期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
Response of Duffing-van der Pol Oscillator under Combined Harmonic and Random Parametric Excitations
摘要/Abstract
研究了一类Duffing-van der Pol系统在谐和与随机噪声联合激励下的主共振响应和稳定性问题.运用多尺度法分离了系统的快慢变量,得到了系统的一阶近似解；运用奇异性理论得到系统是叉形分岔结构；用线性化方法求出了系统响应幅值的一、二阶矩.数值模拟验证了理论结果的有效性.
The principal resonance of Duffing-van der Pol oscillator under combined harmonic and random parametric excitations is investigated.The method of multiple metrics is used to determine the equations of modulation of amplitude an phase.The approximate solution of first order is obtained.The system to respond to the diverge curve is attained by the dynamical characteristic.Accordingly,the linearization process is carried out to determine the steady state moments of the amplitude of the system response.The theoretical analyses are verified with numerical simulation.