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Nonlinear primary resonance analysis for a coupled thermo-piezoelectric-mechanical model of piezoelectric rectangular thin plates

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  • 1. Department of Mechanics, School of Science, North University of China, Taiyuan 030051, China;
    2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

Received date: 2019-01-07

  Revised date: 2019-04-11

  Online published: 2019-08-01

Supported by

Project supported by the National Natural Science Foundation of China (No. 11202190), the Natural Science Foundation for Young Scientists of Shanxi Province of China (No. 201801D221037), and the China Postdoctoral Science Foundation (No. 2018M640373)

Abstract

A model of piezoelectric rectangular thin plates with the consideration of the coupled thermo-piezoelectric-mechanical effect is established. Based on the von Karman large deflection theory, the nonlinear vibration governing equation is obtained by using Hamilton's principle and the Rayleigh-Ritz method. The harmonic balance method (HBM) is used to analyze the first-order approximate response and obtain the frequency response function. The system shows non-linear phenomena such as hardening nonlinearity, multiple coexistence solutions, and jumps. The effects of the temperature difference, the damping coefficient, the plate thickness, the excited charge, and the mode on the primary resonance response are theoretically analyzed. With the increase in the temperature difference, the corresponding frequency jumping increases, while the resonant amplitude decreases gradually. Finally, numerical verifications are carried out by the Runge-Kutta method, and the results agree very well with the theoretical results.

Cite this article

Xun WANG, Chunxia XUE, Haitao LI . Nonlinear primary resonance analysis for a coupled thermo-piezoelectric-mechanical model of piezoelectric rectangular thin plates[J]. Applied Mathematics and Mechanics, 2019 , 40(8) : 1155 -1168 . DOI: 10.1007/s10483-019-2510-6

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