Exponential stabilization of a neutrally delayed viscoelastic Timoshenko beam

Abstract

A Timoshenko type beam subject to a viscoelastic damping in the rotational displacement component isconsidered. Taking into account a neutral type delay, we prove a fast stability result despite the previously observeddestabilizing effect due to delays in such systems. The proof relies on the introduction of nine different functionals withwhich we modify the energy of the system. These functionals are carefully selected and adapted to cope with both theviscoelasticity and the neutral delay.