Exponential Decay of Energy of the Euler--Bernoulli Beam with Locally Distributed Kelvin--Voigt Damping
Exponential Decay of Energy of the Euler--Bernoulli Beam with Locally Distributed Kelvin--Voigt Damping
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DOI：
10.1137/s0363012996310703
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发表时间：
1998-05
影响因子：
2.2
通讯作者：
Kangsheng Liu;Zhuangyi Liu
中科院分区：
文献类型：
--
作者：
Kangsheng Liu;Zhuangyi Liu
本文研究了具有Kelvin-Voigt阻尼的Euler-Bernoulli梁在其所占区域的任意子区间上局部分布的纵向和横向振动。我们证明了与梁的横向运动方程有关的半群是指数稳定的，尽管与梁的纵向运动方程有关的半群不是指数稳定的。由于阻尼的局部分布性和无界性，我们使用频域方法，并结合矛盾论证和乘子技术对预解进行了特殊的分析。我们还证明了伴随半群不是解析的。
In this paper, we consider the longitudinal and transversal vibrations of the Euler--Bernoulli beam with Kelvin--Voigt damping distributed locally on any subinterval of the region occupied by the beam. We prove that the semigroup associated with the equation for the transversal motion of the beam is exponentially stable, although the semigroup associated with the equation for the longitudinal motion of the beam is not exponentially stable. Due to the locally distributed and unbounded nature of the damping, we use a frequency domain method and combine a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent. We also show that the associated semigroups are not analytic.