Allan D. Pierce
Boston Univ., Dept. of Aerospace and Mech. Eng., 110 Cummington St., Boston, MA 02215
Waves propagating along ray paths on shells have various descriptors, such as the dispersion relation that connects frequency and the two principal wave-number components for each point on the surface. Other descriptors include polarization relations: complex ratios of amplitudes of quantities that oscillate under the influence of a propagating wave. Such oscillating quantities include the components of the displacement vector for points on the middle surface, the acoustic pressure at the external surface, and the locally-spatially-averaged passive forces exerted on the shell by the internal structure. Energy balance relations are also wave descriptors. Such descriptors are derivable directly from the equations of elasticity and fluid mechanics. In any frequency and wave-number regime (associated with the ranges of scales for the intended application) there are a limited number of possible waves types, but analogies with waves on flat plates are often not appropriate. The use of wave-based theory depends on whether the wavelength along the direction of propagation is somewhat smaller than the effective shell radius associated with that direction. It is not necessary for the frequency to be high and/or for the wavelength to be smaller than both of the principal radii of curvature. Radiation of sound into the fluid from waves traveling slower than the speed of sound is possible as long as there is some point above the surface at which the extrapolated phase velocity is supersonic; the explanation is analogous to why propellers with subsonic tip speeds radiate sound.