Strongly Nonlinear Subharmonic Resonance and Chaotic Motion of Axially Moving Thin Plate in Magnetic Field

Abstract

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.