Diagnostics Figure 1

Figure 1. Illustration of linear versus nonlinear wave resonance behavior in a bell. In (a), the bell behaves in an expected manner when intact. We ring the bell with a hammer and excite the resonance modes of the bell. The inset at top, right, shows the frequency spectrum of the bell (that is, at what frequencies we have energy present) illustrating that only the resonance modes are present. In (b) we see that if the bell has even a very small crack present, the modal frequencies depend on how hard we strike the bell. Thus, in the frequency spectrum associated with the damaged bell (bottom right), we see that the modal frequencies depend on how hard we strike the bell. This is a nonlinear effect: a change in wave frequency with wave amplitude. We call this method Nonlinear Resonant Ultrasound Spectroscopy (NRUS), a subset of NEWS.