Internal stabilization of a Mindlin-Timoshenko model by interior feedbacks
نویسنده
چکیده
A Mindlin-Timoshenko model with non constant and non smooth coefficients set in a bounded domain of R, d ≥ 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.
منابع مشابه
Existence and Boundary Stabilization of the Semilinear Mindlin-Timoshenko System
We consider dynamics of the one-dimensional Mindlin-Timoshenko model for beams with a nonlinear external forces and a boundary damping mechanism. We investigate existence and uniqueness of strong and weak solution. We also study the boundary stabilization of the solution, i.e., we prove that the energy of every solution decays exponentially as t → ∞. AMS Subject Classifications. 35L70, 35B40, 7...
متن کاملAsymptotic limits and stabilization for the 1D nonlinear Mindlin-Timoshenko system
This paper shows how the so called von Kármán 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...
متن کاملEigenvalue analysis of Timoshenko beams and axisymmetric Mindlin plates by the pseudospectral method
A study of the free vibration of Timoshenko beams and axisymmetric Mindlin plates is presented. The analysis is based on the Chebyshev pseudospectral method, which has been widely used in the solution of fluid mechanics problems. Clamped, simply supported, free and sliding boundary conditions of Timoshenko beams are treated, and numerical results are presented for different thickness-to-length ...
متن کاملControllability of the Kirchhoff System for Beams as Limit of the Mindlin-timoshenko One
We consider the dynamical one-dimensional Mindlin-Timoshenko system for beams. We analyze how its controllability properties depend on the modulus of elasticity in shear k. In particular we prove that the exact boundary controllability property of the Kirchhoff system may be obtained as singular limit, as k → ∞, of the partial controllability of a sharp subspace of low frequency components of t...
متن کاملOn the stability of Mindlin-Timoshenko plates
We consider a Mindlin-Timoshenko model with frictional dissipations acting on the equations for the rotation angles. We prove that this system is not exponentially stable independent of any relations between the constants of the system, which is different from the analogous’ one-dimensional case. Moreover, we show that the solution decays polynomially to zero, with rates that can be improved de...
متن کامل