Modeling and justification of an eigenvalue problem for a plate inserted in a three-dimensional support

Modeling the vibrations of a multi-rod structure

“…The method used consists in scaling each structure independently of the other, 892 N. KERDID passing then to the limit in the variational équations posed over domains independent of the thickness of different structures and finally identifying this limit. This idea was later used to study different problems of junctions in three-dimensional elasticity: Gruais ([12], [13]) for the static case, Kerdid [16] and Lods [23] for the eigenvalue problem and Le Dret [21], Raoult [24] for elastodynamics problems. For the numerical analysis of junctions between rods and plates see Bernadou Fayolle & Léné [3] and Fayolle [10].…”