Uncoupling supersonic Lamb waves on plates and shells from the surrounding fluid: Approximate condition on the phase velocity.

Abstract

Lamb waves propagating with a phase velocity cl along a fluid-loaded plate or shell generally leak or radiate wavefronts at an angle determined by the trace velocity matching condition when cl exceeds the velocity of sound in the surrounding fluid. Ray representations of the backscattering by spherical and cylindrical shells show the leaky wave contributions are proportional to the radiation damping βl of the wave [S. G. Kargl and P. L. Marston, J. Acoust. Soc. Am. 89, 2545–2558 (1991); N. H. Sun and P. L. Marston, J. Acoust. Soc. Am. (accepted for publication)]. A curious numerical result is that for certain leaky rays, the function βl(ka) can exhibit a minimum where βl can be as small as 10−4 Np/rad and the associated resonances are very narrow. An approximate condition for such minima is evident by considering the particle displacement at the surface of a flat plate in a vacuum. It has been shown [D. C. Worlton, J. Appl. Phys. 32, 962–971 (1961)] that there is no normal displacement of the plate’s surface when the phase velocity of a Lamb wave equals the longitudinal wave speed cL of the material. In the present work it is shown that the radiation damping exactly vanishes at this condition for a flat plate with an unbounded fluid on one or both sides. Normal displacements are essential for radiation by curved shells so that βl should be minimized for cl≊cL. This condition was numerically verified. The phenomenon allows for the supersonic transport of mechanical energy with negligible sound production. [Work supported by ONR.]