Stability of weakly dissipative Reissner–Mindlin–Timoshenko plates: A sharp result

Abstract

In the present article, we show that there exists a critical number that stabilizes the Reissner–Mindlin–Timoshenko system with frictional dissipation acting on rotation angles. We identify two speed characteristics v12:=K/ρ1 and v22:=D/ρ2, and we show that the system is exponentially stable if and only if \begin{equation*} v_{1}^{2}=v_{2}^{2}. \end{equation*} For v12 ≠ v22, we prove that the system is polynomially stable and determine an optimal estimate for the decay. To confirm our analytical results, we compute the numerical solutions by means of several numerical experiments by using a finite difference method.