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Dynamic stiffness formulation for vibration characteristics analysis of bi-dimensional functionally graded annular plate of variational thickness

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Abstract

In this paper, a generalized formulation for vibration characteristics investigation of bi-dimensional functionally graded martial annular plates of variational thicknesses is built up using the dynamic stiffness method. The distributions of material attribute both in the radial direction and the thickness direction are in a power-law variation of the constituents’ volume fraction. General solutions of the government equation of an annular plate are solved by a strong-formed algorithm, then the dynamic stiffness formulation is employed to present the vibration study of the bi-dimensional functionally graded annular plate. Various boundary constrains are considered in the modeling process. Results of present formulation are verified by comparison with existing literature and numerical examples. A systematic parametric study is performed to study the influences of boundary constrains, geometric parameters, and functional material distributions on the free vibration characteristic of the annular plate. Results shows that the natural frequency of radial functionally graded annular plate are the largest and the natural frequency of the bi-dimensional functionally graded annular plate are the minimum when the values of the power laws are both 1. When the power-law index is large, the change of frequency with the power-law index is more obvious.

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Acknowledgments

This research is supported by the National Natural Science Foundation of China (No. 52305110), China Postdoctoral Science Foundation (2023M742256), Research Project of State Key Laboratory of Mechanical System and Vibration (MSV 202409) and Natural Science Foundation of Jiangsu Higher Education Institutions of China (22KJB580006).

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Authors and Affiliations

  1. School of Energy and Power Engineering, Jiangsu University of Science and Technology, Zhenjiang, 212003, China

    Chunyu Zhang, Zhenchao Pan, He Yang & Yaqiang Xue

  2. School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Chunyu Zhang

  3. Shanghai Marine Equipment Research Institute, Shanghai, 201108, China

    Shunjun Fu

Authors
  1. Chunyu Zhang
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  2. Zhenchao Pan
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  4. He Yang
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  5. Yaqiang Xue
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Correspondence to Chunyu Zhang.

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Zhang Chunyu is a lecturer of the School of Energy and Power Engineering, Jiangsu University of Science and Technology, Zhenjiang, China. He received his Ph.D. in Harbin Engineering University. His research interests include fault diagnosis, dynamic modeling, vibration analysis

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Zhang, C., Pan, Z., Fu, S. et al. Dynamic stiffness formulation for vibration characteristics analysis of bi-dimensional functionally graded annular plate of variational thickness. J Mech Sci Technol 38, 1649–1660 (2024). https://doi.org/10.1007/s12206-024-0303-x

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