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

Abstract

We study the asymptotic behaviour 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 necessary 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.