摘要
研究了Duffing振子在窄带随机噪声激励下的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,讨论了系统的阻尼项、随机项等对系统响应的影响· 在一定条件下。
The principal resonance of Duffing oscillator to narrow_band random parametric excitation was 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 by means of qualitative analyses. The effects of damping, detuning, bandwidth and magnitudes of deterministic and random excitations were analyzed. The theoretical analyses were verified by numerical results. Theoretical analyses and numerical simulations show that when the intensity of the random excitation increases, the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle. Under some conditions the system may have two steady state solutions.
出处
《应用数学和力学》
EI
CSCD
北大核心
2003年第7期723-729,共7页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(10072049
19972054)
广东省自然科学基金资助项目(000017)
上海交通大学振动
冲击
噪声国家重点实验室开放基金(VSN_2002_04)
关键词
DUFFING振子
主共振
多尺度法
principal resonance
Duffing oscillator
multiple scale method
