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Nonlinear vibration of functionally graded circular nanoplates based on the stress-driven method

Mohammad Shishesaz, Mojtaba Shariati and Reza Mosalmani

Vol. 18 (2023), No. 2, 191–217
Abstract

In this work, the stress-driven method (SDM) was used to investigate the axisymmetric nonlinear vibrational behavior of functionally graded circular nanoplates and the results were compared with those of strain gradient theory (SGT). The governing equations and related boundary conditions were derived using Hamilton’s principle based on the SDM and SGT. Then, the governing equations and related boundary conditions were discretized and solved using the generalized differential quadrature rule (GDQR) in conjunction with the Galerkin weighted residual method (GWRM). The results of this study have been compared and validated with the results of other studies when applicable. The effects of aspect ratio, different boundary conditions, and mode number on the overall behavior of the nanoplates were investigated. The results show that considering the small-scale effect will have a significant influence on the results. Also, the comparison of linear and nonlinear behavior confirms the importance of using nonlinear behavior. Based on the SDM and SGT results, any increase in the magnitude of the material size parameter L results in a decrease in the frequency ratios in all modes for all types of boundary conditions mentioned above. The maximum decrease results from the SGT model. In addition, the differences between the SDM and SGT frequency ratios increase as the material size parameter L increases. Increasing the values of the aspect ratio hR increases the frequency ratios in all modes for all types of boundary conditions. This result appears to be valid for all selected values of the material size parameter L. Furthermore, for any specific value of the initial condition W0 and the material size parameter, the smallest and largest frequency ratios are related to the SGT and SDM, respectively.

Keywords
size effect, nonlinear vibration, functionally graded material, circular nanoplate, nonlocal strain gradient theory
Milestones
Received: 21 April 2022
Revised: 28 August 2022
Accepted: 20 September 2022
Published: 18 April 2023
Authors
Mohammad Shishesaz
Department of Mechanical Engineering
Shahid Chamran University of Ahvaz
Ahvaz
Iran
Mojtaba Shariati
Department of Mechanical Engineering
Shahid Chamran University of Ahvaz
Ahvaz
Iran
Reza Mosalmani
Department of Mechanical Engineering
Shahid Chamran University of Ahvaz
Ahvaz
Iran