## 3aSAa6. Wave-number-based assessment of the doubly asymptotic approximation.

### Session: Wednesday Morning, May 15

### Time: 9:15

**Author: Jerry H. Ginsberg**

**Author: Kuangchung Wu**

**Location: G. W. Woodruff School of Mech. Eng., Georgia Inst. of Technol., Atlanta, GA 30332-0405**

**Abstract:**

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. Because
of a lack of analytical solutions for realistic geometries, prior validation
efforts have not provided definitive guidelines regarding the accuracy of the
method. The present work uses Nicholas--Vuillierme's derivation [Numerical
Techniques in Acoustic Radiation, edited by R. J. Bernhard and R. F. Keltie
(American Society of Mechanical Engineers, New York, 1989), Vol. 6, pp. 7--13]
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
development computes the wet surface impedance matrix relating surface pressure
and velocity variables over a broad frequency band according to two DAA versions
and the surface variational principle. The alternative wet surface impedances
are used to predict the frequency-domain structural response of the shell to a
point force, after which alternative time-domain responses are obtained from the
FFT algorithm. Results for wave-number amplitudes (azimuthal and meridional) are
reported for moderate and large aspect ratios. An overview indicates that a
higher-order DAA version occasionally works extremely well, but that there is no
consistent high/low trend as a function of wave number. [Work supported by the
Office of Naval Research, Code 1222.]

from ASA 131st Meeting, Indianapolis, May 1996