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

• Published in: Journal of low frequency noise, vibration, and active control Vol. 40; no. 3; pp. 1293 - 1308
• Main Authors: Liang, Xu, Cao, Zeng, Deng, Yu, Jiang, Xue, Zha, Xing, Leng, Jianxing
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.09.2021; Sage Publications Ltd; SAGE Publishing
• Subjects: Algorithms; Boundary conditions; Convergence; Differential equations; Differential thermal analysis; Dynamic response; Foundations; Fourier series; Laplace transforms; Plate theory; Quadratures; Rectangular plates; Series expansion; Thermal environments; Transient response; transient behaviors; semi-analytical methodology; thermal environment; different boundary conditions; Plate
• ISSN: 1461-3484; 2048-4046
• DOI: 10.1177/1461348420946574

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.