Vibrational analysis of a cylindrical panel with an FG viscoelastic core and graphene-reinforced composite face sheets based on the theory of elasticity

Abstract

This paper presents a comprehensive analysis of the free vibrations of a sandwich panel composed of a viscoelastic core and composite face sheets reinforced with graphene platelets. It considers various common patterns of graphene distribution throughout the panel’s thickness. The viscoelastic core is modeled using the Boltzmann superposition integral and Prony series. The governing equations are derived from three-dimensional elasticity theory and reformulated into state-space equations. Unlike previous studies, which often utilize simplified models, this research employs exact elasticity theory, combined with rigorous modeling of the viscoelastic core, to achieve greater accuracy and broader applicability. To address the computational complexity associated with the viscoelastic formulation, the equations are transformed from the time domain to the Laplace domain. Radial (through-thickness) boundary conditions are implemented using the state-space technique, while in-plane (axial and circumferential) boundary conditions—such as clamped, simply supported, and free edges—are managed through both analytical solutions (Navier’s method) and the differential quadrature method (DQM). This proposed hybrid approach enables efficient and precise analysis under various boundary conditions. Validation is conducted by comparing the numerical results with those available in existing literature.