Three-dimensional elasticity solution for vibration analysis of functionally graded hollow and solid bodies of revolution. Part II: Application

• Free vibrations of FGM cylinders, cones and spheres with arbitrary boundary conditions are analyzed.
• The method furnishes stable and rapid convergence characteristics for vibration analyses.
• Harmonic responses of hollow and solid cylinders under uniformly axial and normal pressures are calculated.
• Transient vibrations of FGM cones under various impulsive loads are examined.

The semi-analytical method, developed in Part I of this paper, is employed to investigate the free, steady-state and transient vibrations of various FGM bodies of revolution. A comprehensive investigation concerning the convergence, accuracy and efficiency of the method is given for free vibrations of hollow and solid FGM cylinders, cones and spheres with different combinations of free, simply-supported, clamped and elastic-supported boundary conditions. It is shown that the present method enables rapid convergence, stable numerical operation and very high computational accuracy. Both lower- and higher-order frequencies can be accurately obtained by using a small computational effort. The utility and robustness of the method for the application of various polynomial functions are evaluated. New vibration results for FGM bodies of revolution are presented, which could serve as benchmarks for future research. Parametric studies are carried out to highlight the influences of geometrical parameters, boundary conditions, and material profiles on free vibrations of FGM cylinders, cones and spheres. With regard to the forced vibration problems, harmonic responses of hollow and solid cylinders under uniformly axial and normal pressures are calculated, and time domain solutions of FGM cones subjected to several impulsive loads, including a rectangular pulse, a triangular pulse, a half-sine pulse and an exponential pulse, are also examined.