A FEM–BEM coupling procedure to model the propagation of interacting acoustic–acoustic/acoustic–elastic waves through axisymmetric media

In the present work the propagation of waves through axisymmetric bodies is analysed, taking into account acoustic–acoustic/acoustic–elastic interacting media and coupled numerical methodologies. The boundary element method (BEM) is here employed to model acoustic media: its time convolution integrals are evaluated analytically and the theta method is adopted to advance the solution on time. The finite element method (FEM), on the other hand, models wave propagation through elastic and acoustic media, the Newmark Method being employed for time stepping. The FEM–BEM coupling is accomplished through an iterative process in which variables at common interfaces are updated until convergence is achieved. Thus, each sub-domain is analysed independently, so that the numerical algorithm can take full advantage of the favourable features of the different methods involved. Relaxation parameters, which are introduced in order to speed up and/or ensure convergence, and the possibility to consider different time steps within each sub-domain are two factors that improve substantially the efficiency, stability, accuracy and flexibility of the coupled analysis. The potentialities of the proposed procedures are illustrated through numerical examples presented at the end of the paper.