Transient and steady-state nonlinear vibrations of FGM truncated conical shell subjected to blast loads and transverse periodic load using post-difference method

This paper focuses on the transient and steady-state nonlinear dynamic responses of the functionally graded material (FGM) truncated conical shell under the ultra-high temperature and two types of blast loads or uniform load. The volume fractions are modified in the thickness direction gradually, and the material properties depend on the temperature. Using the first-order shear deformation theory, geometrical nonlinear strain-displacement relationship and Hamilton principle, the partial differential governing equation of motion are derived for the FGM truncated conical shell. Galerkin method is utilized to obtain the nonlinear ordinary differential governing equations of motion. The post-difference method is used to simulate the governing equations of motion, and the nonlinear transient and steady-state responses are analyzed for the FGM truncated conical shell subjected to two different blast loads. The effects of the geometric parameters and blast loads on the nonlinear vibrations are studied for the FGM truncated conical shell. The results indicate that two kinds of blast loads have significant the effects on the amplitudes of the vibrations for the FGM truncated conical shell, and the amplitudes of the vibrations decreases with the increase of the length-thickness ratio. The periodic and chaotic vibrations of the FGM truncated conical shell are found.