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Dynamic stiffness formulation for transverse and in-plane vibration of rectangular plates with arbitrary boundary conditions based on a generalized superposition method

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Abstract

Dynamic stiffness formulation is proposed in this paper for both transverse and in-plane vibration of rectangular plates that account for arbitrary boundary conditions. A generalized superposition method is developed to obtain the homogeneous solutions for the governing equations of both transverse and in-plane vibration. Consequently, the dynamic stiffness matrices are formed in a more straightforward way by projection method, the dimensions of which are greatly reduced in comparison with those from the conventional Gorman’s superposition method. The finite element technique is utilized to assemble local stiffness matrix into global coordinates so as to address the dynamics of plate assemblies. Various types of plate-like structures are investigated by the proposed method, through which excellent agreement is found between our results and those from finite element method. The effectiveness, accuracy and convergence of the proposed DSM for both transverse and in-plane vibration are proved in several numerical examples, which demonstrates the proposed DSM is an excellent alternative to the existing DSM.

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Acknowledgements

The authors wish to thank High-Tech Ship Fund from the Ministry of Industry and Information Technology (MIIT): Deepwater Semi-submersible Support Platform (Grant No.: 2016 [546]), High Quality Brand Ship Board Machinery (Grant No.: 2016 [547]), The Seventh Generation of Ultra-deepwater Drilling Platform Innovation (Grant No.: 2016 [24]). This work was also partially supported National Science Foundation of Jiangsu Province-Youth Fund (Grant No.: BK20170217).

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Authors and Affiliations

  1. National Key Laboratory on Ship Vibration and Noise, China Ship Scientific Research Center, Wuxi, 214000, People’s Republic of China

    Zitian Wei, Xuewen Yin & Wenwei Wu

  2. Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, ON, M5B 2K3, Canada

    Shudong Yu

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  1. Zitian Wei
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  2. Xuewen Yin
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  3. Shudong Yu
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  4. Wenwei Wu
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Correspondence to Xuewen Yin.

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Wei, Z., Yin, X., Yu, S. et al. Dynamic stiffness formulation for transverse and in-plane vibration of rectangular plates with arbitrary boundary conditions based on a generalized superposition method. Int J Mech Mater Des 17, 119–135 (2021). https://doi.org/10.1007/s10999-020-09515-9

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