Quasi-Green’s function approach to fundamental frequency analysis of elastically supported thin circular and annular plates with elastic constraints

Free vibration analysis of homogeneous and isotropic thin circular and annular plates with
discrete elements such as elastic ring supports is considered. The general form of quasi-
-Green’s function for thin circular and annular plates is obtained. The nonlinear characteristic
equations are defined for thin circular and annular plates with different boundary conditions
and different combinations of the core and support radius. The continuity conditions at
the ring supports are omitted based on the properties of Green’s function. The fundamental
frequency of axisymmetric vibration has been calculated using the Newton-Raphson method
and calculation software. The obtained results are compared with selected results presented
in literature. The exact frequencies of vibration presented in a non-dimensional form can
serve as benchmark values for researchers to validate their numerical methods when applied
for uniform thin circular and annular plate problems.