This thesis is a study of bifurcation trees of periodic motions in a parametric Duffing oscillator. The bifurcation trees from period-1 to period-4 motions are investigated by a semi-analytic method. For the semi-analytic method, the discretization of differential equations of nonlinear dynamical systems is obtained to attain the implicit mapping structure. Following the development of implicit mapping structure, the periodic nodes of periodic motions are computed. The stability and bifurcation conditions are carried out by the eigenvalue analysis. For a better understanding of nonlinear behaviors of periodic motions, the harmonic frequency-amplitude characteristics are presented by the finite Fourier series. Numerical simulations are illustrated to verify the analytical predictions. Based on the comparison of numerical and analytical result, the trajectory, time history, harmonic amplitude and harmonic phase plots of period-1 to period-4 motions are completed.
|Commitee:||Chen, Xin, Kweon, Soondo|
|School:||Southern Illinois University at Edwardsville|
|Department:||Mechanical and Industrial Engineering|
|School Location:||United States -- Illinois|
|Source:||MAI 56/03M(E), Masters Abstracts International|
|Keywords:||Bifurcation trees, Duffing oscillator, Mathieu equation, Nonlinear dynamical systems, Periodic motions|
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