水轮发电机定子磁固耦合电磁激发的分岔与混沌

为研究水轮发电机定子系统磁固耦合电磁激发非线性振动，以双壳系统模型作为水轮发电机定子系统的数学模型，应用非线性多尺度法分析水轮发电机定子双壳系统在电磁力作用下的主共振问题，并进行数值计算．结果表明，随着激励幅值的增大和阻尼的减小，系统主共振稳态响应的振幅增大．按照奇异性方法得到系统主共振分岔响应方程在开折参数和物理参数平面的转迁集和分岔图．利用Melnikov方法得到系统可能出现混沌运动的临界值．

Bifurcation and Chaos Excited by Electromagnetism Force of Magnetism and Solid Coupling of Hydroelectric-Generator Stator System

A double-shell model of a hydroelectric-generator stator system was adopted as a mathematical model to investigate the nonlinear vibration of magnetism and solid coupling of the hydroelectric-generator stator system excited by electromagnetism force. Numerical analysis of the primary resonance of magnetism and solid coupling of a hydroelectric-generator stator system by the method of multiple scales for nonlinear oscillations indicated that while the excitation amplitude increased and damping decreased, the amplitude of the primary resonance of the system increased. By analyzing the bifurcation equation of the system based on the theory of singularity, the transition varieties and bifurcation diagrams of the physical and unfolding parametric plane were derived, respectively. Applying Melnikov's method, possible chaotic motion condition of the system was obtained.