Vibration analysis of stepped rectangular plates by the discrete singular convolution algorithm

Abstract

A novel scheme in using discrete singular convolution (DSC) algorithm is proposed for analyzing the challenging vibration problem of thin plates with geometric discontinuity . An n th-order interpolation polynomial is employed on each side of a step. Then two jump conditions together with two continuous conditions at the step are established to correlate the two polynomials. Detailed formulations and solution procedures are given. Several numerical examples are analyzed to demonstrate the applicability of the proposed method to the free vibration analysis of the stepped rectangular plates . Results obtained by the modified DSC are compared with existing solutions to verify the proposed method. For lower order mode frequencies, DSC results agree well with existing analytical and numerical solutions or data obtained by the finite element method (FEM). Besides, the DSC can also yield relatively accurate frequencies for higher order modes. This research extends the application range of the DSC method. • A modified DSC is presented for analyzing vibration of stepped rectangular plates. • Jumped conditions at the step are enforced using the interpolation method. • The ability of the modified DSC to obtain accurate higher order frequencies is demonstrated.