AN EULER-BERNOULLI BEAM WITH NONLINEAR DAMPING AND A NONLINEAR SPRING AT THE TIP

作者：Miletic Maja^*; Stuerzer Dominik; Arnold Anton

来源：Discrete and Continuous Dynamical Systems-Series B, 2015, 20(9): 3029-3055.

DOI：10.3934/dcdsb.2015.20.3029

• Flexible beam
• nonlinear spring
• nonlinear damping
• nonlinear semigroups
• trajectory precompactness
• asymptotic stability

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.

• 出版日期2015-11