Modeling phononic crystals
Résumé
Phononic crystals are artificial periodic structures that can alter efficiently the flow of sound, acoustic waves, or elastic waves. One of their most appealing property is the existence of complete bandgaps, or frequency ranges for which the propagation of waves is forbidden. They are best
characterized by their band structure, or the dispersion relation between frequency and wavenumber, often plotted in the first Brillouin zone of the crystal. In this talk, I will describe how Bloch waves and band structures can be obtained with finite element analysis, and discuss the
specific issues that this problem raises : Bloch wave equations, weak forms, the coupling of elastic and acoustic waves, loss and the complex band structure of evanescent Bloch waves. Some open problems will be introduced as well, especially with regards to the description of surface waves and leaky guided waves. The talk will be completed by a poster discussing the stochastic band structure, a method specially conceived to answer the latter types of problems.