Solvability of the rational contact with limited interpenetration of different kind of viscolastic plates is proved. The biharmonic plates, von Kármán plates, Reissner-Mindlin plates, and full von Kármán systems are treated. The viscoelasticity can have the classical (``short memory'') form or the form of a certain singular memory. For all models some convergence of the solutions to the solutions of the Signorini contact is proved provided the thickness of the interpenetration tends to zero.

We consider a dynamical one-dimensional nonlinear von Kármán model for beams depending on a parameter $\epsilon \>0$ and study its asymptotic behavior for $t$ large, as $\epsilon \to 0$. Introducing appropriate damping mechanisms we show that the energy of solutions of the corresponding damped models decay exponentially uniformly with respect to the parameter $\epsilon$. In order for this to be true the damping mechanism has to have the appropriate scale with respect to $\epsilon$. In the limit as $\epsilon \to 0$ we obtain damped Berger–Timoshenko beam models...

We consider a dynamical one-dimensional nonlinear von Kármán model for beams depending on a parameter ε > 0 and study its asymptotic behavior for t large, as ε → 0. Introducing appropriate damping mechanisms we show that the energy of solutions of the corresponding damped models decay exponentially uniformly with respect to the parameter ε. In order for this to be true the damping mechanism has to have the appropriate scale with respect to ε. In the limit as ε → 0 we obtain damped Berger–Timoshenko...