Comparison of discrete singular convolution and generalized differential quadrature for the vibration analysis of rectangular plates

Abstract

This paper presents a comprehensive comparison study between the discrete singular convolution (DSC) and the well-known global method of generalized differential quadrature (GDQ) for vibration analysis so as to enhance the understanding of the DSC algorithm. The DSC method is implemented through Lagrange's delta sequence kernel (DSC-LK), which utilizes local Lagrange polynomials to calculate weighting coefficients, whereas, the GDQ requires global ones. Moreover, it is shown that the treatments of boundary conditions and the use of grid systems are different in the two methods. Comparison study is carried out on 21 rectangular plates of different combinations of simply supported (S), clamped (C) and transversely supported with nonuniform elastic rotational restraint (E) edges, and five rectangular plates of mixed supporting edges, some of which with a range of aspect ratios and rotational spring coefficients. All the results of the DSC-LK agree very well with both those in the literature and newly computed GDQ results. Furthermore, it is observed that the DSC-LK performs much better for plates vibrating at higher-order eigenfrequencies. Unlike the GDQ, the DSC-LK is numerically stable for problems which require a large number of grid points.