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

doi:10.1007/s10483-018-2325-6

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (5): 685-702.doi: https://doi.org/10.1007/s10483-018-2325-6

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

Peng LI¹, Feng JIN², Jianxun MA¹

1. School of Human Settlements and Civil Engineering, Xi'an Jiaotong University, Xi'an 710049, China;
2. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an 710049, China

收稿日期:2017-07-08 修回日期:2017-09-18 出版日期:2018-05-01 发布日期:2018-05-01
通讯作者: Feng JIN,E-mail:jinfengzhao@263.net E-mail:jinfengzhao@263.net
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11672223, 11402187, and 51178390), the China Postdoctoral Science Foundation (No. 2014M560762), and the Fundamental Research Funds for the Central Universities of China (No. xjj2015131)

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

Peng LI¹, Feng JIN², Jianxun MA¹

1. School of Human Settlements and Civil Engineering, Xi'an Jiaotong University, Xi'an 710049, China;
2. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an 710049, China

Received:2017-07-08 Revised:2017-09-18 Online:2018-05-01 Published:2018-05-01
Contact: Feng JIN E-mail:jinfengzhao@263.net
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11672223, 11402187, and 51178390), the China Postdoctoral Science Foundation (No. 2014M560762), and the Fundamental Research Funds for the Central Universities of China (No. xjj2015131)

摘要/Abstract

摘要：

Within the framework of continuum mechanics, the double power series expansion 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 degenerated 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 behaviors. 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, dusty gas, shock wave, boundary layer, relaxation structure, double power series expansion technique, stress relaxation, reduced one-dimensional (1D) equation, initial carrier density

Abstract:

Key words: piezoelectric semiconductor beam, dusty gas, shock wave, boundary layer, relaxation structure, stress relaxation, double power series expansion technique, reduced one-dimensional (1D) equation, initial carrier density

中图分类号:

74H45

Peng LI, Feng JIN, Jianxun MA. One-dimensional dynamic equations of a piezoelectric semiconductor beam with a rectangular cross section and their application in static and dynamic characteristic analysis[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(5): 685-702.

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

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

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