Nonlinear Vibration Analysis of Functionally Graded Imperfection of Cylindrical Panels Reinforced with Different Types of Stiffeners

This study presents an analytical investigation on the effect of stiffener's geometric shape on the nonlinear natural frequencies of eccentrically stiffened functionally graded material cylindrical panels. Based on the classical shell theory with the geometrical shape of nonlinear in von Karman–Donnell means and the smeared stiffeners method (SSM), the governing equations of motion are derived. The properties of nonlinear responses and free vibration are studied. The numerical method utilizing the fourth-order Runge-Kutta are performed for the dynamic analysis of the shells to give expression of nonlinear dynamic responses and the natural frequencies. Effects of stiffener's geometric shape, material properties, and initial geometrical imperfection are presented with obtained results. Some results are presented and compared with the other authors.