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<p>We study the boundary stabilization of a spinning Rayleigh beam system, which is modeled by two coupled Rayleigh beam equations. Thorough analysis is made of the asymptotic expressions for eigenvalues and the expansions for corresponding eigenfunctions of the closed-loop system. The well-posedness of the closed-loop system is established in the framework of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C_{0}\)</EquationSource> </InlineEquation> semigroups as well as the Riesz basis property of the eigenfunctions. The exponential stability of the closed-loop system is deduced from the spectrum determined growth condition.</p>

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Exponential Stability of a Spinning Rayleigh Beam with Boundary Control

  • 期刊论文

  • 发表日期：

    2025年10月13日

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  • Chao Yang,
  • Jun-Min Wang

摘要

We study the boundary stabilization of a spinning Rayleigh beam system, which is modeled by two coupled Rayleigh beam equations. Thorough analysis is made of the asymptotic expressions for eigenvalues and the expansions for corresponding eigenfunctions of the closed-loop system. The well-posedness of the closed-loop system is established in the framework of \(C_{0}\) semigroups as well as the Riesz basis property of the eigenfunctions. The exponential stability of the closed-loop system is deduced from the spectrum determined growth condition.