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针对一般多自由度线性系统弱周期参数激励稳定性问题，尝试建立有效而通用的分析方法。运用复模态理论简要推导了线性系统避免共振的定量关系式。以此作为多尺度方法消去久期项的条件，将线性系统单频弱参激振动的稳定性分析转化为求解若干低阶代数方程组，得到了稳定条件与不稳定区域。借助于线性叠加原理，简要阐述了多频弱参数激励问题稳定性分析的思想与步骤。所建立方法不但能够同时处理存在阻尼与陀螺效应的高维系统，而且可推广用于分析复参数矩阵问题与弱非线性系统。对非对称单圆盘转子系统的计算表明所述方法正确、有效。
Aiming at the problem of weak periodic parameter excitation stability of general multi-degree-of-freedom linear system, an effective and general analysis method is attempted. Using complex mode theory, the quantitative relation of resonance avoidance of linear system is deduced. Using this method as a condition for canceling the long term term in a multi-scale method, the stability analysis of the single-frequency weak parametric vibration of the linear system is transformed into solving a series of low-order algebraic equations, and the stable condition and the unstable region are obtained. With the help of the principle of linear superposition, the ideas and steps of stability analysis of multi-frequency weak parameter excitation are briefly described. The proposed method can not only handle high-dimensional systems with damping and gyroscopic effects simultaneously, but also can be used to analyze complex parametric matrix problems and weak nonlinear systems. The calculation of the asymmetrical single disc rotor system shows that the method is correct and effective.