Nonlinear Vibration Analysis of a Cylindrical FGM Shell on a Viscoelastic Foundation under the Action of Lateral and Compressive Axial Loads

Abstract

In this paper, the nonlinear vibration analysis of a thin cylindrical shell made of Functionally Graded Material (FGM) resting on a nonlinear viscoelastic foundation under compressive axial and lateral loads is studied. Nonlinear governing coupled partial differential equations of motions (PDEs) for cylindrical shell are derived using improved Donnell shell theory. The equations of motions (EOMs) then are solved using the Galerkin method, Volmir's assumption and the forth-order Runge-Kutta method to obtain dynamic response of the shell including nonlinear frequencies, frequency-amplitude curves and nonlinear radial deflection for the shell of revolution. Afterward, the effect of changing the value of different parameters on the nonlinear dynamic response of the FGM cylindrical shell considering compressive axial and lateral loads, geometric characteristics of the shell, FGM material distribution along direction of the thickness of the shell and coefficients of the viscoelastic foundation are all investigated