### Abstract

In high-Tc superconducting magnetic levitation systems, a levitated body can keep stable levitation with no control. However, due to its low damping, the nonlinearity of the electromagnetic force can give rise to notable effects upon motion of the levitated body. Furthermore, the structure of such a levitated body can show elastic deformation if the large electromagnetic force acts on it. Thus, nonlinear characteristics can easily appear in elastic oscillation as follows. When the excitation frequency is the sum of natural frequencies of two modes, both of the two modes can resonate simultaneously. This phenomenon is called combination resonance. When the excitation frequency is a multiple of some mode's natural frequency, that mode can resonate. This phenomenon is called autoparametric resonance. These two resonances derive from the nonlinearity of the electromagnetic force. This research investigates how these two nonlinear resonances affect each other by using a beam that is levitated above superconducting bulks. From numerical and experimental results, it is figured out that, in fact, the above two nonlinear resonances cannot occur simultaneously and transition between them arises, under some conditions.

Original language | English |
---|---|

Article number | 3600604 |

Journal | IEEE Transactions on Applied Superconductivity |

Volume | 23 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2013 |

### Fingerprint

### Keywords

- Bifurcation
- magnetic levitation
- nonlinear equations
- vibrations

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Condensed Matter Physics
- Electronic, Optical and Magnetic Materials

### Cite this

*IEEE Transactions on Applied Superconductivity*,

*23*(3), [3600604]. https://doi.org/10.1109/TASC.2012.2233251

**Transition between nonlinear oscillations of an elastic body levitated above high-Tc superconducting bulks.** / Sasaki, Masahiko; Takabayashi, Tadahiro; Sugiura, Toshihiko.

Research output: Contribution to journal › Article

*IEEE Transactions on Applied Superconductivity*, vol. 23, no. 3, 3600604. https://doi.org/10.1109/TASC.2012.2233251

}

TY - JOUR

T1 - Transition between nonlinear oscillations of an elastic body levitated above high-Tc superconducting bulks

AU - Sasaki, Masahiko

AU - Takabayashi, Tadahiro

AU - Sugiura, Toshihiko

PY - 2013

Y1 - 2013

N2 - In high-Tc superconducting magnetic levitation systems, a levitated body can keep stable levitation with no control. However, due to its low damping, the nonlinearity of the electromagnetic force can give rise to notable effects upon motion of the levitated body. Furthermore, the structure of such a levitated body can show elastic deformation if the large electromagnetic force acts on it. Thus, nonlinear characteristics can easily appear in elastic oscillation as follows. When the excitation frequency is the sum of natural frequencies of two modes, both of the two modes can resonate simultaneously. This phenomenon is called combination resonance. When the excitation frequency is a multiple of some mode's natural frequency, that mode can resonate. This phenomenon is called autoparametric resonance. These two resonances derive from the nonlinearity of the electromagnetic force. This research investigates how these two nonlinear resonances affect each other by using a beam that is levitated above superconducting bulks. From numerical and experimental results, it is figured out that, in fact, the above two nonlinear resonances cannot occur simultaneously and transition between them arises, under some conditions.

AB - In high-Tc superconducting magnetic levitation systems, a levitated body can keep stable levitation with no control. However, due to its low damping, the nonlinearity of the electromagnetic force can give rise to notable effects upon motion of the levitated body. Furthermore, the structure of such a levitated body can show elastic deformation if the large electromagnetic force acts on it. Thus, nonlinear characteristics can easily appear in elastic oscillation as follows. When the excitation frequency is the sum of natural frequencies of two modes, both of the two modes can resonate simultaneously. This phenomenon is called combination resonance. When the excitation frequency is a multiple of some mode's natural frequency, that mode can resonate. This phenomenon is called autoparametric resonance. These two resonances derive from the nonlinearity of the electromagnetic force. This research investigates how these two nonlinear resonances affect each other by using a beam that is levitated above superconducting bulks. From numerical and experimental results, it is figured out that, in fact, the above two nonlinear resonances cannot occur simultaneously and transition between them arises, under some conditions.

KW - Bifurcation

KW - magnetic levitation

KW - nonlinear equations

KW - vibrations

UR - http://www.scopus.com/inward/record.url?scp=84873304781&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84873304781&partnerID=8YFLogxK

U2 - 10.1109/TASC.2012.2233251

DO - 10.1109/TASC.2012.2233251

M3 - Article

AN - SCOPUS:84873304781

VL - 23

JO - IEEE Transactions on Applied Superconductivity

JF - IEEE Transactions on Applied Superconductivity

SN - 1051-8223

IS - 3

M1 - 3600604

ER -