Bloch Waves in an Infinite, Periodically-perforated SheetW. Maysenhölder
Fraunhofer Institute for Building Physics, Stuttgart, Germany
Bloch waves in infinite periodic structures – much in vogue in the present metamaterial age – can be conveniently studied by COMSOL Multiphysics® software. This is demonstrated by a simple, yet rich two-dimensional example: a perforated sheet with square symmetry. Instead of plane waves in homogeneous media, one has to deal with their generalizations: the Bloch waves. The frequencies of such Bloch waves are obtained from the solutions of an eigenvalue problem with prescribed wave vector resulting in dispersion relations. Thanks to two theorems related to the energy of elastic Bloch waves, the numerical accuracy of some unit-cell averages may be checked, though the physical interpretation for higher frequencies becomes more complex. COMSOL® offers a valuable and powerful tool for investigating periodic structures in a wide range of frequencies. In particular, detailed consideration of the energy aspect might open new perspectives, also and especially for metamaterial research.