Principal Response of Van der Pol-Duffing Oscillator Under Combined Deterministic and Random Parametric Exciation
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摘要: 研究了Vander Pol-Duffing振子在谐和与随机噪声联合激励下的参数主共振响应和稳定性问题。用多尺度法分离了系统的快变项,并求出了系统的最大Liapunov指数和稳态概率密度函数,还分析了失稳、分叉和跳跃现象,讨论了系统的阻尼项、非线性项、随机项和确定性参激强度等参数对系统响应的影响。数值模拟表明所提出的方法是有效的。
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关键词:
- 参数主共振 /
- Vander Pol-Duffing振子 /
- 多尺度法 /
- 最大Liapunov指数 /
- 稳态概率密度
Abstract: The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated.The method of multiple scales was used to determine the equations of modulation of amplitude and phase.The behavior,stability and bifurcation of steady state response were studied.Jumps were shown to occur under some conditions.The effects of damping,detuning,bandwidth,and magnitudes of deterministic and random excitations are analyzed. The theoretical analysis were verified by numerical results. -
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