Abstract
This paper deals with harmonic oscillations in a nonlinear two-degree-of-freedom system in which natural frequencies are comparatively close. Six kinds of approximated differential equations are derived and the bifurcation analysis are performed using these equations. By comparing the results of theoretical analyses with the results of the numerical simulation, it is clarified that the 2nd-order approximation in the method of multiple scales using the modified detuning parameters is the best approach to analyze the vibration characteristics of this system with a high accuracy. As a result, it is found that undergoing Hopf bifurcation the periodic solution experiences period doubling bifurcations and results in chaos, and that the bifurcation points obtained by this method are in good agreement with the results of numerical simulations.
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