摘要
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 stability problems of linear systems subjected to weak parametric excitations, this paper tries to establish efficient and general approaches. A quantitative relation that assures linear systems to avoid resonance was derived in state space. Owing to employing this expression to omit the secular terms in the method of multiple scales, the stability analysis concerned turns out to solving some low order algebraic equations. The stable requirements and unstable regions were explicitly obtained. Considering the linear superposition principles, the authors briefly explain the idea and steps of employing the presented approach to the case of excitations of multiple frequencies. The approach is not only suit for the linear systems with both damping and gyroscopic effects, but also can be extended to those problems with complex parametric matrices and systems of weak non linearity. The analyses on rotor systems with asymmetric disk show that the presented method is correct and efficient.
出处
《清华大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
1999年第11期46-49,共4页
Journal of Tsinghua University(Science and Technology)
基金
国家自然科学基金
清华大学青年基金
关键词
弱参数激励
稳定性
线性系统
振动
多自由度系统
weak parametric excitation
stability analysis
condition to avoid resonance
methods of multiple scales
excitations of different frequencies
