On linear and nonlinear bending of functionally graded graphene nanoplatelet reinforced composite beams using Gram-Schmidt-Ritz method

2021 ◽  
pp. 1-27
Author(s):  
Wachirawit Songsuwan ◽  
Chamlong Prabkeao ◽  
Nuttawit Wattanasakulpong
Keyword(s):  
Ritz Method ◽  
Composite Beams ◽  
Functionally Graded ◽  
Nonlinear Bending ◽  
Graphene Nanoplatelet ◽  
Reinforced Composite ◽  
Linear And Nonlinear

Nonlinear Dynamic Analysis of Functionally Graded Graphene Reinforced Composite Truncated Conical Shells

2019 ◽  
Vol 29 (11) ◽  
pp. 1950148 ◽  
Author(s):  
Aiwen Wang ◽  
Youqing Pang ◽  
Wei Zhang ◽  
Pengcheng Jiang
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Ritz Method ◽  
Nonlinear Dynamic Analysis ◽  
Shear Deformation Theory ◽  
Distribution Patterns ◽  
Equation Model ◽  
Functionally Graded ◽  
Conical Shells ◽  
Reinforced Composite

Functionally graded (FG) graphene reinforced composite (GRC) is a new class of advanced composite materials. In GRC, several layers of graphene platelets (GPLs) are randomly or uniformly dispersed in matrix. These GPLs have uniform arrangement, or are arranged with gradient, in the direction of thickness in accordance with three different graphene distribution rules. In this study, the nonlinear dynamic analysis of FG GRC truncated conical shells, subjected to a combined action of transverse excitation and axial force, is performed using the first shear deformation theory (FSDT). Estimation of equivalent Young’s modulus of the composites is calculated using a modified Halpin–Tsai model. In addition, a partial differential equation model is developed based on the Hamilton principle and nonlinear strain-displacement relationship. The Galerkin method and the fourth-order Runge–Kutta method are used to solve the equation. The dimensionless linear natural frequency of an FG GRC truncated conical shell is calculated by the Rayleigh–Ritz method and compared with available results in the literature to verify the accuracy of the present model. Simultaneously, significant effects of the different parameters, such as the total layer numbers, semi-vertex angles, GPLs weight fractions, distribution patterns and the length-to-thickness ratios, on the nonlinear dynamics including bifurcation and chaos of FG GRC truncated conical shells are investigated.

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