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A Mindlin-Timoshenko model with non constant and non smooth coefficients set in a bounded domain  of $\mathbb{R}^d, d\geq 1$ with some internal dissipations is proposed. It corresponds to the coupling between the wave equation and the dynamical elastic system. If the dissipation acts on both equations, we show an exponential decay rate. On the contrary if the dissipation is only active on the elasticity equation, a  polynomial decay is shown; a similar result is proved in one dimension if the dissipation is only active on the wave equation.

Internal stabilization of a Mindlin-Timoshenko model by interior feedbacks