Scattering of plane evanescent waves by cylindrical shells and wave vector coupling conditions for exciting flexural waves

Abstract

The coupling of sound to buried targets can be associated with acoustic evanescent waves when the sea bottom is smooth. To understand the excitation of flexural waves on buried shells by acoustic evanescent waves, the partial wave series for the scattering is found for cylindrical shells at normal incidence in an unbounded medium. The formulation uses the simplifications of thin-shell dynamics. In the case of ordinary waves incident on a shell, a ray formulation is available to describe the coupling to subsonic flexural waves [P. L. Marston and N. H. Sun, J. Acoust. Soc. Am. 97, 777–783 (1995)]. When the incident wave is evanescent, the distance between propagating plane wavefronts is smaller than the ordinary acoustical wavelength at the same frequency and the coupling condition for the excitation of flexural waves on shells or plates is modified. Instead of matching the flexural wave number with the propagating part of the acoustic wave number only at the coincidence frequency, a second low-frequency wave number matching condition is found for highly evanescent waves. Numerical evaluation of the modified partial-wave-series appropriate for an evanescent wave is used to investigate the low-frequency coupling of evanescent waves with flexural wave resonances of shells.