Free vibration investigation of porous bi-layered functionally graded cylindrical shells using quadratic differential method

This article mainly investigates the free vibration behavior of bi-layered functionally graded (FG) porous cylindrical shells under different boundary conditions using a semi-analytical method. For the mechanical modeling, Love’s thin-shell theory is adopted together with the First-Order Shear Deformation Theory to within each layer. The material properties of the FG constituents follow a power-law variation of the volume fraction, allowing a gradual and continuous change of stiffness and density along the thickness direction. The fundamental equations governing the motion of the structure are formulated using the principle of virtual work, which leads to the corresponding system of differential equations. Within the Quadratic Differential Method (QDM) approach, the behavior of the natural frequencies is thoroughly investigated. A comprehensive numerical analysis is performed to assess how support conditions, porosity coefficient, thickness variations, geometric parameters, and material gradation profiles affect the fundamental vibration characteristics of the bi-layered FGM cylindrical shell.