一类机电耦合非线性动力系统的余维2动态分岔

利用含有参数的可逆线性变换和近恒同非线性变换,得到一类机电耦合非线性系统的最简规范形。进一步,得到了该系统的普适开折以及开折参数与原系统参数之间的关系。讨论了该系统的余维2分岔,揭示了各参数对机电耦合系统动力学行为的影响,对系统的参数设计、稳定运行和故障诊断提供了理论依据。给出了该机电耦合系统的数值仿真结果,验证了理论分析结果。

CODIMENSION-2 DYNAMICAL BIFURCATION OF AN ELECTROMECHANICAL COUPLED NONLINEAR DYNAMIC SYSTEM

Applying a reversible linear transformation and a near-identity nonlinear transformation with parameters,the simplest normal form of an electromechanical coupled nonlinear dynamic system was developed.Furthermore,its universal unfolding and the relationship between parameters of this system and those of the original system were also obtained.The codimension-two bifurcation was analyzed and the effect of each parameter on the dynamic behavior of the system mentioned above was revealed,which laid a theoretical foundation for parameter design,stable operation and fault diagnosis of a real system.The numerical simulating result of the electromechanical coupled nonlinear dynamic system was obtained,which verified the corresponding theoretical analysis result.