A simple and accurate Ritz formulation for free vibration of thick rectangular and skew plates with general boundary conditions

Abstract

The Ritz method is one of the most elegant and useful approximate methods for obtaining solutions for the natural frequencies and vibration modes of elastic plates. It is simple to use and also straightforward to implement. In conventional Ritz method, the geometric boundary conditions are only satisfied and hence the Ritz method is known as a method that can produce upper bound solution results for the natural frequencies of elastic plates. On the other hand, the accuracy of the Ritz method for the solution of differential equations with mixed natural boundary conditions at the boundary lines is not very satisfactory. To overcome this difficulty, this paper presents a simple and accurate Ritz formulation in which the natural boundary conditions are exactly implemented. The versatility, accuracy, and efficiency of the proposed method for free vibration analysis of thick rectangular and skew plates are tested against other solution procedures. It is revealed that the proposed method to handle the mixed natural boundary conditions is simple to use and can produce highly accurate solutions for the natural frequencies of thick rectangular and skew plates involving free edges.