Large amplitude free vibrations of long FGM cylindrical panels on nonlinear elastic foundation based on physical neutral surface

In the current investigation, the small and large amplitude free vibration characteristics of long cylindrical panels made of FGMs is investigated using the higher order shear deformation shell theory and Donnell kinematic assumptions. The interaction of the panel with a nonlinear hardening/softening foundation in also included into the formulation. The properties of the panel are assumed to be graded across the thickness of the panel and assumed to be temperature dependent. Using the neutral surface concept, the three coupled motion equations of the shell are established and solved for the case of long panels which are immovable simply supported on straight edges. The solution method is based on the two step perturbation technique which results in a closed form expression for the frequencies of the panel as a function of the mid-point deflection. Numerical studies are first validated for the case of long FGM plates. Afterwards novel numerical results are given to show the effect of geometrical parameters, power law index, foundation stiffnesses and temperature elevation. As shown, temperature elevation results in the reduction in natural frequencies and enhancement of the frequency ratio of the panel. Also temperature dependency reduces the natural frequencies and frequency ratios of the panel.