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

The problem of the dynamic response of an infinite beam resting on a Winkler foundation to a load moving on its surface with variable speed is solved here analytically/numerically under conditions of plane strain. The beam is linearly elastic with viscous damping and obeys the theory of Bernoulli-Euler. The elastic foundation is characterized by its spring constant and hysteretic damping coefficient. The moving point load has an amplitude harmonically varying with time and moves with constant acceleration or deceleration along the top beam surface. The problem is solved by first applying the Fourier transform with respect to the horizontal coordinate x and the Laplace transform with respect to time t to reduce the governing equation of motion of the beam to an algebraic one, which is solved analytically. The transformed beam deflection solution is inverted numerically after some simplifying analytical manipulations to produce the time domain beam response. Parametric studies are conducted in order to assess the effects of the various parameters on the response of the beam, especially those of acceleration and deceleration. Comparisons with the case of a finite beam are also done in order to assess the effect of the beam length.