Doubly asymptotic approximations for transient motions of submerged structures

Doubly asymptotic approximations (DAA) are differential equations for simplified analysis of the transient interaction between a flexible structure and a surrounding infinite medium. These surface interaction approximations approach exactness in the limit of low- and high-frequency motions and effect a smooth transition in the intermediate frequency range. A finite-element DAA formulation for an acoustic medium is presented herein, with attention focused on the first and second members of the DAA hierarchy. The free-vibration and forced-response characteristics of the first and second approximations are examined through specialization to a spherical geometry.