Adv. Appl. Math. Mech., 10 (2018), pp. 1344-1364.
Published online: 2018-09
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This paper is an attempt to investigate the nonlinear free vibration of skew plates reinforced by carbon nanotubes (CNTs) due to finite strain tensor. The material properties of the nano-composite are estimated using the molecular dynamic results and the rule of mixture. Also, the differential equations governing the motions are derived on the basis of Classical Plate Theory (CPT) regarding the nonlinear Green-Lagrange strain tensor. In order to solve the nonlinear equations, Galerkin's method, Frechet derivative and differential quadrature method are used. The effects of volume fraction of functionally graded materials (FGM), skew angle, distribution of CNTs and geometrical features of the plate on the nonlinear vibration of system have been studied. The results of this study have been compared with other researches and a good agreement has been achieved.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2017-0241}, url = {http://global-sci.org/intro/article_detail/aamm/12714.html} }This paper is an attempt to investigate the nonlinear free vibration of skew plates reinforced by carbon nanotubes (CNTs) due to finite strain tensor. The material properties of the nano-composite are estimated using the molecular dynamic results and the rule of mixture. Also, the differential equations governing the motions are derived on the basis of Classical Plate Theory (CPT) regarding the nonlinear Green-Lagrange strain tensor. In order to solve the nonlinear equations, Galerkin's method, Frechet derivative and differential quadrature method are used. The effects of volume fraction of functionally graded materials (FGM), skew angle, distribution of CNTs and geometrical features of the plate on the nonlinear vibration of system have been studied. The results of this study have been compared with other researches and a good agreement has been achieved.