含外激励van der Pol-Mathieu方程的非线性动力学特性分析1)

黄建亮, 王腾, 陈树辉

NONLINEAR DYNAMIC ANALYSIS OF A VAN DER POL-MATHIEU EQUATION WITH EXTERNAL EXCITATION1)

Huang Jianliang, Wang Teng, Chen Shuhui

表2 利用两时间尺度IHB法求出在图3中三个点$\omega=0.987 35,0.985,1.02$处的$\omega_{\rm d}$和$\tilde{A}_{1,-1},\tilde{A}_{1,0},\tilde{A}_{1,1}$

Table 2 A prior unknown $\omega_{\rm d}$ and three amplitudes $\tilde{A}_{1,-1}$, $\tilde{A}_{1,0}$, and $\tilde{A}_{1,1}$ in frequency response curves of the van der Pol-Mathieu equation with external excitation that are calculated by the IHB method with two time-scales at the three points $\omega=0.987 35,0.985,1.02$ in Fig.3