Andrew Norris Douglas Rebinsky
Dept. of Mech. & Aerosp. Eng., Rutgers Univ., P.O. Box 909, Piscataway, NJ 08855-0909
The interaction of an acoustic wave with a smooth thin shell in a fluid is considered. The coupling mechanism between the acoustic field and the supersonic membrane waves, both longitudinal and shear, is discussed in detail. The coupling is mediated by the shell curvature, and vanishes when the curvature vanishes. Ray methods are used to express the membrane waves by curved wave fronts with amplitudes subject to a transport equation over the curved shell surface. The coupling, and decoupling or launching, then reduces to solving an ordinary differential equation for the unknown ray amplitude. In essence, the transport equation is forced, or ``beaten'' by the locally phase-matched background field. Explicit expressions are obtained for the coupling and detachment coefficients on arbitrarily curved regions. These are combined, using ray theory for the propagation over the shell, to give the scattered field due to rays traveling over the shell. The general results are explicitly tested on the cylinder and sphere, for which the ensemble of surface rays can be summed into a resonance form, and numerical comparisons are made with the exact results for these canonical geometries. [Work supported by ONR.]