Effect of boundary conditions in three alternative models of Timoshenko-Ehrenfest beams on Winkler elastic foundation

In this paper we discuss about the free vibrations of a beam on Winkler foundation via original Timoshenko-Ehrenfest beam theory, as well as one of its truncated versions, and a model based on slope inertia. Differences between the three models are indicated. We analyze five different sets of boundary conditions, which are derived from the most typical end constraints: simply supported end, clamped end and free end. A detailed proof about the non-existence of zero frequencies for the free-free beam and for the simply supported-free beam is given. Differences between the models are indicated in the context of free vibrations of the beam on Winkler foundations.