Free‐Vibration Analysis of Point‐Supported Orthotropic Plates

Accurate analytical‐type solutions are obtained for the free vibration of thin rectangular orthotropic plates resting on point supports symmetrically distributed about the plate central axis. Solutions are obtained by the method of superposition. Convergence is found to be rapid. It is pointed out that the same method permits the obtaining of solutions regardless of the number of supports and even when the support points are not symmetrically distributed. Highly accurate eigenvalues are tabulated for the first four modes of the three families of free‐vibration modes characteristic of square plates with four symmetrically distributed point supports located on the plate diagonals. These are modes fully symmetric, and fully antisymmetric, about the plate central axis, as well as modes symmetrical about one axis and antisymmetric about the other. Dimensionless distances from the center of the plate to the support points are allowed to vary from 0.2 to 0.9. Parameters that characterize the orthotropic properties of the plate are permitted to vary within a limited range.