Forced vibrations of a beam on a tensionless foundation

Abstract This paper is concerned with the response of an elastic beam resting on a tensionless Winkler foundation, subjected to a concentrated load, a uniformly distributed load and a concentrated load. The external load are assumed to be time dependent, and the non-linear governing differential equation of forced vibrations is derived by employing the Galerkin method. The free vibration mode functions of the completely free beam are adopted as the co-ordinate functions of the displacement function of the beam. The results, which represent the static and dynamic responses of the beam, are presented in the figures. It is concluded that the presence of the lift-off affects the response of the beam markedly by changing the shape of the displacement curve as well as the foundation reactions.