板-波传输系统的间接稳定性  

Indirect Stabilization of Transmission Plate-Wave Systems

作　　者：王军民 郝江浩[2] 郭雅平[2] WANG Junmin;HAO Jianghao;GUO Yaping(School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,China;School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]北京理工大学数学与统计学院,北京100081 [2]山西大学数学科学学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2022年第3期548-554,共7页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(62073037,11871315);山西省青年科技研究基金(201901D211162)。

摘　　要：文章研究在板上施加摩擦阻尼,板-波传输系统的间接稳定性。应用算子半群理论证明了传输系统的适定性;接着运用频域分析和能量乘子技巧证明了整个传输系统的能量是多项式衰减的。从控制的角度来看,实现了仅由板的阻尼镇定整个传输系统的目的。This paper is devoted to the indirect stabilization of plate-wave transmission systems where the friction damping is only applied to the plate.Firstly,by the linear operator semigroup theory,we show the well-posedness of the transmission systems.Then,we prove that the transmission system is polynominally stable by applying the frequency domain analysis method and energy multiplier technique.From the control perspective,the damping of the plate can be used to stabilize the whole transmission system.

关 键 词：传输系统 阻尼 多项式稳定 

分 类 号：O321[理学—一般力学与力学基础]