DENSITY OF ENERGY OF A PERIODICALLY UNSTUCK ELASTIC BEAM

In the present paper, a method to model a periodically stuck constrained elastic layer applied to a beam is proposed. The periodic distribution of the interface conditions enables one to use an homogenization technique. A simplified homogenization method is presented, which relies on kinematic assumptions on the shape of the displacement field in the beam. The potential and kinetic energies are then calculated to carry out a finite element formulation of the problem. Using the homogenized beam element, the first five natural frequencies are computed. These are compared to a conventional finite element modelling. The two models are in good agreement. However, a tremendous reduction of the number of degrees of freedom (d.o.f.) needed is achieved using the homogenized finite element beam (63 d.o.f.), compared to the classical finite element model (1500 d.o.f.).