Cables may experience noticeable oscillation by "motion-induced" and/or "parametric excitation
" [14, 15].
Equations (26) are typical nonlinear equations governing the vibrations of generalized coordinates undergoing external excitation with frequency [OMEGA] and parametric excitation
with frequency [[OMEGA].sub.1].
Zhang and Zhu analyzed the stability and dynamic response of viscoelastic belt under parametric excitation
by the multiscale method [30,31].
The effect of the tunnel tube on the cable is simplified as a parametric excitation
[T.sub.p] cos [[omega].sub.p]t, and the ends of the cable are hinged [2, 14], where [T.sub.p] is the dynamic tension acting on the cable induced by the motion of the tube, and [[omega].sub.p] is the parametric excitation
The specific behaviour of the microwave effect--its dependence on the modulation frequency whereas the effect is evident at the EEG frequencies close or lower than the modulation frequency--leads us to the idea that the parametric excitation
would be a suitable mechanism for the effect.
Based on the literature , using bifurcation theory and nonlinear vibration theory, the coupling effect on parametric excitation
and external force to the cable vibration is studied.
This phenomenon is to be explained by parametric excitation
of the induction machine .
Lulinsky for their paper entitled "Parametric Excitation
of Flexural Vibrations of Micro Beams by Fringing Electrostatic Fields".
Tong, "Principal response of van der pol-duffing oscillator under combined deterministic and random parametric excitation
," Applied Mathematics and Mechanics, vol.
The chaotic behaviors of a relative rotation nonlinear dynamical system under parametric excitation
and its control were studied in [10,11].
Ozhan and Pakdemirli  considered the primary parametric resonance of the parametric excitation
of nonlinear continuous system.
Different from the external incentive system, in the parametric excitation
system, when the frequency of the excitation is equal to multiple system natural frequency of a certain order, small incentives can also stimulate alarge system response [1-3].