Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams

Abstract

The nonlinear free vibration and postbuckling behaviors of multilayer functionally graded (FG) porous nanocomposite beams that are made of metal foams reinforced by graphene platelets (GPLs) are investigated in this paper. The internal pores and GPL nanofillers are uniformly dispersed within each layer but both porosity coefficients and GPL weight fraction change from layer to layer, resulting in position-dependent elastic moduli, mass density and Poisson's ratio along the beam thickness. The mechanical property of closed-cell cellular solids is employed to obtain the relationship between coefficients of porosity and mass density. The effective material properties of the nanocomposite are determined based on the Halpin-Tsai micromechanics model for Young's modulus and the rule of mixture for mass density and Poisson's ratio. Timoshenko beam theory and von Kármán type nonlinearity are used to establish the differential governing equations that are solved by Ritz method and a direct iterative algorithm to obtain the nonlinear vibration frequencies and postbuckling equilibrium paths of the beams with different end supports. Special attention is given to the effects of varying porosity coefficients and GPL's weight fraction, dispersion pattern, geometry and size on the nonlinear behavior of the porous nanocomposite beam. It is found that the addition of a small amount of GPLs can remarkably reinforce the stiffness of the beam, and the its nonlinear vibration and postbuckling performance is significantly influenced by the distribution patterns of both internal pores and GPL nanofillers.

A Modified Couple Stress Elasticity for Non-Uniform Composite Laminated Beams Based on the Ritz Formulation

“…Several experimental evidences in literature, have revealed that the behavior of micro-structures is size-dependent [2][3][4][5]. Thus, a large number of works has been recently published to conceive novel structural solutions, systems, and devices, while adopting different types of reinforcement phase, such as graphene nanoplatelets [6][7][8][9][10][11][12][13][14], or carbon nanotubes [15][16][17][18][19]. Among a large variety of numerical strategies, higher order theories represent the most useful tool for the investigation of the static and dynamic response of materials at different scales [20][21][22][23][24].…”

Static analysis of piezoelectric functionally graded porous plates reinforced by graphene platelets

“…Based on the Ritz method and Timoshenko beam theory, the authors in Refs. [24,25] studied the free vibration, elastic buckling and the nonlinear free vibration, post-buckling performances of FGP beams, respectively. The uniaxial, biaxial, shear buckling and free vibration responses of FGP-GPLs were also investigated by [26] based on the first-order shear deformation theory (FSDT) and Chebyshev-Ritz method.…”

“…Based on the Ritz method and Timoshen theory, the authors in refs. [24] and [25] studied the free vibration, elastic buc the nonlinear free vibration, post-buckling performances of FGP beams, resp The uniaxial, biaxial, shear buckling and free vibration responses of FGP-G also investigated by [26] based on the first-order shear deformation theory (FS Chebyshev-Ritz method. Additionally, to investigate the static, free vibra buckling of FGP-GPLs, [27] utilized IGA based on both FSDT and the third-or deformation theory (TSDT).…”

Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates

“…Shen et al [29] carried out nonlinear bending and thermal postbuckling analyses of functionally graded graphenereinforced composite laminated beams resting on an elastic foundation and suggested that the functionally graded graphene reinforcement and temperature change have pronounced impacts on the nonlinear bending and thermal postbuckling behaviours. Kitipornchai and his coauthors [30,31] demonstrated that the incorporation of a small amount of GPLs can remarka-…”