广义Van der Pol型强非线性共振的转迁集

Transition Boundary with Generalized Van der Pol Type Strong Nonlinear Co vibration

用改进的Ｌ－Ｐ方法，引入参数变换α＝（εｑ２ω１）／（ｐ２ω２０＋εｑ２ω１），同时用多尺度法求出广义ＶａｎｄｅｒＰｏｌ型强非线性主振、亚谐和次谐共振的分岔响应方程和转迁集，得出主振、ｋ≠１／２的亚谐和次谐具有相同的分岔拓扑结构，而ｋ＝１／２的亚谐振动的分岔结构更加复杂。

The improved L-P method is used, and parameter transformation α=εq 2ω 1/(p 2ω 2 0+εq 2ω 1) is drawn. By means of the multiple scale method, the branching response equation and transition boundary are obtained with the Van der Pol type strong Nonlinear main vibration, sub resonance, and second resonance. The conclusions are: the main vibration, the sub resonance with k≠1/2, and second resonance have the same branching topology structure, and the branching structure of the second resonance vibration would be more complicated when k=1/2 .