Nonlinear free vibration of FG-GPLRPC conical shells reinforced by circular FG-GPLRPC stiffeners in thermal environment

Abstract

This paper presents a comprehensive analytical study on the nonlinear free vibration behavior of functionally graded graphene platelet-reinforced porous composite (FG-GPLRPC) conical shells integrated with circular FG-GPLRPC ring stiffeners under thermal conditions. The theoretical formulation is established within the framework of Donnell shell theory, incorporating von Kármán geometric nonlinearity to account for large deflections. The stiffening effect of circular reinforcements is modeled using an enhanced Lekhnitskii-based smeared stiffener approach. By employing the Ritz method in conjunction with the harmonic balance technique, the nonlinear governing equations are derived and subsequently used to determine the natural frequencies and amplitude–frequency relationships. A detailed parametric investigation is conducted to evaluate the effects of stiffener characteristics, graphene platelet content, porosity distribution, material gradation patterns, and geometric parameters on the nonlinear vibration response. The results provide valuable insights into the dynamic behavior and design optimization of advanced porous graphene-reinforced conical shell structures operating in thermal environments.