K. Wu et Jh. Ginsberg, MID-FREQUENCY RANGE ACOUSTIC RADIATION FROM SLENDER ELASTIC BODIES USING THE SURFACE VARIATIONAL PRINCIPLE, Journal of vibration and acoustics, 120(2), 1998, pp. 392-400
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.