The thermal and Pasternak foundation effect on the transient behaviors of the rectangular plate using a novel semi-analytical method

This paper carries out the transient behaviors of a thin rectangular plate considering different boundary conditions, Pasternak foundation, and thermal environment simultaneously. The governing differential equations of the system are derived by employing the Kirchhoff’s classical plate theory and H...

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Bibliographic Details
Published in:Journal of low frequency noise, vibration, and active control vibration, and active control, 2021-09, Vol.40 (3), p.1293-1308
Main Authors: Liang, Xu, Cao, Zeng, Deng, Yu, Jiang, Xue, Zha, Xing, Leng, Jianxing
Format: Article
Language:English
Subjects:
Algorithms
Boundary conditions
Convergence
Differential equations
Differential thermal analysis
Dynamic response
Fourier series
Laplace transforms
Plate theory
Quadratures
Rectangular plates
Series expansion
Thermal environments
Transient response
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Summary:This paper carries out the transient behaviors of a thin rectangular plate considering different boundary conditions, Pasternak foundation, and thermal environment simultaneously. The governing differential equations of the system are derived by employing the Kirchhoff’s classical plate theory and Hamilton’s principle. This paper proposes a novel semi-analytical methodology, which integrates Laplace transform, the one-dimensional differential quadrature method, Fourier series expansion technique, and Laplace numerical inversion to analyze plates’ transient response. The proposed method can obtain dynamic response of the rectangular efficiently and accurately, which fills the gap of transient behaviors in semi-analytical method. A comparison between semi-analytical results and numerical solutions from the publication on this subject is presented to verify the method. Specifically, the results also agree well with the data generated by the Navier’s method. The convergence tests indicate that the semi-analytical algorithm is a quick convergence method. The effects of various variables, such as geometry, boundary conditions, temperature, and the coefficients of the Pasternak foundation, are further studied. The parametric studies show that geometry and temperature change are significant factors that affect the dynamic response of the plate.
ISSN:1461-3484
2048-4046
DOI:10.1177/1461348420946574