MID-FREQUENCY RANGE ACOUSTIC RADIATION FROM SLENDER ELASTIC BODIES USING THE SURFACE VARIATIONAL PRINCIPLE

The surface variational principle (SVP) yields analytical-type results for radiation and scattering from submerged bodies whose shape does n ot suit classical techniques for analyzing the Helmholtz equation. The approach employs Ritz series expansions for surface pressure and velo city in the frequency domain. The relation between the series coeffici ents is obtained by extremizing the SVP functional. The present work e xtends the earlier developments to the case of an axisymmetric elastic shell that is subjected to an arbitrary excitation. The surface press ure and normal velocity are represented as a sequence of surface waves that are the trace of the waves in the surrounding fluid medium. SVP is used to determine the wavenumber spectrum of pressure amplitudes ge nerated by a specific wave having unit velocity amplitude. The structu ral displacement field is also represented by Ritz expansions, and equ ations governing the generalized coordinates associated with these ser ies are obtained by invoking Hamilton's principle. Difficulties in sat isfying the continuity conditions at the apexes are circumvented by se lecting basis functions that map spherical shell eigenmodes onto the s urface of the shell. The structural dynamic equations are coupled to t he SVP equations by matching the normal velocity in the fluid to the t ime derivative of the normal displacement, as well as using the series expansion for surface pressure to form the acoustic contribution to t he generalized forces. Results for a spherical shell subjected to a tr ansverse point force at the equator, which is a nonaxisymmetric repres entation of the excitation, are compared with analytic results. Predic tions for a long hemi-capped cylindrical shell in the mid-frequency ra nge are compared to those obtained from SARA-2D (Allik, 1991), which i s a finite/infinite element program. In addition to providing validati on of the SVP implementation, the cylinder example is used to illustra te the convergence and error measures provided by an SVP analysis.