Free vibration analysis of elastically supported functionally graded annular plates via quasi-Green's function method

Abstract

Analysis and numerical results for the free axisymmetric and non-axisymmetric vibrations of functionally graded annular plates elastically supported on the ring support have been presented on the basis of classical plate theory. The quasi-Green's function has been employed to solve to boundary value problem of free vibration of functionally graded annular plate with free outer edge and clamped, simply supported and free inner edges. Additional properties of the quasi-Green's function were presented and discussed for the functionally graded annular plate. The influence of volume fraction index, core radius, selected boundary conditions, position and stiffness of ring supports on natural frequencies of an annular plate has been comprehensively studied. Singularities as the core and support radii shrink to zero are calculated for different values of volume fraction index and stiffness of the support. The quasi-Green's function method allows us to obtain universal non-linear multiparametric characteristic equations functional dependent on radius of core, volume fraction index, position and stiffness of any amount of elastic supports or other discrete elements without necessity considering new boundary value problem or find scaling factors. Additionally, the continuity conditions between the supports and plate can be omitted in the obtained solutions of boundary value problem. The presented investigation has not been reported previously. The exact frequencies of vibration presented in non-dimensional form can serve as benchmark values for researchers and engineers to validate their numerical methods applied in many fields of engineering such us mechanical, aeronautical or production engineering.