Thermal vibration analysis of FG-GPLRC doubly curved shells partially resting on Kerr foundation based on higher-order shear deformation theory

Abstract

In this paper, we present a novel analytical approach for investigating the influence of non-homogeneous Kerr elastic foundations on the nonlinear dynamical characteristics of functionally graded graphene platelets reinforced composite (FG-GPLRC) doubly curved shells. A new aspect of this study is the investigation of various distributions of the Kerr foundation, either centrally within or along the edges of the nanocomposite shells, a model not previously explored. Three distinct distributions of graphene nanoplatelets reinforcement are examined, utilizing the rule of mixtures and the Halpin-Tsai micromechanical model. The theoretical framework is based on Reddy's third-order shear deformation theory. The equations of motion, formulated as partial differential equations, are efficiently resolved through the application of Galerkin's method. The effectiveness of this approach resides in its utilization of integration to tackle the distribution issue of the elastic foundation, all without the need for deploying intricate algorithms. The validity of our proposed method is established through meticulous comparisons with findings from prior literature. Furthermore, this paper delves into the effect of material properties, thermal conditions, boundary conditions, geometrical parameters, and four configurations of the shells on the vibrational responses. Of notable significance is our thorough investigation of the impact of variations in the distributions, stiffness, and geometrical parameters of the elastic foundation on natural frequencies and the nonlinear transient response of these shells, all of which hold great importance in structural design. We present the obtained results systematically in various formats, including tables, 2D and 3D graphs, and contour plots, providing a comprehensive overview of the research outcomes. These findings have profound implications for the field of engineering, contributing to advancements in novel structural designs and their diverse applications.