Volume 10, Issue 6
Nonlinear Free Vibration of Reinforced Skew Plates with SWCNs Due to Finite Strain

S. Jafari Mehrabadi & S. M. Nodeh Farahani

Adv. Appl. Math. Mech., 10 (2018), pp. 1344-1364.

Published online: 2018-09

Preview Full PDF 56 1798
Export citation
  • Abstract

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 GreenLagrange 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.

  • Keywords

Finite strains nonlinear vibration skew plate carbon nanotubes functionally graded materials.

  • AMS Subject Headings

34A34

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-10-1344, author = {S. Jafari Mehrabadi and S. M. Nodeh Farahani}, title = {Nonlinear Free Vibration of Reinforced Skew Plates with SWCNs Due to Finite Strain}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {6}, pages = {1344--1364}, abstract = {

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 GreenLagrange 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} }
TY - JOUR T1 - Nonlinear Free Vibration of Reinforced Skew Plates with SWCNs Due to Finite Strain AU - S. Jafari Mehrabadi & S. M. Nodeh Farahani JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1344 EP - 1364 PY - 2018 DA - 2018/09 SN - 10 DO - http://dor.org/10.4208/aamm.OA-2017-0241 UR - https://global-sci.org/intro/aamm/12714.html KW - Finite strains KW - nonlinear vibration KW - skew plate KW - carbon nanotubes KW - functionally graded materials. AB -

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 GreenLagrange 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.

S. Jafari Mehrabadi & S. M. Nodeh Farahani. (1970). Nonlinear Free Vibration of Reinforced Skew Plates with SWCNs Due to Finite Strain. Advances in Applied Mathematics and Mechanics. 10 (6). 1344-1364. doi:10.4208/aamm.OA-2017-0241
Copy to clipboard
The citation has been copied to your clipboard