Vibration of multi-span Timoshenko frames due to moving loads

Abstract An analytical method is presented in this paper to study the vibration of multi-span Timoshenko frames. The combined effects of axial inertia, rotatory inertia and shear deformation of each branch of those frames are simultaneously considered. Any two distinct sets of the mode shape functions are shown to be orthogonal. The method of modal analysis is then adopted to investigate the forced vibration of the frames. A concentrated load and a uniformly distributed load moving on these frames are treated as two examples. Results show that as the span number gets larger, the first modal frequency gets smaller. Furthermore, the longer column implies a smaller first modal frequency. The absolute maximum deflection of the Timoshenko frame is larger than that of the Bernoulli–Euler frame.