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Hierarchic models for the free vibration analysis of functionally gradient plates

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Abstract

Hierarchic models for the modal analyses of ceramic–metal functional gradient (FG) plates are introduced. This study was motivated by the fact that the free vibration analyses of those structures are usually conducted by the first- or higher-order shear deformation theories (SDT). Meanwhile, a hierarchic model does not only include these classical theories, but their model level varies from the first order to the 3D full elasticity. In fact, in the hierarchic models, the part of displacement field through the thickness is assumed a priori using polynomials with the desired highest order. Hence, they can be numerically implemented using 2D finite element or mesh-free method, by discretizing only the mid-surface of 3D structures. The global mass and global stiffness matrices of FG plates are computed by adopting the Gaussian quadrature rules for the mid-surface integral and the trapezoidal rule for the thickness-wise integral. The proposed hierarchic models are numerically illustrated and their characteristics are investigated. In addition, the modal characteristics of FG plates are parametrically examined to the key factors of gradient layer. The hierarchic models approach the same limit and show a sequence of model accuracy. Meanwhile, the modal responses of metal-ceramic FG plate structures are dependent of the volume fraction pattern and the relative thickness ratio of gradient layer.

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Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C1100924).

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  1. Department of Naval Architecture and Ocean Engineering, Hongik University, Jochiwon, 30016, Sejong, Korea

    Jin-Rae Cho

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  1. Jin-Rae Cho
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Correspondence to Jin-Rae Cho.

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Cho, JR. Hierarchic models for the free vibration analysis of functionally gradient plates. Int J Mech Mater Des 17, 489–501 (2021). https://doi.org/10.1007/s10999-021-09543-z

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