On the weakly damped vibrations of a vertical beam with a tip-mass

In this paper the wind-induced, horizontal vibrations of a weakly damped vertical Euler-Bernoulli beam with and without a tip-mass will be studied. The damping is assumed to be boundary damping and global Kelvin-Voigt damping. The boundary damping is assumed to be proportional to the velocity of the beam at the top. The horizontal vibrations of the beam can be described by an initial-boundary value problem. In this paper, the multiple-timescales perturbation method will be applied to construct approximations of the solutions of the problem. Also it will be shown that a combination of boundary damping and Kelvin-Voigt damping can be used to damp the wind-induced vibrations of a vertical beam with tip-mass uniformly.