Stabilization of a 1-D transmission problem for the Rayleigh beam and string with localized frictional damping

We are concerned with the stability of a 1-D coupled Rayleigh beam-string transmission system. We obtain the polynomial decay rate or the exponential decay rate for the given transmission system whether the frictional damping is only effective in the beam part or the string part, respectively. This...

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Bibliographic Details
Published in:Journal of applied analysis 2023-06, Vol.29 (1), p.77-90
Main Authors: Hong, Gimyong, Hong, Hakho
Format: Article
Language:English
Subjects:
35L57
35Q74
74M05
93D15
Beams (structural)
Damping
Decay rate
Energy
energy decay
Polynomials
Rayleigh beam
string
Strings
Transmission problem
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Summary:We are concerned with the stability of a 1-D coupled Rayleigh beam-string transmission system. We obtain the polynomial decay rate or the exponential decay rate for the given transmission system whether the frictional damping is only effective in the beam part or the string part, respectively. This paper generalizes the recent result in [Y.-F. Li, Z.-J. Han and G.-Q. Xu, Explicit decay rate for coupled string-beam system with localized frictional damping, Appl. Math. Lett. 78 2018, 51–58]. The main ingredient of the proof is some careful analysis for the Rayleigh beam and string transmission system.
ISSN:1425-6908
1869-6082
DOI:10.1515/jaa-2021-2082