基于数值解的非线性振动系统定性分析

Qualitative analysis of nonlinear vibration systems based on numerical calculation

针对非线性振动系统定性理论方法对解析解的过分依赖,不能有效地利用数值解对系统的分叉机理等进行深化分析的现状。依靠数值计算原理实现了对部分定性解析方法的数值化,实现对难以解析或不可解析非线性系统的定性分析。利用数值化方法通过对某系统一个类似Flip-NS分叉型的分叉过程进行定性分析,利用数值化的方法求出的近似雅可比矩阵特征值变化规律证明其实质属于Hopf分叉的周期2锁相状态。

Nonlinear qualitative theory methods depend on analytical solutions,so numerical solution cannot be used to analyze bifurcation mechanisms.The numerical realization of partial qualitative analytical methods has been realized by using the principle of numerical calculation.Nonlinear systems that are difficult to analyze or cannot be analyzed could be analyzed qualitatively.The qualitative analysis of a Flip-NS bifurcation process was carried out using the numerical method.The change of the eigenvalue of the approximate Jacobian matrix proves it a double phase-locked state during Hopf bifurcation.