Non uniform stability for the Timoshenko beam with tip load

Denis Mercier (1) , Virginie Régnier (1)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

In this paper we consider a hybrid elastic model consisting of a Timoshenko beam and a tip load at the free end of the beam. Under the equal speed wave propagation condition, we show polynomial decay for the model which includes the rotary inertia of the tip load when feedback boundary moment and force controls are applied at the point of contact between the beam and the tip load.

Mots clés: Timoshenko system; exponential and polynomial stability; locally distributed feedback

Domaines: Equations aux dérivées partielles [math.AP]; Mathématiques [math]

Denis Mercier, Virginie Régnier. Non uniform stability for the Timoshenko beam with tip load. 2015. ⟨hal-01170359⟩