Resonance response of clamped functionally graded cylindrical shells with initial imperfection in thermal environments

Abstract

In this paper, the resonance behavior of initial imperfect functionally graded material (FGM) cylindrical shells with the clamped–clamped boundary condition at two ends is investigated. The material properties considered here are graded in the thickness direction according to a simple power law in terms of the volume fractions and are affected by temperature. The classical deformation theory, von-Karman type nonlinear geometric relations and Hamilton’s principle are employed to derive nonlinear partial differential equation of the clamped circular cylindrical shell at two ends. The partial differential governing equations are truncated by the Galerkin technique. Under the effect of transverse external excitation and in-plane force, averaged equations in term of polar coordinate are obtained by using multiple scales method. It is assumed that the dynamic system is in the case of primary resonance and 1:2 internal resonance. The effects of the volume fraction, temperature, damping, imperfection, transverse external excitation and in-plane force on amplitude frequency response of FGM cylindrical shell with initial imperfection are studied in detail by the application of numerical continuation method. With varying the tuning parameter of the excitation frequency, saddle node bifurcation, hopf bifurcation, saddle node bifurcation and hopf bifurcation are detected.