DSC-Ritz method for the free vibration analysis of Mindlin plates

HOU YUNSHAN

Publication

DSC-Ritz method for the free vibration analysis of Mindlin plates

HOU YUNSHAN

Abstract

This thesis introduces a novel method for the free vibration analysis of Mindlin plates. The proposed method takes the advantage of the discrete singular convolution (DSC) local basis and the pb-2-Ritz boundary function to arrive at a new approach, called DSC-Ritz method. Two basis functions are constructed by using DSC delta sequence kernels of the positive type. The energy functional of the Mindlin plate is represented by the newly constructed basis function and is minimized under the Ritz variational principle. Extensive numerical experiments are conducted on different combinations of boundary conditions of Mindlin plates of rectangular and triangular shapes. The performance of the proposed method is carefully validated by convergence analysis. Numerical results indicate that the proposed DSC-Ritz method is a very efficient and accurate new method for vibration analysis of Mindlin plates