Nonlinear resonance behavior of functionally graded cylindrical shells in thermal environments

This paper deals with the nonlinear vibrations of functionally graded cylindrical shells in thermal environments. The equivalent properties of functionally graded materials are described as a power-law distribution in the thickness direction and are considered to be temperature-dependent. A typical case with a primary resonance excitation and a 1:2 internal resonance between two modes is analyzed. The energy approach and the Lagrangian formulation are employed to derive the reduced low-dimensional nonlinear ordinary differential equations of motion based on Donnell’s nonlinear shell theory. The dynamic behaviors of system are investigated by means of the so-called multiple scale method. The amplitude–frequency curves and the bifurcation behavior of the system are analyzed using numerical continuation method. The effects of temperature and volume fractions of constituent material on the amplitude response of the system are fully discussed.