In this thesis, the approximate analytical solutions of period-m motions in the periodically forced van der Pol oscillator are obtained by the generalized harmonic balanced method. Such an approximate analytical solution of periodic motion is given by the Fourier series expression, and the convergence of such an expression is guaranteed by the Fourier theory of periodic solution. The stability and bifurcation analysis of the period-m solutions is completed through the eigenvalue analysis of the coefficient dynamics of the Fourier series expressions of periodic solutions, and numerical and analytical predictions of period-m motions are compared to verify the analytical solutions of periodic motions. The displacement, velocity, trajectories and analytical harmonic amplitude spectrum for stable and unstable periodic motions are presented. The harmonic amplitude spectrum shows the harmonic term effects on periodic motions, and one can directly know which harmonic terms contribute on periodic motions and the convergence of the Fourier series expression is clearly illustrated.
|Advisor:||Luo, Albert C. J.|
|Commitee:||Kweon, Soondo, Lu, Chunqing|
|School:||Southern Illinois University at Edwardsville|
|Department:||Mechanical and Industrial Engineering|
|School Location:||United States -- Illinois|
|Source:||MAI 52/02M(E), Masters Abstracts International|
|Keywords:||Bifurcation theory, Eigenvalue analysis, Generalized harmonic balance method, Nonlinear dynamics, Van der pol oscillator|
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