Dynamic response of a finite beam resting on a Winkler foundation to a load moving on its surface with variable speed

The dynamic response of a simply supported elastic beam resting on an elastic foundation of Winkler's type with viscous damping to a point load moving with variable speed on the surface of the beam is obtained analytically/numerically. The beam is of the Bernoulli-Euler type with viscous damping. The load is concentrated and varies harmonically with time. The equation of lateral motion of the beam is solved by modal superposition analytically and computation of the resulting Duhamel's integrals is done numerically. The case of two loads representing the two axle system of a vehicle, is also treated here by following the same approach used for the single load. The effects of the various parameters, like foundation stiffness and damping, beam damping and especially acceleration or deceleration of the moving load or loads, on the response of the beam are assessed through extensive parametric studies and useful practical conclusions are presented.