Discrete singular convolution and Taylor series expansion method for free vibration analysis of beams and rectangular plates with free boundaries

Abstract

Since the excellent performance of the discrete singular convolution (DSC) for high order frequency analysis has not been demonstrated for rectangular plates with free edges and corners thus far, this paper proposes a novel approach in applying the DSC for vibration analysis of beams and rectangular plates with arbitrary boundary conditions. The Taylor series expansion method is used to apply the boundary conditions. The existing difficulty encountered at plate corner points is overcome by the proposed method. The essential idea of the novel method is that two Taylor series expansions with different orders are used to eliminate the fictitious points outside the physical domain. Various beam and rectangular plate problems are solved by the proposed DSC and the results are compared with exact solutions, finite element data and results obtained by the differential quadrature method (DQM) using much higher number of grid points. It is demonstrated that the Taylor series expansion method to apply the boundary conditions is general and accurate. It is also found that the performance of the proposed DSC is excellent and independent of boundary conditions.