This paper presents analytical results of non-linear vibrations of a traveling beam levitated by magnetic forces. The problem is modeled as the Euler-Bernoulli beam with a variable cross section supported by non-linear springs. The beam and the springs move on an undulated line. Introducing a new mode shape function which is expressed as the product of the trigonometric function and the power series truncated to the fourth order and utilizing the galerkin procedure, basic equations are reduced to the coupled non-linear equations. The steady state solutions of the beam was obtained using the harmonic balance method. It is found that the non-linear responses show the type of soft-spring, the unsymmetric support of the spring or the unsymetric cross section to the mid-point of the beam show large amplitude vibrations of a rotating motion and that of a translating motion in relatively large frequency range.
