Riou H., Ladeveze P.

Today, the calculation of medium-frequency vibrations is a key element in the design of aerospace structures and constitutes a true industrial challenge. All major numerical modeling techniques are based on finite element or boundary element approaches. But in order to account for small-wavelength phenomena in complex structures (such as car chassis, satellites or ships), these techniques require huge numbers of degrees of freedom. Furthermore, the solutions obtained are highly sensitive to material properties and boundary conditions. Different approaches, such as enhanced finite elements or specific reduced bases, have been investigated in order to solve such problems, but most of these techniques require specific geometries or large numbers of degrees of freedom in order to yield predictive results. High-frequency approaches, such as Statistical Energy Analysis or any of its improved variations, do not appear to be suitable for medium-frequency vibrations: the resulting vibrational behavior is too smooth and, in general, the coupling loss factor cannot be calculated in a predictive way. The Variational Theory of Complex Rays (VTCR) is a predictive computational tool for dealing with medium-frequency vibro-acoustic problems. It uses propagative and evanescent waves (which are solutions of the homogeneous partial differential equation to be solved) as shape functions. These waves are two-scale functions (amplitude and phase) and the VTCR is based on a specific treatment of these two scales, as only the slowly varying scale (amplitude) is discretized. The boundary and interface conditions between substructures are weakly enforced using a variational formulation. The performance of the VTCR for vibro-acoustic 2D and 3D problems will be assessed.