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.