Abstract
The instability regions of the response of a damped, softening-type Duffing oscillator to a parametric excitation are determined via an algorithm that uses Floquet theory to evaluate the stability of second-order approximate analytical solutions in the neighborhood of the non-linear resonances of the system. It is shown that identification of the locus of instabilities of the periodic approximate solutions in the amplitude-frequency parameter space provides valuable information on the overall dynamic behavior of the system. The predictions are verified by using analog- and digital-computer simulations, which exhibit chaos and unbounded motions among other behaviors.
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