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Transverse vibration and buckling analysis of rectangular plate under arbitrary in-plane loads

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Abstract

Stresses are generated in plates under initial loads, which couple with the subsequent transverse deformation to affect the buckling and transverse vibration characteristics of plates. There exists no exact solution method for the stress field of a rectangular plate under arbitrary in-plane loads. In this paper, the stress field of a rectangular plate under arbitrary in-plane loads is solved based on the principle of minimum potential energy. The stress function is decomposed into homogeneous and special solutions. The homogeneous solution is represented by the Chebyshev polynomial while the special solution is expanded by the Fourier series. Then, the Ritz method is used to analyze the transverse vibration and buckling characteristics of the rectangular plate. The product of the boundary function and Chebyshev polynomial is used to build the vibration mode function. The present results are verified by comparing to existing studies and those obtained from finite element method (FEM). The effects of the magnitude and distribution of in-plane boundary stresses and boundary conditions on the dynamic characteristics and stability of the rectangular plate are analyzed. The method used in the paper has demonstrated improved convergence and accuracy with good universality.

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Acknowledgements

This research is financially supported by the National Key Research and Development Program of China (Grant No. 2019YFD1101205).

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Authors and Affiliations

  1. College of Civil Engineering, Nanjing Tech University, Nanjing, 211816, Jiangsu, China

    Ruili Huo, Kun Wang, Fan Zhu & Chuang Feng

  2. Sinodawn Energy Technology Co., Ltd, Beijing, 100086, China

    Guorong Li

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  1. Ruili Huo
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  2. Kun Wang
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  3. Guorong Li
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  4. Fan Zhu
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  5. Chuang Feng
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Contributions

RH helped in methodology, conceptualization and writing and editing; KW helped in writing and editing; GL helped in data curation and analysis and coding; FZ helped in investigation and CF helped in validation and supervision.

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Correspondence to Chuang Feng.

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Huo, R., Wang, K., Li, G. et al. Transverse vibration and buckling analysis of rectangular plate under arbitrary in-plane loads. Acta Mech 234, 3917–3931 (2023). https://doi.org/10.1007/s00707-023-03601-7

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  • DOI: https://doi.org/10.1007/s00707-023-03601-7

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