Résumé
A dimension reduction problem is tackled using Trotter's theory of convergence of semi-groups of operators acting on variable spaces [1, 2]. We show that this framework makes it possible to perform the asymptotic analysis for both viscoelastic thin plates and slender beams in a unifying manner. Several models are provided for the dynamic behavior of such structures in bilateral contact with a rigid body on a part of their boundary with Norton or Tresca friction. It is shown that the relative energetic gap between the real displacement field in the structure and classical fields like Kirchhoff-Love or Reissner-Mindlin on the one hand, and Bernoulli-Navier or Timoshenko on the other, does not vanish when the thinness goes to zero.