Mouvements propres d'un système à 1 D.D.L. avec amortissement viscoélastique

In this note, one considers a 1-d.o.f. oscillator consisting of a mass and a viscoelastic spring, the rheology of which is represented by a generalized so-called Biot's model with 2n+1 parameters. It is proved that its n+2 independent eigenmotions are of the following nature: two eigenmotions damped with or without oscillations (as in the case of classical viscous damping) and n eigenmotions damped without oscillations which are induced by the viscoelastic rheology. To cite this article: P. Muller, C. R. Mecanique 333 (2005).