不确定转子系统动力特性的区间分析方法

Interval analysis method for dynamical properties of rotor system with uncertain parameters

为了研究含不确定参数转子系统的动力特性,提出一种非概率区间分析方法对转子系统进行分析.基于区间数学和区间摄动理论,建立转子系统固有频率的计算公式,用区间分析方法得到了固有频率随系统参数的变化关系,得出了转子临界转速的变化范围.该方法降低了传统的概率分析方法对不确定参数信息的过分要求,为解决含有不确定参数的转子系统的动力特性问题提供了一个新途径.数值算例证明了本文所得结果的有效性,与传统概率方法比较,区间分析方法具有精度高,计算量小等优点.

In order to study the dynamical properties of rotor system with uncertain parameters,a non-probabilistic interval analysis method was proposed to analyze the rotor system.Based on the interval mathematics and interval perturbation theory,the calculation formula of natural frequencies of rotor was established.The variation relationship of natural frequencies with the system parameters was obtained with the interval analysis method,and the variation range of critical speed of rotor was attained.The proposed method decreases the excessive requirements in the uncertain parameter information in the traditional probability analysis,which can provide a new way to solve the dynamical property problems of rotor system with uncertain parameters.The numerical examples prove the validity of the results in the proposed method.The interval analysis method possesses such advantages as high accuracy and low calculated amount.