简谐与随机噪声联合激励下Van der Pol-Duffing系统的响应  

Response of Van der Pol-Duffing Oscillator to Combined Excitation of Harmonic and Ran dom Inputs

作　　者：戎海武[1,2] 王向东[1] 孟光[2] 徐伟[3] 方同[3] 

机构地区：[1]佛山大学数学系,佛山528000 [2]上海交通大学振动、冲击、噪声国家重点实验室,上海200030 [3]西北工业大学数学系,西安710072

出　　处：《振动工程学报》2003年第4期502-505,共4页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(编号 :10 0 72 0 49;199972 0 54);广东省自然科学基金资助项目 (编号 :0 0 0 0 17);上海交通大学振动;冲击;噪声国家重点实验室开放基金资助项目 (编号 :VSN-2 0 0 2 -0 4)

摘　　要：研究了 Van der Pol-Duffing振子在简谐与随机噪声联合激励下的响应问题。用参数变换法使方程出现小参数 ,用多尺度法分离系统的快变项 ,讨论系统的阻尼项、非线性项和随机项等参数对系统响应的影响。理论分析和数值模拟表明 ,当随机激励强度增大时 ,系统的响应可从一个极限环变为一个扩散的极限环 ;在一定的条件下 ,系统可有两个稳定的稳态解及随机跳跃现象。The principal resonance of Van der Pol D uffing oscillator to combined harmonic and random excitations is inves t igated. A new expansion parameter ε=ε(,u 0) is defined, enabling low ord er solution to be obtained for the stron g non linear case. The method of multi ple metrics is used to determine the equ a tions of modulation of amplitude and pha se. The effects of damping, detuning, ba ndwidth, and magnitudes of random excita tions are analyzed. The theoretical anal yses are verified by numerical results. Theoretical analyses and numerical simul ations show that when the intensity of t he random excitation increases, the nont r ivial steady state solution may change f rom a limit cycle to a diffused limit cy cle. Under certain conditions the system ma y have two steady state solutions. Rando m jump may also be observed.

关 键 词：Van der Pol—Duffing振子 简谐运动 随机噪声激励 参数变换法 多尺度法 非线性振动 

分 类 号：O32[理学—一般力学与力学基础]