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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

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Abstract

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.

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Author information

Authors and Affiliations

  1. School of Human Settlements and Civil Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Peng Li & Jianxun Ma

  2. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an, 710049, China

    Feng Jin

Authors
  1. Peng Li
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  2. Feng Jin
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Correspondence to Feng Jin.

Additional information

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)

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Li, P., Jin, F. & Ma, J. One-dimensional dynamic equations of a piezoelectric semiconductor beam with a rectangular cross section and their application in static and dynamic characteristic analysis. Appl. Math. Mech.-Engl. Ed. 39, 685–702 (2018). https://doi.org/10.1007/s10483-018-2325-6

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  • DOI: https://doi.org/10.1007/s10483-018-2325-6

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Chinese Library Classification

2010 Mathematics Subject Classification

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