On the effects of damping on wave propagation in periodic vibro-acoustic meta-materials

In search for novel materials which combine lightweight characteristics with good acoustical behaviour, triggered by ecological and economic reasons, resonant meta-materials come to attention, be it at least in some targeted and tunable frequency ranges, referred to as stop bands. Meta-materials are defined as the general family of materials engineered to have specific properties, uncommon in nature, for dedicated applications. In this paper, an infinite periodic meta-material panel composed of unit cells with local resonators is discussed. The panel is designed to obtain stop band behaviour for bending waves in vibro-acoustic applications. As the panel is periodic, a single unit cell contains all essential information and the Bloch-Floquet theorem can be applied to reduce the computa-tional effort required to analyze its dispersion behaviour. More specifically, the effects of damping are investigated, since this can have an important influence on wave propagation. In order to capture both propagating and attenuated parts of waves, an alternative formulation of the Bloch-Floquet theorem is employed to scan the k-space (wavenumber) for a given frequency and evaluate the dispersion behaviour. Unlike the classic Bloch-Floquet approach, this approach captures complex wavenumbers as the governing equations are reformulated to form a quadratic eigenvalue problem with respect to wavenumber. This allows the investigation of the dispersion behaviour in the complex k-space providing more information on attenuating waves. The alternative formulation can also facilitate the analysis of structures with complex damping configurations allowing direct inclusion of damping in the constitutive law with a more detailed description. In addition, it reduces the computational effort required to analyze structures with frequency-dependent properties as the eigenvalue problem is solved for eigen-wavenumbers at discrete frequency steps. Finally, the dispersion behaviours of infinite structures with various levels of structural damping are compared to capture the effects of damping on wave propagation of such periodic meta-materials.status: accepte