Stability analysis of partially viscoelastic Reissner-Mindlin-Timoshenko plates

This paper investigates the asymptotic stability of a partially viscoelastic Reissner-Mindlin-Timoshenko (RMT) plate system, incorporating the Boltzmann principle in the in-plane strain tensor related to rotation angles. Our main mathematical results include: $ (i) $ the asymptotic stability of solutions independent of any relations on the coefficients, using refined contradiction arguments through spectral analysis; $ (ii) $ additionally, we establish qualitative uniform and semi-uniform decay rates under the equal wave speeds assumption, achieved through direct estimates with new multipliers and the resolvent equation. These findings highlight the intricate nature of the bi-dimensional RMT-system and the role of the dissipative effect given by the memory.