Abstract
This paper presents a numerical method, the BF-spline Ritz method, for free vibration analysis of rectangular Mindlin plates with arbitrary boundary conditions. The proposed method utilizes admissible functions comprising the B-spline functions multiplied by a boundary function to define the Ritz trial function for the transverse displacement and rotations of the Mindlin plates. The geometric boundary conditions of the plate at edges are automatically satisfied using boundary functions. To demonstrate the validity and accuracy of the BF-spline Ritz method, several examples are solved, and results are compared with those obtained by exact and other numerical methods. Excellent convergence and high accuracy are obtained by the present method regardless of arbitrary boundary conditions. The effects of thickness-width ratio, aspect ratio and boundary conditions on frequency parameters of rectangular Mindlin plates are shown in tabular forms to serve as benchmark data for future development of new numerical methods.
