Comparison study of discrete singular convolution and three other traditional numerical methods for the free vibration analysis of non-prismatic shafts

In this paper, the free torsional vibration of non-prismatic shafts is investigated. The governing equation for this problem is a nonlinear equation, so there is no general analytical solution for the problem. Using numerical techniques is efficient in such circumstances. There is a wide range of numerical methods which each one has some abilities and benefits. So, choosing the proper numerical method is important in the solution procedure. In this paper, the discrete singular convolution (DSC) which is a relatively novel numerical approach is applied for the first time. A comprehensive comparison study is carried out between the DSC and three other traditional numerical approaches, i.e. finite element (FE), second order finite difference (FD 2nd) and differential quadrature (DQ). The convergence, ability and efficiency of the DSC are evaluated in comparison with three other methods by solving several examples. The results indicate the efficiency of each method and beneficial conclusions are given for choosing the proper method in solving torsional vibration analysis of non-prismatic shafts.

Keywords:

Discrete singular convolution , Numerical analysis , Shaft , Non-prismatic , Torsional vibration