e.g., extensional motion, coupled extensional and flexural motion with shear deformations, and elementary flexural motion without shear deformations. As a typical application, the extensional motion of a ZnO beam is analyzed sequentially. It is revealed that semi-conduction has a great effect on the performance of the piezoelectric semiconductor beam, including static deformations and dynamic be- haviors. A larger initial carrier density will evidently lead to a lower resonant frequency and a smaller displacement response, which is a little similar to the dissipative effect. Both the derived approximate equations and the corresponding qualitative analysis are general and widely applicable, which can clearly interpret the inner physical mechanism of the semiconductor in the piezoelectrics and provide theoretical guidance for further experimental design.

关 键 词：piezoelectric semiconductor beam reduced one-dimensional （1D） equation double power series expansion technique stress relaxation initial carrier density 

分 类 号：O33[理学—一般力学与力学基础]