Effect of the boundary conditions on the vibrations of functionally graded shells

In this paper, the effect of the boundary conditions on the nonlinear vibration of functionally graded circular cylindrical shells is analyzed. The Sanders-Koiter theory is applied to model the 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. Numerical analyses are carried out in order to characterize the nonlinear response when the shell is subjected to an harmonic external load; different geometries and material distributions are considered. A convergence analysis is carried out in order to determine the correct number of the modes to be used; the role of the axisymmetric and asymmetric modes is carefully analyzed. The effect of the geometry on the nonlinear response is investigated; i.e. thickness and radius are varied; simply supported, clamped-clamped and free-free shells are considered. The effect of the constituent volume fractions and the configurations of the constituent materials on the natural frequencies and nonlinear response are studied.