Nonlinear Oscillation of a Magnetically Levitated Body.

Abstract

The pair of nonlinear differential equations which governs the bouncing and pitching oscillations of a simple levitated body is solved by using the method of the harmonic balance with the help of the spectral analysis of the numerical solution, for the special case when the magnetic lift force changes harmonically in the neighborhood of twice the natural frequency of the bouncing oscillation Ωz, and the natural frequency of the pitching oscillation is equal to Ωz/2. As a result, the bouncing oscillation is not only excited parametrically, but the pitching oscillation is also excited by the internal resonance even if the levitated body shows a symmetry between the front and rear halves. Also, the constant component of the bouncing oscillation occurs in this case. The experimental results are shown to be in qualitative agreement with the theoretical ones.