Nonlinear dynamics of fluid-filled nanocomposite cylindrical shells surrounded by non-uniform Kerr elastic substrates

This paper presents a novel analytical framework for investigating the nonlinear dynamic response of functionally graded graphene platelets reinforced composite (FG-GPLRC) cylindrical shells filled with fluids and supported by non-uniform Kerr elastic substrates. The significance of this research lies in its comprehensive exploration of various substrate configurations achieved through discretizing the elastic substrates along the shell’s length. The fluid within the shell is characterized as non-viscous and incompressible, while material properties are rigorously determined using the rule of mixtures and the Halpin–Tsai micromechanical model. At the core of our method lies the establishment of nonlinear kinematic relationships rooted in Donnell shell theory and von Kármán’s nonlinear geometric postulates. We rigorously solve the equations of motion using Galerkin’s technique and the fourth-order Runge–Kutta method. Notably, our enhanced model efficiently accounts for the effect of discontinuities in the elastic foundation’s stiffness solely through integration operations, eliminating the need for intricate algorithms. This approach optimizes computational time and costs. The study conducts a comparative analysis of its results with existing literature, contributing to a thorough understanding of the validity of the proposed approach. We investigate various factors — including material properties, fluid characteristics, and geometric parameters — and their influence on the nonlinear response of nanocomposite shells. Our comprehensive analysis highlights the significant impact of substrate distribution, emphasizing its importance in structural design. Expanding the elastic base area and gradually shifting the elastic foundation toward the central region of the shell positively will affect various factors such as elevating natural frequency and reducing vibrational amplitudes.