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Thermal Vibration Analysis of Functionally Graded Porous Plates Reinforced by Graphene Platelets Supported by Arbitrarily Distributed Kerr Foundations Under a Nonlinear Temperature Profile

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Abstract

Purpose

Functionally graded porous plates reinforced by graphene platelets (FGP-GPLs) have great potential value in areas such as aerospace and high-temperature electronic components. The analysis of vibrational characteristics of FGP-GPLs plates in thermal environments is important for the safety performance and optimization of these structures. However, the current thermal vibration analysis of FGP-GPLs plates does not use the nonlinear temperature profile (NTP), and the case of a plate supported by an arbitrarily distributed elastic foundation is not considered in the vibration analysis of FGP-GPLs plates. The purpose of this paper is to investigate the thermal vibrational characteristics of FGP-GPLs plates supported by arbitrarily distributed elastic foundations under NTP.

Methods

First, the shape and location of the three-parameter Kerr foundations are determined by mathematical functions. Four typical foundation distributions pattern are given in the paper. Second, the NTP model is obtained by solving the steady-state heat transfer model. This distribution model considers the effects of pores and GPLs. Third, the control equations of the plate are obtained using Hamilton's principle and refined plate theory. Galerkin's method is used to solve the governing equations.

Results

To verify the accuracy of the computational model in this paper, the results obtained are compared with those of the existing literature. In addition, the effects of parameters such as the distribution pattern of elastic foundation, stiffness, geometrical parameters, temperature profile model, pore distribution, and GPLs pattern on the vibration characteristics of FGP-GPLs plates were investigated.

Conclusions

The results show that a reasonable foundation distribution pattern can significantly improve the stiffness of FGP-GPLs plates when the foundation area is the same. When the pore distribution and the GPLs pattern are asymmetric, the results of NTP versus uniform temperature profile (UTP) and linear temperature profile (LTP) differ significantly. The results of this study are informative for the structural design of FGP-GPLs plates supported by elastic foundations. In addition, the numerical results in this paper can be used as a reference for other researchers' studies.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

This research was funded by the National Natural Science Foundation of China (11862012, 12062010) and the Natural Science Foundation of Shandong Province (ZR2020KA006).

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Authors and Affiliations

  1. School of Science, Lanzhou University of Technology, Lanzhou, China

    Xiang-Yu Gao

  2. School of Civil Engineering, Southeast University, Nanjing, China

    Zhuang-Zhuang Wang

  3. School of Architecture Engineering, Weifang University of Science and Technology, Weifang, China

    Lian-Sheng Ma

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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by [Lian-Sheng Ma], [Zhuang-Zhuang Wang] and [Xiang-Yu Gao]. The first draft of the manuscript was written by [Xiang-Yu Gao] and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Gao, XY., Wang, ZZ. & Ma, LS. Thermal Vibration Analysis of Functionally Graded Porous Plates Reinforced by Graphene Platelets Supported by Arbitrarily Distributed Kerr Foundations Under a Nonlinear Temperature Profile. J. Vib. Eng. Technol. (2024). https://doi.org/10.1007/s42417-024-01323-1

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