Exponential stability and numerical simulation of a Bresse-Timoshenko system subject to a neutral delay

In the present work, we consider a one-dimensional Bresse-Timoshenko system with neutral delay term and a viscous damping acting on vertical displacement of the beam. Under appropriate assumptions on the kernel of this kind of delay and based on the multipliers method, we construct a suitable Lyapunov functional that allows us to establish an exponential decay of the energy in spite of the existence of the delay. Moreover, our result does not depend on any condition on the coefficients of the system. Finally, we present some numerical results to illustrate the theoretical result obtained.