1自由度磁気浮上系のカオス様振動のシミュレーション

抄録

In this paper, a single-degree-of-freedom magnetic levitation dynamical system, the spring of which is composed of a magnetic repulsion force, is numerically analyzed. The magnetic repulsion force is described by the formula : A[D/(B+x)]^P+C, where P=8. This has been reported in our previous paper [ref. (1)]. By means of the free vibration analysis, it was found that the system has soft spring properties and acts like a collision system. When the base on which the system is installed is moved harmonically, the body levitated by the magnetic force shows many kinds of vibrations upon adjusting the system parameters, viz., damping, excitation amplitude and excitation frequency. For a suitable combination of the parameters, an aperiodic vibration occurs after a sequence of doubling-period bifurcations. Several typical aperiodic vibrations are identified as chaotic by examining their bifurcation diagrams, Poincare Maps, Fourier spectra, and fractal dimension analyses.