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 2 to be strongly stable. Furthermore, polynomial stability of certain orders are proved. The cases in group 1 are left for future study.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1479-1510 |
| Number of pages | 32 |
| Journal | Mathematical Methods in the Applied Sciences |
| Volume | 46 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jan 30 2023 |
Bibliographical note
Funding Information:The authors would like to thank the referees for their valuable comments and helpful suggestions.
Publisher Copyright:
© 2022 John Wiley & Sons, Ltd.
Keywords
- beam
- frictional damping
- polynomial stability
- semigroup