Modal bifurcation in a high-Tc superconducting levitation system

D. Taguchi, S. Fujiwara, Toshihiko Sugiura

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

This paper deals with modal bifurcation of a multi-degree-of-freedom high-Tc superconducting levitation system. As modeling of large-scale high-Tc superconducting levitation applications, where plural superconducting bulks are often used, it can be helpful to consider a system constituting of multiple oscillators magnetically coupled with each other. This paper investigates nonlinear dynamics of two permanent magnets levitated above high-Tc superconducting bulks and placed between two fixed permanent magnets without contact. First, the nonlinear equations of motion of the levitated magnets were derived. Then the method of averaging was applied to them. It can be found from the obtained solutions that this nonlinear two degree-of-freedom system can have two asymmetric modes, in addition to a symmetric mode and an antisymmetric mode both of which also exist in the linearized system. One of the backbone curves in the frequency response shows a modal bifurcation where the two stable asymmetric modes mentioned above appear with destabilization of the antisymmetric mode, thus leading to modal localization. These analytical predictions have been confirmed in our numerical analysis and experiments of free vibration and forced vibration. These results, never predicted by linear analysis, can be important for application of high-Tc superconducting levitation systems.

Original languageEnglish
Article number055006
JournalSuperconductor Science and Technology
Volume24
Issue number5
DOIs
Publication statusPublished - 2011 May

Fingerprint

levitation
Permanent magnets
Bifurcation (mathematics)
Nonlinear equations
Equations of motion
Frequency response
Magnets
Numerical analysis
permanent magnets
degrees of freedom
forced vibration
free vibration
destabilization
Experiments
frequency response
nonlinear equations
numerical analysis
equations of motion
magnets
oscillators

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics
  • Ceramics and Composites
  • Materials Chemistry
  • Metals and Alloys

Cite this

Modal bifurcation in a high-Tc superconducting levitation system. / Taguchi, D.; Fujiwara, S.; Sugiura, Toshihiko.

In: Superconductor Science and Technology, Vol. 24, No. 5, 055006, 05.2011.

Research output: Contribution to journalArticle

@article{3c6a176f280140db871410f8ed2a6ecd,
title = "Modal bifurcation in a high-Tc superconducting levitation system",
abstract = "This paper deals with modal bifurcation of a multi-degree-of-freedom high-Tc superconducting levitation system. As modeling of large-scale high-Tc superconducting levitation applications, where plural superconducting bulks are often used, it can be helpful to consider a system constituting of multiple oscillators magnetically coupled with each other. This paper investigates nonlinear dynamics of two permanent magnets levitated above high-Tc superconducting bulks and placed between two fixed permanent magnets without contact. First, the nonlinear equations of motion of the levitated magnets were derived. Then the method of averaging was applied to them. It can be found from the obtained solutions that this nonlinear two degree-of-freedom system can have two asymmetric modes, in addition to a symmetric mode and an antisymmetric mode both of which also exist in the linearized system. One of the backbone curves in the frequency response shows a modal bifurcation where the two stable asymmetric modes mentioned above appear with destabilization of the antisymmetric mode, thus leading to modal localization. These analytical predictions have been confirmed in our numerical analysis and experiments of free vibration and forced vibration. These results, never predicted by linear analysis, can be important for application of high-Tc superconducting levitation systems.",
author = "D. Taguchi and S. Fujiwara and Toshihiko Sugiura",
year = "2011",
month = "5",
doi = "10.1088/0953-2048/24/5/055006",
language = "English",
volume = "24",
journal = "Superconductor Science and Technology",
issn = "0953-2048",
publisher = "IOP Publishing Ltd.",
number = "5",

}

TY - JOUR

T1 - Modal bifurcation in a high-Tc superconducting levitation system

AU - Taguchi, D.

AU - Fujiwara, S.

AU - Sugiura, Toshihiko

PY - 2011/5

Y1 - 2011/5

N2 - This paper deals with modal bifurcation of a multi-degree-of-freedom high-Tc superconducting levitation system. As modeling of large-scale high-Tc superconducting levitation applications, where plural superconducting bulks are often used, it can be helpful to consider a system constituting of multiple oscillators magnetically coupled with each other. This paper investigates nonlinear dynamics of two permanent magnets levitated above high-Tc superconducting bulks and placed between two fixed permanent magnets without contact. First, the nonlinear equations of motion of the levitated magnets were derived. Then the method of averaging was applied to them. It can be found from the obtained solutions that this nonlinear two degree-of-freedom system can have two asymmetric modes, in addition to a symmetric mode and an antisymmetric mode both of which also exist in the linearized system. One of the backbone curves in the frequency response shows a modal bifurcation where the two stable asymmetric modes mentioned above appear with destabilization of the antisymmetric mode, thus leading to modal localization. These analytical predictions have been confirmed in our numerical analysis and experiments of free vibration and forced vibration. These results, never predicted by linear analysis, can be important for application of high-Tc superconducting levitation systems.

AB - This paper deals with modal bifurcation of a multi-degree-of-freedom high-Tc superconducting levitation system. As modeling of large-scale high-Tc superconducting levitation applications, where plural superconducting bulks are often used, it can be helpful to consider a system constituting of multiple oscillators magnetically coupled with each other. This paper investigates nonlinear dynamics of two permanent magnets levitated above high-Tc superconducting bulks and placed between two fixed permanent magnets without contact. First, the nonlinear equations of motion of the levitated magnets were derived. Then the method of averaging was applied to them. It can be found from the obtained solutions that this nonlinear two degree-of-freedom system can have two asymmetric modes, in addition to a symmetric mode and an antisymmetric mode both of which also exist in the linearized system. One of the backbone curves in the frequency response shows a modal bifurcation where the two stable asymmetric modes mentioned above appear with destabilization of the antisymmetric mode, thus leading to modal localization. These analytical predictions have been confirmed in our numerical analysis and experiments of free vibration and forced vibration. These results, never predicted by linear analysis, can be important for application of high-Tc superconducting levitation systems.

UR - http://www.scopus.com/inward/record.url?scp=79955004754&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955004754&partnerID=8YFLogxK

U2 - 10.1088/0953-2048/24/5/055006

DO - 10.1088/0953-2048/24/5/055006

M3 - Article

AN - SCOPUS:79955004754

VL - 24

JO - Superconductor Science and Technology

JF - Superconductor Science and Technology

SN - 0953-2048

IS - 5

M1 - 055006

ER -