耦合相对转动非线性动力系统的稳定性与近似解

研究了一类含三次非线性耦合项的相对转动非线性动力系统的动力学行为. 建立了具有非线性弹性力、广义摩阻力耦合项的系统动力学方程. 运用多尺度法求解谐波激励下耦合非自治系统的近似解，通过讨论系统的主共振和内共振特性，分析了耦合项对系统响应的影响. 应用奇异性理论研究了主振稳态响应分岔方程的稳定性，得到了系统的转迁集和分岔曲线的拓扑结构. 关键词： 相对转动 非线性耦合动力系统 奇异性理论 稳定性

Stability and approximate solution of a relative-rotation nonlinear dynamical system with coupled terms

The dynamic behaviors of a relative-rotation nonlinear dynamic system with cubic coupled terms are studied. First, the dynamic equation of coupled system with nonlinear elastic force and generalized friction and harmonic excitation is deduced. The approximate solution of coupled unautonomous equation under harmonic excitation is obtained by the method of multiple scales. The effect of coupled terms on system resonance is analyzed in respect of principal resonance and internal resonance. The singularity stability of bifurcation function of principal resonance is studied by singularity theory, and the transfer concourse and topological structure of bifurcation function are obtained.