The transverse vibration of a beam excited axially by an harmonic motion transmitted through intermittent or permanent elastic contact is studied. It is shown that this vibration is governed by a non-linear argumental equation, which means that a vibration in the fundamental transverse mode of the beam can occur when the frequency of the excitation is many times the frequency of the fundamental transverse mode. Two cases are considered : the hinged-(hinged-guided) case, and the clamped-(clamped-guided) case. A "natural" model is given. An approached smoothed model is derived. The averaging method gives a standard system of differential equations for the smoothed model. Symbolic relations are derived for the smoothed model. Numeric simulations allow a comparison between the natural model and the smoothed model. They also constitute a guide to the choice of parameters for the natural model. Experimental results are given and compared to the natural and the smoothed models.