In this thesis, the bifurcation trees of period-1 to period-2 motions in a periodically forced, nonlinear spring pendulum system are predicted by a semi-analytic method. The differential equations of periodically forced, nonlinear spring pendulum system are discretized for the predication of the semi-analytic method. To obtain the periodic solutions, the corresponding mapping structure of the implicit mapping is presented. Based on the eigenvalue analysis, the corresponding stability of the periodical solutions are shown on the bifurcation trees as well. The harmonic frequency-amplitude for periodical motions are analyzed from the finite discrete Fourier series. From the harmonic amplitudes, the bifurcation trees of periodic motions are presented as well. From the analytical prediction, numerical illustrations of periodic motions are completed, the comparison of numerical solution and analytical solution are given. Through the numerical illustration, the spring possess dynamical behavior of a parametric nonlinear systems, which is different from the pendulum. The method presented in this paper can be applied to other nonlinear dynamical systems to obtain the bifurcation trees of periodic motions to chaos.
|Advisor:||Luo, Albert C.J|
|Commitee:||Chen, Xin, Wang, Fengxia|
|School:||Southern Illinois University at Edwardsville|
|School Location:||United States -- Illinois|
|Source:||MAI 58/04M(E), Masters Abstracts International|
|Subjects:||Engineering, Mechanical engineering|
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