VIBRATIONS OF A HANGING TIMOSHENKO BEAM UNDER GRAVITY

Abstract The vibration characteristics of uniform hanging beams under gravity are investigated. The governing differential equations for free vibrations of a vertically hanging Timoshenko beam subjected to its own weight are first derived from Hamilton's principle. The spatial dependence of these equations is then discretized by using a finite element procedure. The influences of gravity, shear deformation and rotatory inertia on the flexural vibrations of the hanging beam are examined. In particular, the natural frequencies and the associated mode shapes obtained for the classical Euler-Bernoulli beam, which is a special case of the present model, show good agreement with the available experimental and numerical results. The present results provide a better understanding of the dynamic characteristics of a large flexible space beam under gravity.