Surface Wave Modes on Spherical Cavities Excited by Incident Ultrasound

Abstract

It has been shown both experimentally and theoretically1 that ultrasonic waves propagate circumferentially around the surface of cavities in an elastic medium, besides being reflected from its “flash points”. Surface wave returns were seen to decisively influence the time structure of the echo return from incident ultrasonic pulses. Nagase2 has solved a characteristic equation applicable to the spherical cavity problem, from which it could be shown3 that the surface of a spherical cavity supports a Rayleigh-type and two (P and S) Franz-type surface waves, of known speeds and dispersions. On the other hand, the complex eigenfrequencies of cavities were recently obtained numerically4. We have used these numerical results in order to satisfy Nagase’s solutions, presented in the form of propagation constants of the surface waves as series of fractional powers of the frequency, and have obtained in this way a mode number assignment for all the complex eigenfrequencies. Using this, we calculate dispersion curves for the Rayleigh, P and S- type surface wave phase velocities; their knowledge will permit an accurate interpretation of ultrasonic scattering experiments1, which previously could be analyzed in a qualitative way only.KeywordsDispersion CurveRayleigh WavePropagation ConstantPhase MatchSpherical CavityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.