Doubly asymptotic approximations as non-reflecting boundaries in fluid-structure interaction problems

Abstract Acoustic approximations are differential relations between induced fluid pressure and velocity in an acoustic medium. The plane wave approximation (PWA) is valid for high frequency response while doubly asymptotic approximations (DAA) are valid at very high and very low frequencies and, in advanced versions, at selected intermediate frequencies. These relations have been applied extensively on the wet surface of submerged structures to completely uncouple the equations of motion of the structure from those of the surrounding fluid. If DAA are used, a different virtual mass matrix and, in the advanced versions, fitting matrices must be evaluated for each structural geometry. In this paper, the approximations are used on a fluid surface which encloses the structure and has a geometry for which virtual mass and fitting matrices are known. The response is obtained by solving numerically the coupled fluid-structure equations within this approximation to a non-reflecting boundary. A numerical example of the dynamic response of a spheroidal shell is solved using a sphere as the absorbing boundary and the response obtained is compared to exact results.