### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 4aPAa1. Waves and rays on fluid-immersed shells: Beyond spheres,
cylinders, Donnell, and Watson.

**Allan D. Pierce
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*Boston Univ., Dept. of Aerospace and Mech. Eng., 110 Cummington St.,
Boston, MA 02215
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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.