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Article Dans Une Revue Journal of Sound and Vibration Année : 2020

Superelement modelling of elastic metamaterials: Complex dispersive properties of three-dimensional structured beams and plates

Résumé

In this article, we offer a fast calculation method for the dispersive properties of three-dimensional micro-structured solids with one-dimensional and two-dimensional translation symmetry. We review mathematical methods to obtain the complex dispersion diagram for such structures (i.e. the Bloch vector as a function of frequency). This can be done by solving a Bloch-Floquet eigenvalue problem which is non-linear in the Bloch vector. Such a problem inevitably calls for reduction methods as the required number of degrees of freedom of the unit cell increases. Therefore, an asymptotic-in-frequency technique is implemented in order to approximate the dynamic stiffness matrix of the unit cell. This is done by identifying and retaining the most significant nodal degrees-of-freedom, which are used to generate a unit cell "superelement". The accuracy of the Bloch vectors and corresponding eigenvectors asso-ciated with the reduced non-linear eigenvalue problem is demonstrated by direct comparison to full-size computations and shows excellent agreement combined with considerable computing time reduction and controllable limitations.

Domaines

Matériaux
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Origine : Publication financée par une institution

Dates et versions

hal-03321536 , version 1 (17-08-2021)

Licence

Paternité - Pas d'utilisation commerciale - Pas de modification

Identifiants

Citer

Domenico Tallarico, Gwenael Hannema, M. Miniaci, Andrea Bergamini, Armin Zemp, et al.. Superelement modelling of elastic metamaterials: Complex dispersive properties of three-dimensional structured beams and plates. Journal of Sound and Vibration, 2020, 484, pp.115499. ⟨10.1016/j.jsv.2020.115499⟩. ⟨hal-03321536⟩
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