液体火箭纵向耦合振动特性的快速求解方法

Fast Matrix Algorithm for POGO Instability Prediction in Liquid Rocket

针对POGO稳定性分析方法中矩阵法难以进行特征值求解这一问题,在其基础上对扰动力的阻抗函数矩阵进行有理多项式逼近,采用引入辅助变量的技术,将结构与推进耦合系统的控制方程等效地变换成与结构动力学方程一致的形式,因此可以通过快速求解矩阵特征值来确定耦合系统的动力学特性,判断系统的稳定性。经过验证,此方法不仅求解快速,且具有很高的精度。

Matrix Algorithm is by far the most accurate one regarding the POGO instability prediction problem, but it can be too complicated to solve directly. Based on the Matrix Algorithm, the approximation of the impedance matrix of the exciting force is carried out by using rational fit method and the governing transfer functions of the coupled structure- propulsion system is converted into the form of typical structural dynamic equations with the aid of auxiliary variables. In this way, eigenvalues of POG0 system can be obtained much faster with almost the same accuracy as Matrix Algorithm, and relevant dynamics properties and stability of the coupled system can be determined conveniently.