风力驱动下带有参激、外激和自激的双塔系统的动力学行为

摘要

Using the asymptotic perturbation method, the averaged equations of a two-tower system under wind-induced parametric, external and self-excitation are obtained with the case of 1:2 internal resonance.With the aid of Hurwitz criterion, the stability and local bifurcations of the averaged equations are investigated.All the critical bifurcation values of the parameters and the types of the eigenvalues of the jacobian of the initial equilibrium solu-tion are studied.According to the signal of the real part of the eigenvalues or the maple programs provided by Yu Pei, the stability and local bifurcations of the initial equilibrium solution, in the vicinity of the critical bifurcation values of the parameters, can be easily analyzed.%对于风力驱动下带有参数激励、外部激励和自激的双塔模型，运用近似扰动法得到模型在1∶2共振条件下的平均方程。借助于霍尔维茨准则分析平均方程的稳定性和分岔情况，得到关于参数的所有临界分岔值和各临界分岔值下雅克比矩阵的特征值类型，从而根据特征值实部的正负号，或者郁培提出的maple程序分析在一些参数临界值附近小扰动下初始平衡点的稳定性和分岔情况。