Spectrum and Stability for Elastic Systems with Global or Local Kelvin-Voigt Damping
Spectrum and Stability for Elastic Systems with Global or Local Kelvin-Voigt Damping
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DOI：
10.1137/s0036139996292015
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发表时间：
1998-11
期刊：
影响因子：
--
通讯作者：
Kangsheng Liu;Shuping Chen;Zhuangyi Liu
中科院分区：
文献类型：
--
作者：
Kangsheng Liu;Shuping Chen;Zhuangyi Liu
本文研究了一类变分二阶发展方程的数学性质，该方程包括具有整体或局部Kelvin-Voigt（K-V）阻尼的Euler-Bernoulli梁和Rayleigh梁的振动方程。特别地，我们的结果描述了半群的设置，半群的强渐近稳定性和指数稳定性，半群的解析性，以及在各种阻尼条件下半群生成元的谱特征.我们还举例说明，当K-V阻尼只分布在一端与弦的一端重合的子区间上时，振动弦的能量不会指数衰减。
In this paper, we study the mathematical properties of a variational second order evolution equation, which includes the equations modelling vibrations of the Euler--Bernoulli and Rayleigh beams with the global or local Kelvin--Voigt (K--V) damping. In particular, our results describe the semigroup setting, the strong asymptotic stability and exponential stability of the semigroup, the analyticity of the semigroup, as well as characteristics of the spectrum of the semigroup generator under various conditions on the damping. We also give an example to show that the energy of a vibrating string does not decay exponentially when the K--V damping is distributed only on a subinterval which has one end coincident with one end of the string.