A novel approach to the dynamic response analysis of Euler-Bernoulli beams resting on a Winkler soil model and subjected to impact loads

This work presents a novel approach to the dynamic response analysis of a Euler-Bernoulli beam resting on a Winkler soil model and subjected to an impact loading. The approach considers that damping has much less importance in controlling the maximum response to impulsive loadings because the maximum response is reached in a very short time, before the damping forces can dissipate a significant portion of the energy input into the system. The development of two sine series solutions, relating to different types of impulsive loadings, one involving a single concentrated force and the other a distributed line load, are presented. This study revealed that when a simply supported Euler-Bernoulli beam, resting on a Winkler soil model, is subject to an impact load, the resulting vertical displacements, bending moments and shear forces produced along the span of the beam are considerably affected. In particular, the quantification of this effect is best observed, relative to the corresponding static solution, via an amplification factor. The computed impact amplification factors, for the sub-grade moduli used in this study, were in magnitude greater than 2, thus confirming the multiple-degree-of-freedom nature of the problem.