On aspects of damping for a vertical beam with a tuned mass damper at the top |
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Authors: | J W Hijmissen W T van Horssen |
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Institution: | (1) Delft Institute of Applied Mathematics (DIAM), Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Mekelweg 4, 2628 Delft, CD, The Netherlands |
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Abstract: | In this paper, the wind-induced, horizontal vibrations of a vertical Euler–Bernoulli beam will be considered. At the top of
the beam, a tuned mass damper (TMD) has been installed. The horizontal vibrations can be described by an initial-boundary
value problem. Perturbation methods will be applied to construct approximations of the solutions of the initial-boundary value
problem, and it will be shown that the TMD uniformly damps the oscillation modes of the beam. In the analysis, it will be
assumed that damping, wind-force, and gravity effects are small but not negligible. |
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Keywords: | Asymptotics Boundary damping Euler– Bernoulli beam Stability Tall building Tuned mass damper Two-timescales perturbation method |
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