Density of energy of a periodically unstuck elastic beam

In the present paper, a method to model a periodically stuck constrained el astic layer applied to a beam is proposed. The periodic distribution of the interface conditions enables one to use an homogenization technique. A sim plified homogenization method is presented, which relies on kinematic assum ptions on the shape of the displacement field in the beam. The potential an d kinetic energies are then calculated to carry out a finite element formul ation of the problem. Using the homogenized beam element, the first five na tural frequencies are computed. These are compared to a conventional finite element modelling. The two models are in good agreement. However, a tremen dous reduction of the number of degrees of freedom (d.o.f.) needed is achie ved using the homogenized finite element beam (63 d.o.f.), compared to the classical finite element model (1500 d.o.f.). (C) 2000 Academic Press.