Extension of the variational theory of complex rays to the coupling between thin structure and acoustic cavities

The variational theory of complex rays is an alternative to classical methods, such as finite elements or statistical analysis, for studying dynamics in the mid-frequency range. The VTCR is part of the Trefftz methods, and its use of plane waves to reconstruct system response makes it very computationally efficient. This paper presents an extension of 2D acoustics VTCR to coupling with thin structures. Our approach takes advantage of the acoustic shape functions by directly expressing structural displacement in terms of acoustic unknowns. After presenting the mathematical aspects, the method is validated on an analytical case. Then it is compared with finite elements in a transmission case. Finally, we apply the method to a half-wall, for which the finite elements exhibit a singularity at the tip.