Quasi-Green's function approach to free vibration analysis of elastically supported functionally graded circular plates

The analysis and numerical results regarding free vibrations of functionally graded circular plates elastically supported on a concentric ring are presented on the basis of the classical plate theory. The quasi-Green's function was employed to solve the boundary value problem of the free vibrations of functionally graded circular plates with clamped, free and simply supported edges. The influence of the boundary conditions, the volume fraction index, the position and the stiffness of ring supports on natural frequencies of circular plates was studied comprehensively. Dimensionless frequencies for singularities that emerge when the support radius approaches zero are calculated for different values of the volume fraction index. The quasi-Green's function method enables obtaining non-linear characteristic equations that are functionally dependent on the volume fraction index, the position and the stiffness of elastic supports or other discrete elements without the necessity to consider a new boundary value problem or find scaling factors. The presented investigation has not been hitherto reported. The exact frequencies of vibrations presented in the non-dimensional form can serve as benchmark values for researchers to validate their numerical methods applied in the frequency analysis of functionally graded circular plates.