Multi-mode propagation and diffusion in structures through finite elements

The present work addresses the question of guided wave properties in structures. Guided multi-modal dispersion curves and diffusion of waves at singularities are the main concern. A propagative approach, based on a finite element model, is formulated. It provides an effective way to calculate the dispersion curves of complex guided structures. Some properties of guided waves are deduced from the formulation. The question of wave diffusion at substructures coupling locations is also considered. A closed formulation of the problem using Lagrange multipliers is presented. Its numerical implementation is detailed. Ultimately, a numerical test is offered. The case study concerns a thin walled structure.