Fast metamaterial design optimization using reduced order unit cell modeling

Abstract

Metamaterials have recently emerged and shown potential as lightweight and compact noise and vibration solutions. By adding or embedding resonant structures to or in a flexible host structure on a sub-wavelength scale, stop bands can be created, which enable frequency ranges of strong vibration and noise attenuation. These often periodic structures are typically analyzed using infinite periodic structure theory, based on a representative unit cell model. The stop bands in metamaterials are generally analyzed by means of dispersion curves. For complex unit cell models, however, this rapidly becomes computationally expensive. Therefore, in this work, model order reduction is applied to finite element unit cell models for stop band predictions. In view of designing metamaterials for a targeted frequency range, the reduced order modeling approach is next introduced in a design optimization routine. The results show that the reduced order models for stop band predictions enable substantial gains in metamaterial analysis and fast metamaterial design optimization.