The discrete singular convolution for analyses of elastic wave propagations in one-dimensional structures

In this paper, the problem of wave propagations in one-dimensional (1D) structures is investigated for the first time by using the discrete singular convolution (DSC), a relatively new and promising numerical approach. For simplicity, the non-regularized Lagrange’s delta sequence kernel is adopted in the DSC for most cases. For comparisons, the Regularized Shannon’s delta kernel is also adopted in the DSC for two cases. Methods for applying the free boundary conditions, concentrated loads and concentrated masses are proposed and validated. Detailed formulations and solution procedures are given. Travelling waves in an isotropic aluminum bar and Timoshenko beam are studied. A high degree of accuracy in simulations by the DSC is observed. Numerical results are compared to those obtained from the spectral finite element (SFE) approach, proved a very efficient method in modeling elastic wave propagations. The comparison highlights the efficiency of the DSC in modeling elastic wave propagations. The present research extends the application range of the discrete singular convolution to problems of elastic wave propagations.