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  • Mohammad AKIL,
  • Zhuangyi Liu
Mohammad AKIL
Université Polytechnique Hauts-de-France

Corresponding Author:[email protected]

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Zhuangyi Liu
University of Minnesota Duluth
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In this paper, we consider the stabilization of the generalized Rao-Nakra beam equation, which consists of four wave equations for the longitudinal displacements and the shear angle of the top and bottom layers and one Euler-Bernoulli beam equation for the transversal displacement. Dissipative mechanism are provided through viscous damping for two displacements. The location of the viscous damping are divided into two groups, characterized by whether both of the top and bottom layers are directly damped or otherwise. Each group consists of three cases. We obtain the necessary and sufficient conditions for the cases in group two to be strongly stable. Furthermore, polynomial stability of certain orders are proved. The cases in group one are left for future study.
01 Dec 2021Submitted to Mathematical Methods in the Applied Sciences
02 Dec 2021Submission Checks Completed
02 Dec 2021Assigned to Editor
21 Dec 2021Reviewer(s) Assigned
26 Apr 2022Review(s) Completed, Editorial Evaluation Pending
18 May 2022Editorial Decision: Revise Major
23 May 20221st Revision Received
24 May 2022Submission Checks Completed
24 May 2022Assigned to Editor
26 May 2022Reviewer(s) Assigned
14 Jul 2022Editorial Decision: Accept
30 Jan 2023Published in Mathematical Methods in the Applied Sciences volume 46 issue 2 on pages 1479-1510. 10.1002/mma.8591