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Stabilization of an Euler-Bernoulli Beam with Distributed Dam** Under Time Delays in the Boundary

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Abstract

In this paper, we investigate the exponential stability of an Euler-Bernoulli beam system with distributed dam** subjected to a time-delay in the boundary. At first, applying the semigroup theory of bounded linear operators we prove the well posedness of the system. And then we give the exponential stability analysis of the system by constructing an appropriate Lyapunov function. Different from the earlier results, we use the dam** coefficient \(\alpha \) and delay coefficient \(\beta \) together with the parameters of the system to give a description of the stability region. The simulation are presented to prove the effectiveness of this results.

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Acknowledgements

This research was supported by the Doctoral Scientific Research Foundation of Henan Normal University under Grant No. qd18088, the Natural Science Foundation of China under Grant No. 61773277 and the central university basic scientific research project of civil aviation university of China under Grant No. 3122019140.

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Authors and Affiliations

  1. Department of Mathematics, Henan Normal University, Henan, 453007, P.R. China

    Yanfang Li

  2. School of Mechatronical Engineering, Bei**g Institute of Technology, Bei**g, 100081, P.R. China

    Hao Chen

  3. Department of Mathematics, Civil Aviation University of China, Tian**, 300300, P.R. China

    Yaru **e

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  1. Yanfang Li
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  2. Hao Chen
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  3. Yaru **e
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Correspondence to Yaru **%20Under%20Time%20Delays%20in%20the%20Boundary&author=Yanfang%20Li%20et%20al&contentID=10.1007%2Fs10440-022-00466-1&copyright=The%20Author%28s%29%2C%20under%20exclusive%20licence%20to%20Springer%20Nature%20B.V.&publication=0167-8019&publicationDate=2022-01-19&publisherName=SpringerNature&orderBeanReset=true">Reprints and permissions

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Li, Y., Chen, H. & ** Under Time Delays in the Boundary. Acta Appl Math 177, 5 (2022). https://doi.org/10.1007/s10440-022-00466-1

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