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

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

    Citation:

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