Free vibrations of axially moving strings: Energy estimates and boundary observability

被引：0
|
作者：
Ghenimi, Seyf Eddine [1 ]
Sengouga, Abdelmouhcene [1 ,2 ]
机构：
[1] Univ MSila, Lab Funct Anal & Geometry Spaces, Msila, Algeria
[2] Univ MSila, Dept Math, PB 166, Msila 28000, Algeria
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2023年 / 46卷 / 13期
关键词：
axially moving strings; boundary observability; energy estimates; Fourier series; WAVE-EQUATION; CONTROLLABILITY;
D O I：
10.1002/mma.9285
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the small vibrations of axially moving strings described by a wave equation in an interval with two endpoints moving in the same direction with a constant speed. The solution is expressed by a series formula where the coefficients are explicitly computed in function of the initial data. We also define an energy expression for the solution that is conserved in time. Then, we establish boundary observability inequalities with explicit constants.
引用
收藏
页码：13716 / 13730
页数：15
相关论文
共 50 条
  • [1] Stability analyses for axially moving strings in nonlinear free and aerodynamically excited vibrations
    Wang, Yuefang
    Liu, Xuetao
    Huang, Lihua
    CHAOS SOLITONS & FRACTALS, 2008, 38 (02) : 421 - 429
  • [2] Boundary observability of elastic vibrations in a system of sequentially connected strings
    Egorov, A. I.
    Znamenskaya, L. N.
    COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2012, 52 (09) : 1233 - 1238
  • [3] Eigenvalue and stability analysis for axially moving strings in transverse vibrations
    Wang, YF
    Liu, XT
    Huang, LH
    2005 INTERNATIONAL CONFERENCE ON PHYSICS AND CONTROL (PHYSCON), 2005, : 194 - 201
  • [4] Boundary observability of elastic vibrations in a system of sequentially connected strings
    A. I. Egorov
    L. N. Znamenskaya
    Computational Mathematics and Mathematical Physics, 2012, 52 : 1233 - 1238
  • [5] Nonlinear vibrations of axially moving beams with nonhomogeneous boundary conditions
    Zhang D.
    Tang Y.
    Chen L.
    Lixue Xuebao/Chinese Journal of Theoretical and Applied Mechanics, 2019, 51 (01): : 218 - 227
  • [6] On boundary observability estimates for semi-discretizations of a dynamic network of elastic strings
    Brauer, U
    Leugering, G
    CONTROL AND CYBERNETICS, 1999, 28 (03): : 421 - 447
  • [7] Eigenvalue and stability analysis for transverse vibrations of axially moving strings based on Hamiltonian dynamics
    Yuefang Wang
    Lihua Huang
    Xuetao Liu
    Acta Mechanica Sinica, 2005, 21 : 485 - 494
  • [8] Eigenvalue and stability analysis for transverse vibrations of axially moving strings based on Hamiltonian dynamics
    Wang, YF
    Huang, LH
    Liu, XT
    ACTA MECHANICA SINICA, 2005, 21 (05) : 485 - 494
  • [9] Eigenvalue and stability analysis for transverse vibrations of axially moving strings based on Hamiltonian dynamics
    Y.F.Wang X.T.Liu Department of Engineering Mechanics
    Acta Mechanica Sinica, 2005, 21 (05) : 485 - 494
  • [10] Boundary layers and non-linear vibrations in an axially moving beam
    Pellicano, F
    Zirilli, F
    INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 1998, 33 (04) : 691 - 711
12345