Floquet-Bloch decomposition for the computation of dispersion of two-dimensional periodic, damped mechanical systems

Manuel Collet (1) , Morvan Ouisse (1) , Massimo Ruzzene (2) , Mohamed Ichchou (3)

1 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
2 Georgia Institute of Technology [Atlanta]
3 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes

Floquet–Bloch theorem is widely applied for computing the dispersion properties of periodic structures, and for estimating their wave modes and group velocities. The theorem allows reducing computational costs through modeling of a representative cell, while providing a rigorous and well-posed spectral problem representing wave dispersion in undamped media. Most studies employ the Floquet–Bloch approach for the analysis of undamped systems, or for systems with simple damping models such as viscous or proportional damping. In this paper, an alternative formulation is proposed whereby wave heading and frequency are used to scan the k-space and estimate the dispersion properties. The considered approach lends itself to the analysis of periodic structures with complex damping configurations, resulting for example from active control schemes, the presence of damping materials, or the use of shunted piezoelectric patches. Examples on waveguides with various levels of damping illustrate the performance and the characteristics of the proposed approach, and provide insights into the properties of the obtained eigensolutions.

Mots clés: Waves; Bloch theorem; Damping; Mid-frequency

Domaines: Sciences de l'ingénieur [physics]

Manuel Collet, Morvan Ouisse, Massimo Ruzzene, Mohamed Ichchou. Floquet-Bloch decomposition for the computation of dispersion of two-dimensional periodic, damped mechanical systems. International Journal of Solids and Structures, 2011, 48, pp.2837-2848. ⟨10.1016/j.ijsolstr.2011.06.002⟩. ⟨hal-01516397⟩