On transverse vibrations of a vertical Timoshenko beam

In this paper the transverse vibrations of a standing, uniform Timoshenko beam will be considered. Due to gravity and the self-weight of the beam a linearly varying compression force is acting on the beam. It will be assumed that this compression force is small but not negligible. The transverse vibrations of the beam can be described by an initial-boundary value problem. Approximations of the solution of this problem will be constructed by using a multiple time-scales perturbation method. Also approximations of the frequencies will be obtained. Moreover, the effect of the linearly varying compression force on the magnitude of the frequencies of the oscillation modes of the beam will be discussed.