Long-time behaviour of a translational thermoelastic Timoshenko system with second sound

被引：0

作者：

Guesmia, Aissa ^{[1
]}

Kafini, Mohammad ^{[2
]}

Tatar, Nasser Eddine ^{[2
]}

机构：

[1] Univ Lorraine, Inst Elie Cartan Lorraine, UMR 7502, Metz 03, France

[2] King Fahd Univ Petr & Minerals, IRC Intelligent Mfg & Robot, Dept Math, Dhahran, Saudi Arabia

来源：

APPLICABLE ANALYSIS | 2023年 / 102卷 / 05期

关键词：

Vibration control; exponential decay; polynomial decay; translational Timoshenko beam; second sound; VIBRATION CONTROL; GLOBAL EXISTENCE; STABILIZATION; STABILITY; DECAY; BEAMS;

D O I：

10.1080/00036811.2021.1983544

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a Timoshenko system coupled with heat equations modelled by Cattaneo's law. The coupling is through the transverse displacement. Both ends of the beam are dynamic. One end of the beam is fixed to a base in a translational motion and a tip mass is attached to the other end. We design a feedback control acting at the base. It is shown that this feedback control is a reasonable one and is capable of stabilizing the system. We prove an exponential and a polynomial stability result using the multiplier technique. To this end, we introduce new functionals to form a suitable Lyapunov functional.

引用

页码：1335 / 1363

页数：29

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