An efficient computational technique for 3D vibro-acoustic thanks to the VTCR

The Variational Theory of Complex Rays (VTCR) is a wave computational approach which was proposed for the resolution of medium frequency problems. It uses a variational formulation of the problem which enables one to use any type of shape function within the substructures provided that it verifies the governing equation. Thus, the solution can be approximated using plane waves, which is very interesting in the medium-frequency vibration domain and also leads to an exponential convergence of the method. In this paper, the VTCR is extended to the analysis of the steady-state dynamic 3D coupled vibro-acoustic problems in the mid-frequency range. It uses a specific dedicated variational formulation and a representation of the amplitude of the waves through a Fourier series (2D problems) or a Laplace series (3D problems). An illustration on a 3D vibro-acoustic example and its comparison with a FEM analysis will show the efficiency of a such an approach.