Bistatic echoes from elastic bodies in the resonance scattering regime

The experimental technique that we described earlier [C. Y. Tsui et al., J. Acoust. Soc. Am. Suppl. 1 77, S79 (1985)] which extracts the active resonance spectrum of any scatterer from the echo it returns, was applied to solid elastic cylinders and to cylindrical shells of various thicknesses immersed in water. This technique consists in sampling the tailend of the returned pings, which contain the elastic (whispering gallery) resonances of the bodies, in order to isolate them from the (rigid) backgrounds they are usually mixed with. We now study various experimentally obtained differential scattering (bistatic) cross sections for the above mentioned objects. It is found that at certain resonance frequencies, the background-suppressed, bistatic cross section, which is a measure of the free-vibration target reradiation, ideally consists of a symmetric rosetta pattern, having twice the number of lobes as the modal order n of the body resonance being excited. Using theoretically computed plots of the actual spectral shapes of the body's individual modal resonances, we explain that the anomalous angular plots, which have more than 2n lobes, are caused by a superposition of several modes for which other broad modal resonances having wide tails, interfere with the chosen resonance frequency within the nth mode. Theory and experiment complement each other to elucidate the resulting aliasing effect.