非自伴随动力学系统的工况模态分析

Operational modal analysis of non-self-adjoint dynamic system

非自伴随动力学系统主要存在于转子动力学、自激颤振和反馈控制中,伴随着系数矩阵的对称性破坏而出现。非自伴随系统动力学特征信息的辨识在颤振的预测、控制律的识别、结构动力学特性的优化等方面尤为重要。然而工程中的非自伴随动力学系统,如受稳流风载的大跨度桥梁、高速飞行的飞行器、转子动力学系统、汽车的制动系统,由于系统的激励信息未知,只能依靠系统的响应信号对系统进行辨识。该研究围绕非自伴随动力学系统的工况模态分析展开,首先推导了非自伴随动力学系统在白噪声激励下响应的相关函数与系统自由衰减响应之间的等价关系;继而将迭代整体最小二乘算法引入到相关函数的辨识中;最后通过两自由度桥梁节段模型和多自由度系统的算例验证了方法的有效性。

Non-self-adjoint dynamical system commonly appears in rotor dynamics,flutter analysis and control synthesis,where the symmetry of the system matrices are destroyed.The asymmetry of the system matrices leads to challenges to system identification when the difference arises between the right and left eigenvectors corresponding to the same eigenvalue.The identification of non-self-adjoint system is of great importance for the prediction of flutter boundary,the identification of control law,the optimal design of structures etc.However,for the non-self-adjoint system in engineering(e.g.bridge flutter,the aerodynamic drag forces acting on airplane wings and fuselages,the forces acting on the rotor in turbines,brake system of a vehicle),the identification is based on the output data of the system because of the unknown input data.This research concerns the operational modal analysis(OMA)of a typical non-self-adjoint system.Specifically,the equivalence between the correlation functions of random responses and the free decay responses of the original structure is proved for the non-self-adjoint system.The ERA method is applied to reconstruct the non-self-adjoint system.Case examples on the identification of a six-degree-of-freedom system and the flutter derivatives of bridge sections are performed to validate the method.