The rate at which energy decays in a viscously damped hinged Euler-Bernoulli beam.

Kais Ammari (1) , Mouez Dimassi (2) , Maher Zerzeri (3)

1 FSM - Faculté des Sciences de Monastir
2 IMB - Institut de Mathématiques de Bordeaux
3 LAGA - Laboratoire Analyse, Géométrie et Applications

We study the best decay rate of the solutions of a damped Euler-Bernoulli beam equation with a homogeneous Dirichlet boundary conditions. We show that the fastest decay rate is given by the supremum of the real part of the spectrum of the infinitesimal generator of the underlying semigroup, if the damping coefficient is in $L^\infty(0,1)$.

Mots clés: Riesz Basis.; Riesz Basis; Rate of Decay; Euler-Bernoulli beam; Spectral Abscissa

Domaines: Equations aux dérivées partielles [math.AP]

Kais Ammari, Mouez Dimassi, Maher Zerzeri. The rate at which energy decays in a viscously damped hinged Euler-Bernoulli beam.. Journal of Differential Equations, 2014, 257 (9), pp.3501-3520. ⟨10.1016/j.jde.2014.06.020⟩. ⟨hal-01018783⟩