Prediction of pulse dispersion in tapered waveguides

In this work, we propose a procedure to predict the group delay of stress waves propagating in tapered waveguides. The group delay is numerically calculated as a summation of group delays that the wave ideally experiences propagating in a sequence of waveguides with uniform cross-section. The procedure is applied to longitudinal waves propagating in tapered steel rods and to symmetric Lamb-type waves propagating in aluminum tapered plates. The method is validated by comparing the calculated group delay with that extracted from time transient signals, artificially generated by finite element simulations, processed with the short time Fourier transform. Results show that the proposed procedure well captures the dispersive spectro-temporal behavior of guided waves in uniformly tapered waveguides, and that it can also be applied to waveguides with stepped and triangular profiles.