: Nonlinear Vibration Analysis of Imperfect Stiffened Functionally Graded Cylindrical Panel Under the Effect of Thermal-Mechanical Loads

Abstract

ABSTRACT This study displays an analytical investigation of the influence of stiffener's geometric shape on nonlinear natural frequencies of imperfect eccenkically stiffened functionally graded material for the simply supported cylindrical panels strengthened with various forms of the stiffeners for both longitudinal and transverse directions rest on elastic foundation subject to thermal-mechanical loads. Based on the classical shell theory with the geometrical shape of nonlinear in von Karman-Donnell means, smeared stiffeners metho{ and first-order shear defomration theory, the goveming equations of motion are derived in order to determine the difference between tJrese two theories. The properties of nonlinear responses and free vibration are studied. The mechanical properties assumed to be graded smoothly and continuously toward the thickness of the cylindrical panel according to power law distribution. The numerical approach that employs the fourth-order Runge-Kutta and Galerkin's procedure are conducted for the dynamic analysis of the shells to provide expression of non-linear dyramic responses and the natural frequencies. The validation of the current study is gained by comparing the results with other researchers, where a very good agreement obtained in the results presented. The effect ofdifferent geometric stiffener's shape, volume fraction index, radius to thickness ratio, excitation force, imperfection, angular velocity, (FGM) thickness, elastic foundation, and finally the temperature were studied on the natural frequency