A dynamic contact problem for a thermoelastic diffusion beam with the rotational inertia

被引:11
作者
Aouadi, M. [1 ]
Copetti, M. I. M. [2 ]
机构
[1] Univ Carthage, UR Syst Dynam & Applicat, UR Ecole Natl Ingn Bizerte 17ES21, BP 66, Tunis 7035, Tunisia
[2] Univ Fed Santa Maria, Dept Matemat, Lab Anal Numer & Astrofis, BR-97105900 Santa Maria, RS, Brazil
关键词
Thermoelastic diffusion; Beam; Existence; Exponential decay; Numerical approximation; NONLINEAR THERMOVISCOELASTIC BEAM; 2; STOPS; VISCOELASTIC BEAM; TIMOSHENKO BEAM; VIBRATIONS;
D O I
10.1016/j.apnum.2017.12.007
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study the dynamic behaviour of a thermoelastic diffusion beam with the rotational inertia, clamped at one end and free to move between two stops at the other. The contact with the stops is modelled with the normal compliance condition. The system, recently derived by Aouadi (2015) 12], describes the behaviour of thermoelastic diffusion thin plates. This problem poses new mathematical difficulties due to the nonlinear boundary conditions. We prove the existence and uniqueness of weak solution using the Faedo-Galerkin method as well as the exponential stability at a rate proportional to the rotational inertia parameter. We propose a finite element approximation and we prove that the associated discrete energy decays to zero. Finally, we give an error estimate assuming extra regularity on the solution and we present some results of our numerical experiments. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码:113 / 137
页数:25
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