On the spectrum of Euler-Bernoulli beam equation with Kelvin-Voigt damping

被引：9
|
作者：
Zhang, Guo-Dong [1 ,2 ]
Guo, Bao-Zhu [2 ,3 ,4 ]
机构：
[1] Heilongjiang Univ, Sch Math Sci, Harbin 150080, Peoples R China
[2] Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa
[3] Acad Sinica, Acad Math & Syst Sci, Beijing 100190, Peoples R China
[4] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2011年 / 374卷 / 01期
基金：
新加坡国家研究基金会; 中国国家自然科学基金;
关键词：
Beam equation; Spectrum; Variable coefficients; Kelvin-Voigt damping; RIESZ BASIS PROPERTY; EXPONENTIAL DECAY; WAVE-EQUATION; STABILITY; ENERGY; SYSTEM; CONTROLLABILITY; STABILIZATION; ANALYTICITY; OPERATOR;
D O I：
10.1016/j.jmaa.2010.08.070
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The spectral property of an Euler-Bernoulli beam equation with clamped boundary conditions and internal Kelvin-Voigt damping is considered. The essential spectrum of the system operator is rigorously identified to be an interval on the left real axis. Under some assumptions on the coefficients, it is shown that the essential spectrum contains continuous spectrum only, and the point spectrum consists of isolated eigenvalues of finite algebraic multiplicity. The asymptotic behavior of eigenvalues is presented. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：210 / 229
页数：20
相关论文
共 50 条
  • [1] Stability for Euler-Bernoulli Beam Equation with a Local Degenerated Kelvin-Voigt Damping
    Hassine, Fathi
    [J]. ACTA APPLICANDAE MATHEMATICAE, 2023, 184 (01)
  • [2] Stability for Euler-Bernoulli Beam Equation with a Local Degenerated Kelvin-Voigt Damping
    Fathi Hassine
    [J]. Acta Applicandae Mathematicae, 2023, 184
  • [3] A Transmission Problem for Euler-Bernoulli beam with Kelvin-Voigt Damping
    Raposo, C. A.
    Bastos, W. D.
    Avila, J. A. J.
    [J]. APPLIED MATHEMATICS & INFORMATION SCIENCES, 2011, 5 (01): : 17 - 28
  • [4] Identifiability of stiffness and damping coefficients in Euler-Bernoulli beam equations with Kelvin-Voigt damping
    Ito, K
    Nakagiri, S
    [J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1997, 18 (1-2) : 107 - 129
  • [5] A Numerical Method of the Euler-Bernoulli Beam with Optimal Local Kelvin-Voigt Damping
    Yu, Xin
    Ren, Zhigang
    Zhang, Qian
    Xu, Chao
    [J]. JOURNAL OF APPLIED MATHEMATICS, 2014,
  • [6] Exponential decay of energy of the Euler-Bernoulli beam with locally distributed Kelvin-Voigt damping
    Liu, KS
    Liu, ZG
    [J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1998, 36 (03) : 1086 - 1098
  • [7] ASYMPTOTIC BEHAVIOR OF THE TRANSMISSION EULER-BERNOULLI PLATE AND WAVE EQUATION WITH A LOCALIZED KELVIN-VOIGT DAMPING
    Hassine, Fathi
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2016, 21 (06): : 1757 - 1774
  • [8] Disturbance attenuation in the Euler-Bernoulli beam with viscous and Kelvin-Voigt damping via piezoelectric actuators
    Selivanov, Anton
    Fridman, Emilia
    [J]. 2023 62ND IEEE CONFERENCE ON DECISION AND CONTROL, CDC, 2023, : 1961 - 1966
  • [9] Dynamic boundary stabilization of Euler-Bernoulli beam through a Kelvin-Voigt damped wave equation
    Lu, Lu
    Wang, Jun-Min
    [J]. 26TH CHINESE CONTROL AND DECISION CONFERENCE (2014 CCDC), 2014, : 223 - 228
  • [10] Inverse problems of identifying the unknown transverse shear force in the Euler-Bernoulli beam with Kelvin-Voigt damping
    Kumarasamy, Sakthivel
    Hasanov, Alemdar
    Dileep, Anjuna
    [J]. JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2024, 32 (01): : 75 - 106
12345