Research On Nonlinear Dynamic Of Chaotic And Bifurcation For Axially Moving Thin Plate In Magnetic Field

The axially moving plate exists widely in our lives and actual engineering projects.From escalator, transport tape, saw bland and paper which can be seen everywhere toflexible spacecraft and flexible manipulator that are rich in high-tech, axially moving plateplays important roles in them. With the rapid development of science and technology levelin recent decades magneto-elastic theory got a booming development. Especially, thestudy on axially moving current-conducting thin plate in magnetic field become a hot spot.The aim of the thesis focuses on the bifurcation and chaos behavior of axially moving thinplate in transverse magnetic field were derived by theoretical analysis and numericalcalculation.Firstly, considering geometric nonlinear, based on the expressions of total kinetic energy,strain energy and virtual work done by external force of the thin plate, the nonlinearmagneto-elastic vibration equations of axially moving thin plate were derived by usingHamilton principle. Based on the Maxwell equations and the corresponding electromagne-tic relations, the electromagnetic forces expressions and moments expressions of electro-magnetic forces for axially moving current-conducting strip thin plate in magnetic fieldwere derived.Secondly, the primary resonance, superharmonic resonance and subharmonic resonanceof strip thin plate which is simply supported on two opposite edges in transverse magneticfield was studied. Considering the primary resonance, superharmonic resonance andsubharmonic resonance, the bifurcation-response equation and the corresponding transiti-on variety of universal unfolding were derived by means of the multi-scale method, impro-ved multi-scale method and singularity theory.Finally, numerical simulation of primary resonance, superharmonic resonance and sub-harmonic resonance of strip thin plate was carried out to plot the bifurcation diagrams,corresponding maximum Lyapunov exponent diagrams and Poincaré map with respect tothe bifurcation parameters such as magnetic induction intensity, axial speed, external forceand external force frequency. The influences of different bifurcation parameters on period motion, period doubling motion and chaotic motion of resonance system were analyzed.The results show that the complex dynamic behaviors of resonance system can be control-led by changing the corresponding parameters.