摘要
假设陀螺力、Ｒａｙｌｅｉｇｈ阻尼和有势力分别依赖于某些参数，用瑞利商考察这些参数的变化如何影响约束阻尼系统稳定性。三个新定理表明，陀螺力、Ｒａｙｌｅｉｇｈ阻尼和有势力对约束阻尼系统的作用与非约束阻尼系统相比有本质不同：１）足够大的陀螺力既可以使约束阻尼系统渐近稳定，也可能使约束阻尼系统失稳，其作用效果取决于陀螺力矩阵和约束阻尼矩阵的性质；２）Ｒａｙｌｅｉｇｈ阻尼过小会使约束阻尼系统失稳，而大Ｒａｙｌｅｉｇｈ阻尼对系统稳定性的影响取决于Ｐｏｉｎｃａｒｅ稳定系数的符号；３）有势力的大小会影响系统的稳定性。
It is assumed that the gyroscopic, potential forces and Rayleigh damping depend on the parameters, respectively. The stability of the systems with constraint damping under the influence of the varying parameters is studied by means of the Rayleigh quotients. Three new theorems show that the essential distincitions of the influence of the gyroscopic, potential forces and Rayleigh damping on the stability of the systems with constraint damping from the systems without constraint damping are: ① The systems with constraint damping may be asymptotically stable as well as unstable under sufficiently large gyroscopic force, depending on the characters of the gyroscopic and constraint damping matrices. ② The systems with constraint damping are unstable under sufficiently small Rayleigh damping. The influence of sufficiently large Rayleigh damping on the stability of the systems depends upon the positive or negative signs of the poincare stability coefficients. ③ The value of the potential force has influence on the stability of the systems with constraint damping.
出处
《清华大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
1998年第11期84-86,共3页
Journal of Tsinghua University(Science and Technology)
基金
国家自然科学基金
关键词
稳定性
约束阻尼系统
陀螺力
Rayleigh阻尼
stability of motion
constraint damping systems
gyroscopic force
Rayleigh damping
