Nonlinear vibration of functionally graded cylindrical shells: effect of constituent volume fractions and configurations

In this paper, the nonlinear vibration of functionally graded (FGM) cylindrical shells under different constituent volume fractions and configurations is analyzed. The Sanders-Koiter theory is applied to model nonlinear dynamics of the system in the case of finite amplitude of vibration. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. Displacement fields are expanded by means of a double mixed series based on harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. Both driven and companion modes are also considered, allowing for the travelling-wave response of the shell. The functionally graded material considered is made of stainless steel and nickel, properties are graded in the thickness direction according to a real volume fraction power-law distribution. In the nonlinear model, shells are subjected to an external radial excitation. Nonlinear vibrations due to large amplitude of excitation are considered. Specific modes are selected in the modal expansions; a dynamical nonlinear system is then obtained. Lagrange equations are used to reduce nonlinear partial differential equations to a set of ordinary differential equations, from the potential and kinetic energies, and the virtual work of the external forces. Different geometries are analyzed; amplitude-frequency curves are obtained. Convergence tests are carried out considering a different number of asymmetric and axisymmetric modes. The present model is validated in linear field (natural frequencies) by means of data present in the literature.