一类耦合的Euler-Bernoulli梁的渐近稳定性  

Asymptotic Stability of a Coupled Euler-Bernoulli Beam

作　　者：赵转萍[1] ZHAO Zhuan-ping(Dept. of Public Courses, Business College of Shanxi University, Taiyuan 030031, China)

机构地区：[1]山西大学商务学院基础教学部,山西太原030031

出　　处：《中北大学学报（自然科学版）》2018年第3期266-269,315,共5页Journal of North University of China(Natural Science Edition)

摘　　要：考虑Euler-Bernoulli梁方程和一类抽象系统组成的耦合系统解的适定性和稳定性.利用控制的思想来研究偏微分方程的问题.通过将耦合系统分解为控制系统和其动态反馈组成的闭环系统,利用算子半群的方法得到系统解的适定性和渐近稳定性.举例说明了不同的抽象系统代表不同的动态反馈,形成不同的耦合系统,从而进一步验证了给出的方法的有效性.The well posedness and asymptotical stability of a coupled system that consists of the Euler- Bernoulli equation and an abstract system are considered. The problem of partial differential equation is considered by the control idea. By exploiting the semigroup theory, the well-posedness and asymptotical stability of the coupled system, which can be decoupled by the control plant and its dynamical feedback, are obtained. Different abstract system implies the different dynamical feedback and thus leads to differ ent coupled system. This fact and the proposed method are validated by examples.

关 键 词：耦合系统 EULER-BERNOULLI梁 稳定性 

分 类 号：O231[理学—运筹学与控制论]