Modal Analysis of a Multi-Supported Beam: Macroscopic Models and Boundary Conditions - Ecole Nationale des Travaux Publics de l'Etat Accéder directement au contenu
Article Dans Une Revue Mathematics Année : 2024

Modal Analysis of a Multi-Supported Beam: Macroscopic Models and Boundary Conditions

Résumé

This paper deals with the long-wavelength behaviour of a Euler beam periodically supported by co-located rotation and compression springs. An asymptotic homogenization method is applied to derive the several macroscopic models according to the stiffness contrasts between the elastic supports and the beam. Effective models of differential order two or four are obtained, which can be merged into a single unified model whose dispersion relations at long and medium wavelengths fit those derived by Floquet-Bloch. Moreover, the essential role of rotation supports is clearly evidenced. A mixed “discrete/continuous” approach to the boundary conditions is proposed, which allows the boundary conditions actually applied at the local scale to be expressed in terms of Robin-type boundary conditions on macroscopic variables. This approach can be applied to both dominant-order and higher-order models. The modal analysis performed with these boundary conditions and the homogenised models gives results in good agreement with a full finite element calculation, with great economy of numerical resources.
Fichier principal
Vignette du fichier
mathematics-12-01844-v2.pdf (1.4 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
licence

Dates et versions

hal-04625202 , version 1 (26-06-2024)

Licence

Identifiants

Citer

Antoine Rallu, Claude Boutin. Modal Analysis of a Multi-Supported Beam: Macroscopic Models and Boundary Conditions. Mathematics , 2024, 12 (12), pp.1844. ⟨10.3390/math12121844⟩. ⟨hal-04625202⟩
0 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More