摘要
根据模态综合法并借助二阶非完整约束系统的Routh型方程,建立了考虑全部代数和微分对接条件下,非线性转子—支承系统的运动微分方程。然后采用一种新的等效线性化技术,求解系统的次谐共振,大大简化了分析过程并提高了计算效率。通过对对接条件之作用的定量研究,结果表明:微分对接条件对次谐共振影响较大,而由不独立的微分对接条件转化得来的代数对接条件,对次谐共振影响很小;考虑微分对接条件,能明显提高方法的收敛速度。因此,应当考虑微分对接条件,尽管这会增加推导工作量和综合后矩阵的阶数,但并不影响计算效率。
With the aid of Routh＇s equation for non-holonomic constraints the motion equations of a nonlinear rotor-bearing system are derived by the modal synthesis method, considering all the algebraic and the differential linking conditions. Sub-harmonic resonance of the system are solved by an equivalent linearization method, which transforms the problem from solving differential equations into solving algebraic equations. This technique significantly simplified the analysis procedures and improves the computational efficiency. The effect of the differential linking condition on sub-harmonic resonance are studied quantitatively by analyzing the computational results fitting different kinds of the linking conditions. The results show that the differential linking conditions have a significant influence on sub-harmonic resonance. Thus, the differential linking conditions need to satisfy, which does not affect the computational efficiency even though the derivation effort and assembled matrix rank are increased.
出处
《工程力学》
EI
CSCD
北大核心
2006年第4期62-66,共5页
Engineering Mechanics
基金
陕西省教育厅专项科研计划资助项目(01JK138)
关键词
次谐共振
微分对接条件
模态综合法
非线性
转子-支承系统
sub-harmonic resonance
differential linking condition
the modal synthesis method
nonlinearity
rotor-bearing system
