# American Institute of Mathematical Sciences

July  2020, 19(7): 3531-3557. doi: 10.3934/cpaa.2020154

## General decay for a viscoelastic rotating Euler-Bernoulli beam

 Laboratory of SDG, Faculty of Mathematics, University of Science and Technology Houari Boumedienne, P.O. Box 32, El-Alia 16111, Bab Ezzouar, Algiers, Algeria

* Corresponding author

Received  February 2019 Revised  January 2020 Published  April 2020

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 $q$, namely, $q^{\prime}(t) \leq -\zeta(t)H(q(t))$, where $H$ is an increasing and convex function near the origin and $\zeta$ is a nonincreasing function, we establish optimal explicit and general energy decay results from which we can recover the optimal exponential and polynomial decay.

Citation: Ammar Khemmoudj, Imane Djaidja. General decay for a viscoelastic rotating Euler-Bernoulli beam. Communications on Pure & Applied Analysis, 2020, 19 (7) : 3531-3557. doi: 10.3934/cpaa.2020154
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