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

Maja  Miletić; Dominik  Stürzer; Anton  Arnold

doi:10.3934/dcdsb.2015.20.3029

Article Contents

2015, Volume 20, Issue 9: 3029-3055. Doi: 10.3934/dcdsb.2015.20.3029

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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
2.
Institute for Analysis and Scientic Computing, Vienna University of Technology, Wiedner Hauptstraße 8, 1040 Vienna

Received: November 2014

Revised: July 2015

Published: November 2015

Abstract / Introduction Related Papers Cited by

Abstract

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.

Keywords:

Mathematics Subject Classification: 35B40, 70K20, 74K10, 47H20, 35Q70.

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