Vibration analysis of corner supported Mindlin plates of arbitrary shape using the Lagrange multiplier method

This paper presents the first known of the problem of the free flexural vibration of corner supported Mindlin plates of arbitrary shape. A hybrid numerical approach combining the Rayleigh-Ritz method and the Lagrange multiplier method has been developed to solve the plate vibration problem. The algorithm uses the pb-2 shape functions to account for different geometries, and Lagrange multipliers to impose zero lateral defection constraints at plate corners. The method of solution is applicable to arbitrarily shaped plates with corner supports. In this however, only triangular, skew and annular sector plates are chosen for the purpose of demonstration. Some comparison studies for corner supported thin square plates are made to verify the accuracy of the derived solutions.