On the stochastic natural frequency of graphene reinforced functionally graded porous panels with unconventional boundary conditions

Abstract

The present study explores the stochastic natural frequency of graphene reinforced functionally graded porous panels with unconventional boundary conditions. The material uncertainty is considered in the parameters associated with constituents that is, metal and graphene nanoplatelets (GPLs) individually and simultaneously. The metal matrix is reinforced with ultra-lightweight and high stiffness carbonaceous nanofiller, that is, GPLs. Halpin-Tsai micromechanics model is adopted to estimate effective Young’s modulus of the metal-GPLs composite whereas effective mass density and Poisson’s ratio are calculated using the Voigt model. The micro-structural gradation by creating pores is accomplished along the thickness direction of the panel employing certain continuous functions. These functions describe symmetric and asymmetric porosity distributions and associated patterns of GPLs. The equation of motion is developed using Euler-Lagrange’s equation which is based on C0-continuous structural kinematics with 7 degrees of freedom. Finite element modeling in conjunction with the first-order perturbation technique has been applied to quantify the stochastic natural frequency in terms of the mean and standard deviation of the natural frequency. Various results have been examined to highlight the influence of parameters especially related to porosity, and graphene nanoplatelets on the stochastic natural frequency of FG-GPLs porous panel constrained with conventional and unconventional boundary conditions.