%A Andrea Bacigalupo
%A Luigi Gambarotta
%D 2017
%K Lattice metamaterials; inertial resonators; viscoelasticity; dispersive waves; Lagrangian model; generalized micropolar model
%L eprints3786
%X The present paper is focused on the acoustic behaviour of periodic beam-lattices metamaterials containing inertial viscoelastic resonators connected with elastic slender ligaments. A simplified model is considered where the ligaments are considered as massless and the viscoelastic resonators are contained inside rigid rings located at the lattice nodes. Firstly, a Lagrangian model is formulated in order to assess the influence of the dynamic and viscoelastic properties of the resonators on the acoustic behaviour. An equivalent generalized micropolar model is obtained through a continualization of the discrete model and the constitutive tensors and the equation of motion are formulated. The propagation of harmonic waves is assumed and the Christoffel equation for both the discrete and the continuum model are obtained. It is shown that the hermitian matrix governing the Christoffel equation of the Lagrangian model is approximated by the corresponding one from the micropolar model with an error O (|k|3)
%I Elsevier
%V 199
%O Proceedings of the X International Conference on Structural Dynamics, EURODYN 2017, Rome 10-13 September, 2017
%P 1441-1446
%J Procedia Engineering
%R doi:10.1016/j.proeng.2017.09.374
%T Damped Bloch Waves in Lattices Metamaterials with Inertial Resonators