General energy decay and stability analysis of a nonlinear euler-bernoulli beam with a boundary control and viscoelastic damping

被引：0

作者：

Lekdim, Billal ^{[1
,2
]}

Bchatnia, Ahmed ^{[3
]}

Mtiri, Foued ^{[4
]}

机构：

[1] Univ Ziane Achour Djelfa, Fac Exact Sci & Comp Sci, POB 3117, Djelfa, Algeria

[2] Univ Sci & Technol Houari Boumediene, Fac Math, SD Lab, POB 32,El-Alia, Algiers 16111, Algeria

[3] Univ Tunis Manar, Fac Sci Tunis, Dept Math, LR Anal Nonlineaire & Geometrie, LR21ES08,El Manar 2, Tunis 2092, Tunisia

[4] Univ King Khaled, Appl Coll Mahayil, Dept Math, Abha, Saudi Arabia

来源：

RICERCHE DI MATEMATICA | 2025年

关键词：

Well-Posedness; Boundary Control; Nonlinear Euler-Bernoulli Beams; Viscoelastic Damping; ASYMPTOTIC-BEHAVIOR; WELL-POSEDNESS; SYSTEM;

D O I：

10.1007/s11587-025-00977-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper investigates the energy decay of a nonlinear Euler-Bernoulli beam, focusing on longitudinal boundary control and viscoelastic damping in the transverse directions. Using the Faedo-Galerkin method, the study demonstrates the existence and uniqueness of solutions. A Lyapunov function is constructed to analyze the stability of the beam.

引用

页数：28

共 30 条

[1] Existence and stability of a weakly damped laminated beam with a nonlinear delay [J].

Al-Mahdi, Adel M. ;

Al-Gharabli, Mohammed M. ;

Feng, Baowei .

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2024, 104 (12)

[2] Asymptotic behavior of solutions of a viscoelastic Shear beam model with no rotary inertia: General and optimal decay results [J].

Al-Mahdi, Adel M. .

OPEN MATHEMATICS, 2024, 22 (01)

[3] New decay results for a viscoelastic-type Timoshenko system with infinite memory [J].

Al-Mahdi, Adel M. ;

Al-Gharabli, Mohammad M. ;

Guesmia, Aissa ;

Messaoudi, Salim A. .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2021, 72 (01)

[4] Polynomial Decay of the Energy of Solutions of the Timoshenko System with Two Boundary Fractional Dissipations [J].

Alfalqi, Suleman ;

Khiar, Hamid ;

Bchatnia, Ahmed ;

Beniani, Abderrahmane .

FRACTAL AND FRACTIONAL, 2024, 8 (09)

[5]

[Anonymous], 2013, Mathematical methods of classical mechanics, V60

[6] Nonlinear damping effects for the 2D Mindlin-Timoshenko system [J].

Bchatnia, Ahmed ;

Chebbi, Sabrine ;

Hamouda, Makram .

ARABIAN JOURNAL OF MATHEMATICS, 2024, 13 (03) :485-512

[7] Vibration Control of a Viscoelastic Translational Euler-Bernoulli Beam [J].

Berkani, Amirouche ;

Tatar, Nasser-eddine ;

Kelleche, Abdelkarim .

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2018, 24 (01) :167-199

[8] Fractional derivative boundary control in coupled Euler-Bernoulli beams: stability and discrete energy decay [J].

Boukhari, Boumediene ;

Mtiri, Foued ;

Bchatnia, Ahmed ;

Beniani, Abderrahmane .

AIMS MATHEMATICS, 2024, 9 (11) :32102-32123

[9] Global well-posedness and exponential stability results of a class of Bresse-Timoshenko-type systems with distributed delay term [J].

Choucha, Abdelbaki ;

Ouchenane, Djamel ;

Zennir, Khaled ;

Feng, Baowei .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2024, 47 (13) :10668-10693

[10] Boundary control design for extensible marine risers in three dimensional space [J].

Do, K. D. .

JOURNAL OF SOUND AND VIBRATION, 2017, 388 :1-19

← 1 2 3 →