An Efficient Use of the Symbolic Spline-based Differential Quadrature Method in Vibration Analysis of Shells

The paper presents the differential quadrature method (DQM) based on a modified spline interpolation and the application of the method in vibration analysis of laminated, composite shells. The goal of the modification of the spline interpolation is to improve the rate of convergence and preserve the stability of the method. The modification changes the definition of the end conditions for the spline interpolation. Two types of the end conditions are combined and appropriately applied at the stage of the determination of the weighting coefficients for the DQM. With the aid of the symbolic computation the weighting coefficients can be successfully determined for any spline degree. The efficiency of the method is examined by the example of the free vibration of composite, conical shells. The influence of the modified end conditions, number of nodes and spline degree on the convergence and accuracy is studied. The achieved results are compared with the results obtained using conventional DQM and using other numerical techniques.