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November  2015, 20(9): 3029-3055. doi: 10.3934/dcdsb.2015.20.3029

## An Euler-Bernoulli beam with nonlinear damping and a nonlinear spring at the tip

 1 Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8, 1040 Vienna, Austria, Austria 2 Institute for Analysis and Scienti c Computing, Vienna University of Technology, Wiedner Hauptstraße 8, 1040 Vienna, Austria

Received  November 2014 Revised  July 2015 Published  September 2015

We study the asymptotic behavior for a system consisting of a clamped flexible beam that carries a tip payload, which is attached to a nonlinear damper and a nonlinear spring at its end. Characterizing the $\omega$-limit sets of the trajectories, we give a sufficient condition under which the system is asymptotically stable. In the case when this condition is not satisfied, we show that the beam deflection approaches a non-decaying time-periodic solution.
Citation: Maja Miletić, Dominik Stürzer, Anton Arnold. An Euler-Bernoulli beam with nonlinear damping and a nonlinear spring at the tip. Discrete & Continuous Dynamical Systems - B, 2015, 20 (9) : 3029-3055. doi: 10.3934/dcdsb.2015.20.3029
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