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Advances in Nano Research Volume 8, Number 2, February 2020 , pages 115-134 DOI: https://doi.org/10.12989/anr.2020.8.2.115 |
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Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates |
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Kasra Dehshahri, Mohammad Zamani Nejad, Sima Ziaee, Abbas Niknejad and Amin Hadi
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| Abstract | ||
| In this paper, the free vibrations analysis of the nanoplates made of three-directional functionally graded material (TDFGM) with small scale effects is presented. To study the small-scale effects on natural frequency, modified strain gradient theory (MSGT) has been used. Material properties of the nanoplate follow an arbitrary function that changes in three directions along the length, width and thickness of the plate. The equilibrium equations and boundary conditions of nanoplate are obtained using the Hamilton's principle. The generalized differential quadrature method (GDQM) is used to solve the governing equations and different boundary conditions for obtaining the natural frequency of nanoplate made of three-directional functionally graded material. The present model can be transformed into a couple stress plate model or a classic plate model if two or all parameters of the length scales set to zero. Finally, numerical results are presented to study the small-scale effect and heterogeneity constants and the aspect ratio with different boundary conditions on the free vibrations of nanoplates. To the best of the researchers' knowledge, in the literature, there is no study carried out into MSGT for free vibration analysis of FGM nanoplate with arbitrary functions. | ||
| Key Words | ||
| vibration; nanoplate; three-directional functionally graded material (TDFGM); modified strain gradient theory (MSGT); generalized differential quadrature method (GDQM); size effect | ||
| Address | ||
| (1) Kasra Dehshahri, Mohammad Zamani Nejad, Sima Ziaee, Abbas Niknejad: Department of Mechanical Engineering, Yasouj University, Yasouj, Iran; (2) Amin Hadi: Cellular and Molecular Research Center, School of Medicine, Yasuj University of Medical Sciences, Yasuj, Iran. | ||