### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 5aSA2. Frequency domain assessment of the doubly asymptotic approximation.

**Jerry H. Ginsberg
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*School of Mech. Eng., Georgia Inst. of Technol., Atlanta, GA 30332-0405
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The most widely implemented technique for modeling fluid--structure
interaction effects associated with shock response is the doubly asymptotic
approximation (DAA), which has been developed in a variety of versions.
Analytical validations of this method have thus far only been performed for
spherical and infinitely long cylindrical shells. The present work uses
Nicholas-Vuillierme's derivation [Numerical Techniques in Acoustic Radiation,
edited by R. J. Bernhard and R. F. Keltie (ASME-NCA, Vol. 6, 7--13 1989)] of
the frequency-domain version of DAA as the basis for examining the accuracy and
limitations of DAA for a slender hemi-capped cylindrical shell. The basic
concept is to use DAA to determine the wet surface impedance matrix relating
surface pressure and velocity variables, whose values are compared to those
obtained from the surface variational principle (SVP) using the same set of
basis functions. After such comparison is made, the alternative wet surface
impedances are used to predict the structural response of the hemi-capped
cylindrical shell to a ring force. Assessments for frequencies in the range
ka<10 for a shell whose length to diameter ratio is L/2a=6 indicate that DAA
fails to recognize effects associated with transition from supersonic to
subsonic structural waves. The implications of this shortcoming for structural
response are discussed. [Work supported by the Office of Naval Research, Code
1222.]