Buckling and vibration of annular mindlin plates with internal concentric ring supports subject to in-plane radial pressure

This paper is concerned with the buckling and vibration of annular Mindlin plates with internal concentric ring supports subjected to external and internal isotropic in-plane radial pressure. The governing eigenvalue equation is obtained, by using the Rayleigh-Ritz approach with the transverse displacement and rotations being approximated by the product of a complete one-dimensional polynomial function and a basic function. The basic function is the product of the boundary equations and ensures the automatic satisfaction of the kinematic boundary conditions. Comprehensive sets of buckling factors and vibration frequencies for the aforementioned Mindlin plate problems are tabulated, for the first time, to the author's knowledge. Additionally, useful design charts are presented for a large number of annular Mindlin plates on multiple concentric ring supports with the outer and inner edges subjected to isotropic in-plane radial pressure. Computations based on the model reveal the significant effect of internal rings on the buckling factors and vibration frequencies of the plates.