FREQUENCY SOLUTIONS FOR CIRCULAR PLATES WITH INTERNAL SUPPORTS AND DISCONTINUOUS BOUNDARIES

The paper presents a study of the free-flexural vibration analysis of circular plates continuous over point supports, partial internal curved supports, and with mixed-edge boundary conditions. An approximate model which combines the advantages of the Rayleigh-Ritz and the Lagrangian multiplier methods is developed for analyzing this class of circular plate problems. The Rayleigh-Ritz method is used to formulate plates with classical boundary conditions, such as free, simply-supported or clamped, while the Lagrangian multiplier method is used to handle plates with point supports, partial internal curved supports and mixed-edge boundary conditions. The admissible pb-2 Ritz function consists of the product of a two-dimensional polynomial and a basic function. The basic function is defined by the product of the equations of the prescribed piecewise-continuous boundary shape each raised to the power of 0, 1 or 2, corresponding to free, simply-supported or clamped edge, respectively. The set of functions automatically satisfies all the kinematic boundary conditions of the plate at the outset. The geometric boundary conditions associated with the internal supports and discontinuous edges are simulated using a sufficient number of closely-spaced point constraints. Numerical results for several selected plate problems are presented to demonstrate the various features and accuracy of the present method.