Open AccessExponential stability of axially moving Kirchhoff-beam systems with nonlinear boundary damping and disturbance
Author(s) -
Yi Cheng,
Zhihui Dong,
Donal 'Regan
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021230
Subject(s) - nonlinear system , axial symmetry , uniqueness , exponential stability , control theory (sociology) , mathematics , mathematical analysis , lyapunov function , disturbance (geology) , boundary value problem , beam (structure) , physics , geometry , computer science , optics , control (management) , paleontology , quantum mechanics , artificial intelligence , biology
This paper examines the stabilization problem of the axially moving Kirchhoff beam. Under the nonlinear damping criterion established by the slope-restricted condition, the existence and uniqueness of solutions of the closed-loop system equipped with nonlinear time-delay disturbance at the boundary is investigated via the Faedo-Galerkin approximation method. Furthermore, the solution is continuously dependent on initial conditions. Then the exponential stability of the closed-loop system is established by the direct Lyapunov method, where a novel energy function is constructed.