Nonlinear Vibration of Functionally Graded Cylindrical Shells under Radial Harmonic Load

Abstract

In this paper, the nonlinear vibration of functionally graded (FGM) cylindrical shells subjected to radial harmonic excitation is investigated. The nonlinear formulation is based on a Donnell's nonlinear shallow-shell theory, in which the geometric nonlinearity takes the form of von Karman strains. The Lagrange equations of motion were obtained by an energy approach. In order to reduce the system to finite dimensions, the middle surface displacements were expanded by using trial functions. These functions were expressed in terms of Fourier series containing linear mode shapes, which were obtained from free vibration analysis. The large-amplitude response and amplitude frequency curves of shell were computed by using numerical method for both linear and nonlinear analysis.