Stability and Vibration of Mindlin Sector Plates: An Analytical Approach.
This study presents a simple analytical formulation for the eigenvalue problem of buckling and free-vibration analysis of Mindlin sector plates. The nonaxisymmetric formulation in cylindrical coordinates is discretized in the space domain in terms of two-dimensional Chebyshev polynomials. The formulation facilitates application of several combinations of simply supported, clamped, and free-edge conditions. Convergence study has been carried out, and the obtained results are compared with those available in the literature. Extensive results pertaining to critical buckling loads and natural frequencies are presented. Effects of boundary conditions, plate thickness, and annularity are studied.