Acoustic coupling to membrane waves on elastic shells

The interaction of an acoustic field with a smooth thin shell in a fluid is described by the superposition ofa background field plus membrane waves on the shell. The former is defined by a local impedance condition, which accounts for the inertia of the shell, but takes no account of the in-surface, membrane effects. The shell's flexural stiffness tums out to be of secondary importance. The bulk of the paper deals with the coupling mechanism between the acoustic field and the supersonic membrane waves, both longitudinal and shear. 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 ubject o 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.