The propagation and scattering of torsional wave sin circular rods of infinite length with a free surface that have an abrupt diameter change is discussed. A mode expansion technique involving propagating and cut-off modes is applied to obtain numerical results for a range of parameter values. The calculated results are compared with simplified models valid in the high- and low-frequency regions, respectively. The calculations show that higher radial modes have strong influence at higher frequencies. In particular, near the cut-off frequencies both amplitude and phase responses are strongly influenced. It is further found that the approximation accuracy results depend on the number of modes used in the modal expansion. It is demonstrated that in order to obtain an accuracy (as judged from convergence) that is sufficient for typical parameters chosen, all propagating modes plus a few cut-off modes should be included in the calculations.
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