STABILIZATION OF THE GENERALIZED RAO-NAKRA BEAM BY PARTIAL VISCOUS
DAMPING
- Mohammad AKIL,
- Zhuangyi Liu
Abstract
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