Experiments of " detuned subharmonic resonance " or " tri - wave coupling " were also carried out with the technique of bicoherence analysis
3.
( 3 ) we investigate the nonlinear dynamics of the rotor - ambs system in 1 / 3 and 1 / 2 subharmonic resonances . using the multiple method of scale , the averaged equations of the rotor - ambs system are obtained
4.
By the method of double - frequency acoustic excitations , experiments were conducted on the influences of phase differences between the fundamental and subharmonic waves upon the " subharmonic resonance " - the nonlinear interaction between the waves
5.
For the nonlinear planar cantilever , the two resonant cases are considered . one of the two cases is primary resonance - principal parametric resonance and 1 : 3 internal resonance . the other is 1 / 2 subharmonic resonance - principal parametric resonance and 1 : 3 internal resonance
6.
In chapter 4 , the bifurcation of the complex nonlinear oscillator of van der pol - duffing - mathieu ' s is studied and the common bifurcation property of the oscillator in the situations of nonresonance , principal resonance , ultraharmonic resonance and non - subharmonic resonance is revealed . the bifurcation of strongly nonlinear oscillator is also explored in this chapter
7.
By means of the precise integration method with lagrangian interpolation the trajectory of the shaft center , the poincare mapping and the bifurcation graphs are numerically given . the results predicted by the floquet theory are checked and the long - term dynamic behavior of the system is predicted . it is shown that the system has rich nonlinear behaviors at some m combination of the four parameters , for examples , multi - frequency subharmonic resonance , as well as chaos phenomenon from doubling bifurcation and twice hopf bifurcation
8.
In this paper periodically perturbed hopf bifurcation to lienard equation with limited time delay is sdudied in detail . that is , the influence of small periodic perturbations on system exhibiting hopf bifurcation is sdudied . in particular , the excitation frequency and the critical natural frequency of hopf bifurcation in the cases of harmonic resonance . subharmonic resonance , ultraharmonic resonance , and ultrasubharmonic resonance is discussed . it is shown that in some parameter regions the sestyms exhibit harmonic solution bifurcation , subharmonic solution bifurcation , ultraharmonic solution bifurcation , ultrasubharmonic solution bifurcation and quasi - periodic solution
9.
The second case is 1 / 2 subharmonic resonance - principal parametric resonance and 1 : 1 internal resonance . the final case is primary resonance for the second mode - principal parametric resonance and 1 : 2 internal resonance . the adjoint operator method and the theory of normal form are used to investigated the normal forms in the four dimensional nonlinear systems with cubic nonlinearities
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