The transverse vibration of a beam excited axially by an harmonic motion transmitted through intermittent contact is studied. It is shown that this vibration is governed by a nonlinear 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 model is derived. The averaging method gives a standard system of differential equations for the approached model. Symbolic relations are derived for the approached model. Numeric simulations allow a ccomparison between the exact model and the approached model. They also constitute a guide to the choice of parameters for the natural model.