Abstract
The principal resonance of a Duffing oscillator to combined deterministic and narrow-band random parametric excitations is investigated. In particular, the case in which the parametric terms share close frequencies is examined. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response are studied by means of qualitative analyses. Jumps are shown to occur if the random excitation is small. The effects of damping, detuning, and magnitudes of deterministic and narrow-band parametric excitations are analyzed. The theoretical analyses are verified by numerical results.
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