谐和与随机噪声联合激励下Duffing-van der Pol系统的响应  

Response of Duffing-van der Pol Oscillator under Combined Harmonic and Random Parametric Excitations

作　　者：仲淑娟[1] 王坤[1] 吴海花[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《河北师范大学学报（自然科学版）》2011年第5期460-463,468,共5页Journal of Hebei Normal University：Natural Science

基　　金：国家杰出青年科学基金(60525303)

摘　　要：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.

关 键 词：Duffing-van der Pol系统 多尺度法 奇异性理论 随机噪声 

分 类 号：O324[理学—一般力学与力学基础]