Stabilization of Berger–Timoshenko's equation as limit of the uniform stabilization of the von Kármán system of beams and plates
Stabilization of Berger–Timoshenko's equation as limit of the uniform stabilization of the von Kármán system of beams and plates
复制标题
Berger-Timoshenko 方程的稳定性作为梁和板的 von Kármán 系统均匀稳定的极限
DOI：
10.1051/m2an:2002029
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
E. Zuazua
中科院分区：
文献类型：
--
作者：
G. Menzala;A. Pazoto;E. Zuazua
我们考虑了一个依赖于参数e b> 0的动态一维非线性von Karman模型，并研究了它在t大，即e→0时的渐近行为。引入适当的阻尼机制，我们证明了相应阻尼模型的解的能量相对于参数e呈指数均匀衰减。为了使这是正确的，阻尼机制必须具有相对于e的适当尺度。在e→0的极限下，我们得到阻尼Berger-Timoshenko梁模型，其能量也呈指数趋向于零。在内部和边界阻尼的情况下都是这样做的。对于有内部阻尼的板，我们也处理同样的问题。
We consider a dynamical one-dimensional nonlinear von Karman model for beams depending on a parameter e > 0 and study its asymptotic behavior for t large, as e → 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 e. In order for this to be true the damping mechanism has to have the appropriate scale with respect to e. In the limit as e → 0 we obtain damped Berger–Timoshenko beam models for which the energy tends to zero exponentially as well. This is done both in the case of internal and boundary damping. We address the same problem for plates with internal damping.