Asymptotic limits and stabilization for the 1D nonlinear Mindlin-Timoshenko system

Abstract

This paper shows how the so called von Karman model can be obtained as a singular limit of a modified Mindlin-Timoshenko system when the modulus of elasticity in shear k tends to infinity, provided a regularizing term through a fourth order dispersive operator is added. Introducing damping mechanisms, the authors also show that the energy of solutions for this modified Mindlin-Timoshenko system decays exponentially, uniformly with respect to the parameter k. As k → ∞, the authors obtain the damped von Karman model with associated energy exponentially decaying to zero as well.