### ASA 127th Meeting M.I.T. 1994 June 6-10

## 4pSAa4. Extension of the surface variational principle to nonaxisymmetric
response of submerged thin shells of revolution.

**Jerry H. Ginsberg
**

**
Kuangcheng Wu
**

**
**
*School of Mech. Eng., Georgia Inst. of Technol., Atlanta, GA 30332
*

*
*
Previously, the surface variational principle (SVP) was implemented for
rigid and elastic submerged structures under axisymmetric excitations. More
recent developments extended SVP to address nonaxisymmetric problems of
acoustic radiation and scattering situations for rigid bodies of revolution. In
this presentation, SVP is applied jointly with Hamilton's principle governing
nonaxisymmetric responses of elastic thin shells of revolution. Complex Fourier
expansions of the azimuthal dependence are combined with Ritz expansions of the
spatial dependence to represent the displacement field and surface pressure.
This representation is equivalent to a wave-number decomposition of the surface
response into a series of helical-type waves. By enforcing continuity of normal
velocity on the fluid--structure interface, a set of coupled algebraic
equations is formed for each azimuthal harmonic. Problems addressed here are
radiation due to arbitrary loading, and scattering associated with arbitrary
incidence of a plane wave on a stationary elastic thin shell. The rigid body
modes are included in the scattering case. Numerical results are assessed for
the convergence qualities of an SVP simulation, particularly regarding series
length requirement as the frequency is increased. [Work support by ONR.]