Partition of Unity Finite Element Method applied to 2D vibroacoustic coupling

International audienceThe Finite Element Method is one of the most popular methods used to solve problems involving wave propagations. Yet, this method is computationally intensive as the number of wavelength increases in the domain of study. As an alternative, the Partition of Unity Finite Element Method (PUFEM) emerges as a promising method to tackle short-wave problems for both acoustics and vibration problems. The method is an extension of the classical Finite Element Method in which enrichment basis functions are added at nodes. This entails a reduction in the number of degrees of freedom in the model while maintaining its accuracy. In the present work, the PUFEM method is extended and applied to 2D vibroacoustic problems. The system under investigation consists of a Timoshenko beam coupled either with an enclosed acoustic cavity or an open semi-infinite acoustic medium. In both cases, propagating and evanescent wave functions are used as the enrichment basis for the beam and plane waves for the acoustic domain. Computational performances in terms of accuracy and model size are demonstrated through numerical analyses. It is shown that, in the short-wave domain, the method outperforms classical FEM, as evidenced by the highly satisfactory level of errors reached by using a very small number of degrees of freedom