Complex-Eigenfrequency Band Structure of Viscoelastic Phononic Crystals

Tingting Wang (1) , Vincent Laude (2) , Muamer Kadic (2) , Yan Wang (1) , Yue Wang (1)

1 BJTU - Beijing Jiaotong University
2 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)

The consideration of material losses in phononic crystals leads naturally to the introduction of complex valued eigenwavevectors or eigenfrequencies representing the attenuation \textcolor{blue}{of elastic waves} in space or in time, respectively. Here, we propose a new technique to obtain \textcolor{blue}{phononic} band structures with complex eigenfrequencies but real wavevectors, in the case of viscoelastic materials, whenever elastic losses are proportional to frequency. Complex-eigenfrequency band structures are obtained for a sonic crystal in air, and steel/epoxy and silicon/void phononic crystals, with realistic viscous losses taken into account. It is further found that the imaginary part of eigenfrequencies are well predicted by perturbation theory and are mostly independent of periodicity, i.e. they do not account for propagation losses but for temporal damping of Bloch waves.

Domaines: Acoustique [physics.class-ph]; Matériaux; Micro et nanotechnologies/Microélectronique

Tingting Wang, Vincent Laude, Muamer Kadic, Yan Wang, Yue Wang. Complex-Eigenfrequency Band Structure of Viscoelastic Phononic Crystals. Applied Sciences, 2019, 9 (14), pp.2825 (11). ⟨hal-02300035⟩