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\begin{document}

\title{STABILIZATION OF THE GENERALIZED RAO-NAKRA BEAM BY PARTIAL VISCOUS
DAMPING}



\author[1]{Mohammad AKIL}%
\author[2]{Zhuangyi Liu}%
\affil[1]{Université Polytechnique Hauts-de-France}%
\affil[2]{University of Minnesota Duluth}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\begin{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.%
\end{abstract}%



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