On the Response of a Beam Structure to a Moving Mass Using Green’s Function

The dynamic responses of a beam structure acted upon by a moving mass or moving load have been of great importance in the design and study of bridges, railway tracks, etc. It also plays a vital role for studying many applications in the field of transportation, overhead cranes, cableways, roadways, pipelines, tunnels, bridges, guideways, etc. All the above-mentioned structures are designed to support moving loads. The structures while supporting the moving loads face the inertial effect of the moving mass which cannot be ignored comparing with the gravitational effect of the moving load. The equation of motion of an Euler–Bernoulli beam acted upon by a concentrated mass moving at a uniform speed is formulated in matrix form. The solutions of the above problems for cantilever beams are evaluated by using dynamic Green’s function approach. The present work focuses on the effect of the mass of the moving load and its speed on the response of a cantilever-type beam. The cantilever beam is divided into twenty divisions, and the deflection of beam at the free end is measured, while the mass moves with uniform velocity over the beam through different stations. The deflection results so obtained are plotted in the form of graphs for different velocities of mass.