A numerical technique for two‐dimensional transient wave propagation analyses

Abstract

Abstract A numerical technique is proposed for solving two‐dimensional transient wave propagation problems. The technique involves the use of the combination of a transform (such as Fourier, sine, cosine) for one space variable and the method of characteristics. Because of its inclusion of the latter method in the analysis, the proposed technique is capable of describing the sharp variations of the disturbances which may occur in the neighbourhood of wave fronts. In the study, an example problem is presented which involves transient waves in an elastic layer generated by out‐ofplane shear stresses acting on its top surface. The formulation of the example problem is kept general in the sense that the variations of the applied shear tractions in the horizontal direction of the layer and in time are kept arbitrary. In the analysis, the Fourier transform is used for the horizontal co‐ordinate. The numerical results are obtained and presented for the uniform strip loading case. The assessment of the proposed technique is made by obtaining the results for the case in which the width of the strip load is very large compared to the height of the layer, and by comparing them with exact ones. It is found that the proposed technique yields the results which compare very well with the exact ones and that it is capable of describing the sharp variations at the wave fronts.