Simplified analysis method for inherent frequency and stability of rotational symmetric structure

一种旋转对称结构固有频率和稳定性的简化分析方法

Abstract

The invention discloses a simplified analysis method for an inherent frequency and the stability of a rotational symmetric structure. The method comprises the steps of establishing a complete dynamic differential equation of a system, a dynamic differential equation adopting a no-extension hypothesis, and a dynamic differential equation adopting an extension hypothesis: establishing the complete dynamic differential equation of the system; establishing the dynamic differential equation adopting the no-extension hypothesis; establishing the dynamic differential equation adopting the extension hypothesis; introducing coordinate conversion for converting the three dynamic differential equations to a support follow-up coordinate system so as to obtain corresponding three constant coefficient partial differential dynamic equations; performing discrete processing on the three constant coefficient partial differential dynamic equations in the support follow-up coordinate system to obtain three constant differential matrix equations; obtaining an eigenvalue of the complete dynamic differential equation and eigenvalues of two simplified dynamic differential equations; and analyzing a parametrically excited vibration mode characteristic and a dynamic stability change law of the rotational symmetric structure according to the three eigenvalues. According to the method, a specific analysis expression of system eigenvalues can be obtained more clearly.
一种旋转对称结构固有频率和稳定性的简化分析方法:分别建立系统的完整动力学微分方程、采用无延展假设的动力学微分方程和延展假设的动力学微分方程,包括:建立系统的完整动力学微分方程;建立采用无延展假设的动力学微分方程;建立采用延展假设的动力学微分方程;引入坐标变换将三个动力学微分方程转换到支撑随动坐标系下,得到相对应的三个常系数偏微分动力学方程;将支撑随动坐标系下的三个常系数偏微分动力学方程离散处理为三个常微分矩阵方程;分别得到一个完整动力学微分方程的特征值和两个简化动力学微分方程的特征值;根据三个特征值分析旋转对称结构的参激振动模态特性和动力稳定性变化规律。本发明能够更清晰的得到系统特征值的具体解析表达式。

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