Abstract
In this paper, analytical routes of periodic motions to chaos in a parametric, quadratic oscillator are investigated. The analytical solutions of period-m motions in such a parametric oscillator are presented from the finite term Fourier series, and the stability and bifurcation of the period-m motions are discussed through the eigenvalue analysis. The routes of periodic motions to chaos in such parametric oscillator are illustrated through harmonic amplitudes varying with excitation amplitude in the finite term Fourier series solution. From the routes of period-m motion to chaos, numerical illustrations of periodic motions are given through trajectories and analytical harmonic amplitude spectrum.
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