Abstract
A unified solution for free in-plane vibration analysis of elastically functionally graded restrained porous plates (FGPP) with porosity distributions in the thickness and in-plane directions in the framework of a semi-analytical solution is proposed for the first time. The segment technique, penalty function and energy principle are used to establish the motion equation of porous plates. The boundary conditions are simulated by setting of penalty function. The displacement tolerance function of porous plates is expressed by Jacobian series, which is introduced into the energy expression. Then a set of simple linear equations can be obtained by partial differential operation of unknown expansion coefficients. By compared results obtained by the current method, FEM and experiment, the correctness and accuracy of this model are validated. On the above basis, comprehensive parametric investigations are carried out to analyze the behavior of vibration of FGPP with respect to a several factors. The numerical results presented in this paper can lay a foundation for future research in this field.
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The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 11902368).
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Chen, Z., Qin, B., Zhong, R. et al. Free in-plane vibration analysis of elastically restrained functionally graded porous plates with porosity distributions in the thickness and in-plane directions. Eur. Phys. J. Plus 137, 158 (2022). https://doi.org/10.1140/epjp/s13360-021-02153-w
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DOI: https://doi.org/10.1140/epjp/s13360-021-02153-w