Jerry H. Ginsberg
School of Mech. Eng., Georgia Inst. of Technol., Atlanta, GA 30332-0405
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.]