(A) study on approximation models for acoustic - structure interactions in exterior problems

Abstract

Improved approximate models for external acoustic field interacting with flexible structures are developed. The basic form of the proposed models is obtained by a combination of the Laplace-transformed retarded and advanced potentials with the weighting parameter as part of the model equation. It is shown that the maximum attainable time-derivative of convergent approximate models is two, hence any attempt to include higher orders will lead to non-convergent models. First, the proposed model is theoretically compared to the analytic solution and the classical models of the first-order and second-order Doubly Asymptotic Approximations ($DAA_1$ and $DAA_2$) using modal equations for a sphere. Second, transient responses of submerged spherical and cylindrical shells subjected to a series of incident waves are performed using the proposed second-order boundary-element pressure equation. To evaluate its performance, the results calculated by the proposed model are compared with the classical analytical solutions and the Doubly Asymptotic Approximations(DAAs)`s results. Finally, through the application to a complex submerged structure, the possibility for general applications of our approximation is shown. The results show that proposed model offers improved accuracy especially for early time responses, exhibits computational robustness, and maintains the desirable consistency in its impulse response functions. Hence, our proposing model can be recommended as a candidate model equation for system realization involving acoustic-structure interactions.