Thermomechanical Nonlinear Vibration of Axially Loaded Functionally Graded Material Cylindrical Panels Including Porosity

For the first time, the combined influences of axial compressive load, porosity, geometric imperfection, elastic edge restraint, and elevated temperature on the nonlinear free vibration of functionally graded material (FGM) cylindrical panels are investigated in this paper. Unlike previous studies, the structural model considered in this paper includes practical situations and conditions arising in the design process and application of FGM cylindrical panels. The properties of material constituents are assumed to be temperature-dependent, and the effective properties of porous FGM are determined using a modified rule of mixture. Governing equations in terms of deflection and stress function are established based on first-order shear deformation theory, taking into account von Kármán–Donnell nonlinearity and initial geometric imperfection. Analytical solutions are assumed to satisfy simply supported boundary conditions, and the Galerkin method is applied to derive a time differential equation containing both quadratic and cubic nonlinear terms. This differential equation is numerically integrated employing the fourth-order Runge–Kutta scheme to determine the frequencies of nonlinear free vibration. Parametric studies are carried out to assess numerous effects on both linear and nonlinear frequencies of porous FGM cylindrical panels. The study reveals that natural frequencies are strongly decreased and that frequency nonlinearity is more significant due to axial compressive loads.