Attenuation prediction in 1D waveguides using locally resonant metamaterials

Metamaterials are generally assemblies of conventional materials, engineered to have properties that are not conventional. The addition of resonant structures to a host structure on a subwavelength scale generates Fano-type interference in targeted frequency zones resulting in stop bands. In these stop bands waves cannot freely propagate, and vibration is attenuated. Consequently, metamaterials come as a possible solution for noise and vibration problems. In this paper a method is adapted to model a 1D metamaterial waveguide as a semi-infinite structure using a unit cell modelling approach to predict the level of attenuation in those stop bands after a certain number of unit cells. In order to reduce the computational time, model reduction is implemented. The numerical results of this unit cell based attenuation prediction with model reduction are compared to measurements for three different metamaterial configurations. A good agreement is obtained, especially inside the zone of attenuation.