In this paper, the nonlinear vibration and chaotic motion of the axially moving current-conducting thin plate under external harmonic force in magnetic field is studied. Improved multiple-scale method is employed to derive the strongly nonlinear subharmonic resonance bifurcation-response equation of the strip thin plate in transverse magnetic field. By using the singularity theory, the corresponding transition variety and bifurcation, which contain two parameters of the universal unfolding for this nonlinear system, are obtained. Numerical simulations are carried out to plot the bifurcation diagrams, corresponding maximum Lyapunov exponent diagrams, and dynamical response diagrams with respect to the bifurcation parameters such as magnetic induction intensity, axial tension, external load, external excited frequency, and axial speed. The influences of different bifurcation parameters on period motion, period times motion, and chaotic motion behaviors of subharmonic resonance system are analyzed. The results show that the complex dynamic behaviors of resonance system can be controlled by changing the corresponding parameters.
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March 2015
Research-Article
Strongly Nonlinear Subharmonic Resonance and Chaotic Motion of Axially Moving Thin Plate in Magnetic Field
Hu Yuda,
Hu Yuda
1
Key Laboratory of Mechanical Reliability
for Heavy Equipments
and Large Structures of Hebei Province,
e-mail: huyuda03@163.com
for Heavy Equipments
and Large Structures of Hebei Province,
Yanshan University
,Qinhuangdao 066004
, China
e-mail: huyuda03@163.com
1Corresponding author.
Search for other works by this author on:
Hu Peng,
Inspection and Technical Research,
Hu Peng
Shanghai Institute of Special Equipment
Inspection and Technical Research,
Shanghai 200333
, China
Laboratory of Mechanical Reliability
for Heavy Equipments
and Large Structures of Hebei Province,
e-mail: hupenghhu@163.com
for Heavy Equipments
and Large Structures of Hebei Province,
Yanshan University
,Qinhuangdao 066004
, China
e-mail: hupenghhu@163.com
Search for other works by this author on:
Zhang Jinzhi
Zhang Jinzhi
Key Laboratory of Mechanical Reliability
for Heavy Equipments
and Large Structures of Hebei Province,
e-mail: zhangjinzhi86@163.com
for Heavy Equipments
and Large Structures of Hebei Province,
Yanshan University
,Qinhuangdao 066004
, China
e-mail: zhangjinzhi86@163.com
Search for other works by this author on:
Hu Yuda
Key Laboratory of Mechanical Reliability
for Heavy Equipments
and Large Structures of Hebei Province,
e-mail: huyuda03@163.com
for Heavy Equipments
and Large Structures of Hebei Province,
Yanshan University
,Qinhuangdao 066004
, China
e-mail: huyuda03@163.com
Hu Peng
Shanghai Institute of Special Equipment
Inspection and Technical Research,
Shanghai 200333
, China
Laboratory of Mechanical Reliability
for Heavy Equipments
and Large Structures of Hebei Province,
e-mail: hupenghhu@163.com
for Heavy Equipments
and Large Structures of Hebei Province,
Yanshan University
,Qinhuangdao 066004
, China
e-mail: hupenghhu@163.com
Zhang Jinzhi
Key Laboratory of Mechanical Reliability
for Heavy Equipments
and Large Structures of Hebei Province,
e-mail: zhangjinzhi86@163.com
for Heavy Equipments
and Large Structures of Hebei Province,
Yanshan University
,Qinhuangdao 066004
, China
e-mail: zhangjinzhi86@163.com
1Corresponding author.
Manuscript received November 20, 2013; final manuscript received April 19, 2014; published online January 12, 2015. Assoc. Editor: D. Dane Quinn.
J. Comput. Nonlinear Dynam. Mar 2015, 10(2): 021010 (12 pages)
Published Online: March 1, 2015
Article history
Received:
November 20, 2013
Revision Received:
April 19, 2014
Online:
January 12, 2015
Citation
Yuda, H., Peng, H., and Jinzhi, Z. (March 1, 2015). "Strongly Nonlinear Subharmonic Resonance and Chaotic Motion of Axially Moving Thin Plate in Magnetic Field." ASME. J. Comput. Nonlinear Dynam. March 2015; 10(2): 021010. https://doi.org/10.1115/1.4027490
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