Uniform stability of a semilinear coupled Timoshenko beam and an elastodynamic system in an inhomogeneous medium

In this paper, we consider a semilinear coupled Timoshenko beam and an elastodynamic system posed in an inhomogeneous one-dimensional medium subject to localized damping mechanisms acting in the three equations. We show uniform decay rates for the energy of the solutions of such a problem without assuming any restrictions on the non-constant coefficients. To establish these results, refined arguments of the Microlocal Analysis Theory are applied.