Nonlinear Resonance of Functionally Graded Porous Circular Cylindrical Shells Reinforced by Graphene Platelet with Initial Imperfections Using Higher-Order Shear Deformation Theory

Abstract

This paper uses the higher-order shear deformation theory (HOSDT) to analyze the nonlinear resonance of functionally graded graphene platelet-reinforced porous (FG-GPL-RP) circular cylindrical shell with geometrical imperfections subjected to the harmonic transverse loading. The shell considered is surrounded by the elastic Winkler–Pasternak foundation. Based on Hamilton’s principle, the nonlinear governing equations of motion of the imperfect system considered are established using the first-order and various higher-order shear deformation shell theories that contain a unified higher-order displacement field. Four types of porosity and graphene nanoplatelet distribution patterns are considered. The modified Halpin-Tsai scheme and rule of mixture are utilized to calculate the effective properties of FG-GPL-RP materials. Explicit expressions of the nonlinear primary resonance of imperfect FG-GPL-RP cylindrical shells for simply-supported boundary conditions are achieved by the Galerkin technique and method of multiple scales. After verifying the accuracy of the model used and the results obtained, the influences of the geometric parameters, material properties and distribution and imperfection value on the nonlinear primary resonant response of the imperfect FG-GPL-RP circular cylindrical shells are examined in detail.