转子动响应灵敏度分析的多复域摄动法  

Multi-complex domain perturbation method for sensitivity analysis of rotor dynamic response

作　　者：姜东[1] 王贞露 钱慧 杭晓晨 曹芝腑 朱锐 JIANG Dong;WANG Zhenlu;QIAN Hui;HANG Xiaochen;CAO Zhifu;ZHU Rui(School of Mechanical and Electronic Engineering,Nanjing Forestry University,Nanjing 210037,China;College of Aerospace Engineering,Chongqing University,Chongqing 400044,China;School of Engineering and Design,Technical University of Munich,Munich 80539,Germany)

机构地区：[1]南京林业大学机械电子工程学院,江苏南京210037 [2]重庆大学航空航天学院,重庆400044 [3]慕尼黑工业大学工程与设计学院,慕尼黑80539

出　　处：《振动工程学报》2025年第3期469-479,共11页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(11602112,52202445);江苏高校“青蓝工程”优秀青年骨干教师项目;江苏省高校自然科学基金资助项目(20KJB460003)。

摘　　要：动响应灵敏度分析广泛应用于转子模型修正、参数识别和结构优化等问题。本文提出了一种基于多复域摄动的转子动响应一阶、二阶和混合灵敏度分析方法。分别在两个复数方向对设计参数进行摄动,得到双复数域的转子系统动力学方程,运用柯西-黎曼矩阵将复数运动方程扩维得到等价实数运动方程,求解等价实数运动方程,从而同时得到系统响应、一阶灵敏度和二阶灵敏度,并获得动响应灵敏度的Hessian矩阵。以单盘转子系统和燃气发生器转子系统为研究对象进行数值仿真分析,验证所提转子动响应灵敏度分析方法的正确性。相较于传统的有限差分法,多复域摄动法对摄动步长引起误差的不敏感,求解精度更高。Rotor dynamic response sensitivity analysis is widely used in rotor model updating,parameter identification and structural optimization.In this paper,a first-order,second-order and mixed sensitivity analysis method for dynamic response of rotor system based on multi-complex domain perturbation method is proposed.The design parameters are perturbed in two complex directions respectively,and the motion equation of the rotor system in the double complex domain is obtained.Using the real matrix expression of the complex number,the complex motion equation is extended to obtain the equivalent real motion equation.By solving the equivalent real motion equation,the system response,first-order sensitivity and second-order sensitivity can be obtained simultaneously,and the Hessian matrix of dynamic response sensitivity can also be obtained.The numerical simulation analysis of singledisk rotor system and gas generator rotor system is carried out to verify the correctness of the rotor dynamic response sensitivity analysis method of multi-complex domain perturbation method.Compared with the traditional finite difference method,the multicomplex domain perturbation method shows insensitivity to the error caused by the perturbation step size,and the solution accuracy is higher.

关 键 词：转子动响应 多复域摄动法 二阶灵敏度 混合灵敏度 

分 类 号：O347.6[理学—固体力学]