Optimal decay rate for a Rayleigh beam–string coupled system with frictional damping

This paper addresses the stability of a coupled system that consists of a conservative Rayleigh beam and a damped elastic string, the latter being equipped with frictional damping. By estimating the growth of the resolvent along the imaginary axis, we employ the frequency domain method to demonstrat...

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Bibliographic Details
Published inApplied mathematics letters Vol. 158; p. 109229
Main Authors Zhao, Zhi-Xue, Su, Yu-Hang, Han, Zhong-Jie
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.12.2024
Subjects
Coupled Rayleigh beam–string
Frequency domain method
Frictional damping
Polynomial stability
Spectral analysis
Frequency domain method
Polynomial stability
Frictional damping
Spectral analysis
Coupled Rayleigh beam–string
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Summary:This paper addresses the stability of a coupled system that consists of a conservative Rayleigh beam and a damped elastic string, the latter being equipped with frictional damping. By estimating the growth of the resolvent along the imaginary axis, we employ the frequency domain method to demonstrate that the coupled Rayleigh beam–string system exhibits polynomial stability, characterized by a decay rate t−1/4. Furthermore, we establish the optimality of the decay rate, t−1/4, through a rigorous spectral analysis. Finally, a numerical example is present to validate the theoretical findings.
ISSN:0893-9659
DOI:10.1016/j.aml.2024.109229