Vibration of mindlin plates on point supports using constraint functions

This paper presents the first known solutions for free flexural vibration of Mindlin plates of arbitrary shape with internal point supports. A new approach for modeling the point supports in vibration analysis is proposed. The method is based on the use of a set of pb-2 shape functions to account for prescribed boundary conditions of different shapes. Internal point supports are imposed as geometric constraints in the final formulation of the governing eigenvalue equation. The proposed method is employed to determine the vibration frequencies of square and circular plates having an arbitrary number of internal point supports. Comparisons with known thin-plate solutions are carried out, where possible, to verify the accuracy of the proposed method. © ASCE.