The Fourier version of the Variational Theory of Complex Rays for medium-frequency acoustics

The Variational Theory of Complex Rays (VTCR) is a wave-based computational approach dedicated to 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 satisfies 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 a strong convergence of the method. In the previous works, this was shown in the case of acoustic problems in which the amplitudes of the plane waves were calculated as wavebands. In this paper, we propose a new approximation of these amplitudes based on Fourier series. We show that this approach increases the robustness of the method, makes it more efficient numerically and extends its applicability to somewhat higher frequencies.