General decay for a viscoelastic rotating Euler-Bernoulli beam

Abstract

In this paper, we consider a viscoelastic rotating Euler-Bernoulli beam that has one end fixed to a rotated motor in a horizontal plane and to a tip mass at the other end. For a large class relaxation function \begin{document}$ q $\end{document} , namely, \begin{document}$ q^{\prime}(t) \leq -\zeta(t)H(q(t)) $\end{document} , where \begin{document}$ H $\end{document} is an increasing and convex function near the origin and \begin{document}$ \zeta $\end{document} is a nonincreasing function, we establish optimal explicit and general energy decay results from which we can recover the optimal exponential and polynomial decay.