Study on Bifurcation and Chaotic Motion of a Strongly Nonlinear Torsional Vibration System under Combination Harmonic Excitations
نویسندگان
چکیده
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.
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