Study on bifurcation and chaotic motion of a strongly nonlinear torsional vibration system under combination harmonic excitations
By using dissipative system Lagrange equation, the strongly nonlinear dynamic equation of torsional vibration system is deduced, which contains a class of square and cube nonlinear rigidity and combination harmonic excitations. Bifurcation characteristics of the strongly nonlinear system are analyzed in the autonomous and non-autonomous situations by means of singular point stability theory and singularity theory, respectively. The bifurcation diagram of system response corresponding to the change of torsional rigidity is derived by using numerical simulations, and evolution process of period, period doubling and chaotic motions is studied. Finally, chaotic motion is further verified by the maximum Lyapunov exponent, phase trajectory and Poincare map.
Keywords: Strongly Nonlinear, Torsional Vibration, Bifurcations, Chaos
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ABOUT THE AUTHOR
Wenming Zhang
He was born in 1979. He received the M.Sc. and Ph.D. degrees in Instrument Science and Technology from Yanshan University, China, in 2006 and 2010, respectively. He is currently an instructor in the Electrical Engineering Department at the Yanshan University, China. His research interests include nonlinear system vision and dynamics.
Wenming Zhang
He was born in 1979. He received the M.Sc. and Ph.D. degrees in Instrument Science and Technology from Yanshan University, China, in 2006 and 2010, respectively. He is currently an instructor in the Electrical Engineering Department at the Yanshan University, China. His research interests include nonlinear system vision and dynamics.
