Modal Analysis Method for the Moving Load-induced Vibrations of Timoshenko Beams

초록

The modal analysis method (MAM) has been widely used for obtaining dynamic responses of a continuous structure into the closed forms. For the MAM, accurate information on the natural frequencies, mode shapes, and orthogonality of the mode shapes are required. Thus, we present accurate natural frequencies, mode shapes, and orthogonality of those mode shapes in complete forms for a simply supported uniform Timoshenko beam. By using this modal information, we apply the MAM to obtaining closed-form dynamic responses of a simply supported Timoshenko beam subjected to a moving point load: a point transverse force or point bending moment. We also consider two cases: undamped vibration and damped vibration. Then, we numerically investigate the effects of the mode shapes and damping on the vibrations of an example Timoshenko beam subjected to a moving point load.