| 1. | Subharmonic resonance response
分谐波共振响应 |
| 2. | Experiments of " detuned subharmonic resonance " or " tri - wave coupling " were also carried out with the technique of bicoherence analysis
应用双相干分析技术，还实验研究了“失调亚谐共振”或“三波耦合”非线性过程。 |
| 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
( 3 )利用多尺度方法，研究了电磁轴承-转子系统的1 3亚谐共振和1 2亚谐共振情况下的非线性动力学，得出了两种共振情况下的频幅响应方程。 |
| 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
用双频声激励方法，实验研究了剪切流中基波及其亚谐波的相位差对“亚谐共振”非线性过程的影响。 |
| 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
对于平面运动悬臂梁研究了二种共振情况，一是主共振-主参数共振和1 ： 3内共振的情形，另一是1 2亚谐共振-主参数共振和1 ： 3内共振的情形。 |
| 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
第四章对非线性振动中最常见的vanderpol - duffing - mathieu复合非线性振子的分岔性质进行了系统的研究，发现了该复合系统在非共振、主共振、超谐共振和非1 2阶次谐共振情况下具有相同的分岔特性。 |
| 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
通过lagrange插值精细积分法数值给出系统的轴心轨迹图、 poincar映射图、分叉图，检验floquet理论预测结果并预测系统的长期性态，显示系统在四个参数组合的某些范围内具有丰富的非线性特性，还存在多形式次谐波解，以及由倍周期分叉、二次hopf分叉通往混沌的现象。 |
| 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
本文详细研究了具有限时滞li nard方程的周期扰动hopf分支，即在该系统经历hopf分支时，研究小周期扰动对系统的影响，特别是讨论了扰动频率与hopf分支周期解的固有频率在共振、次调和共振、超调和共振、超次调和共振的情形。 |
| 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
第一种共振情况是主共振-主参数共振和1 ： 1内共振的情形；第二种共振情况是1 2亚谐共振-主参数共振和1 ： 1内共振的情形；第三种共振情况是第二模态主共振-主参数共振和1 ： 2内共振的情形。 |
