基于多复域的频响函数灵敏度分析

Sensitivity analysis of frequency response functions based on multicomplex domain

频响函数灵敏度分析被广泛应用于结构模型修正、损伤识别及振动控制等领域。考虑结构频率响应中已存在虚部,该研究提出了一种基于多复域的频响函数灵敏度分析方法。首先,构造设计参数所在的复域,并在该复域上对设计参数进行虚部摄动。然后,将多复域上的运动控制方程与灵敏度分析方程扩展为实数矩阵表达,实现频率响应与设计参数所在复域的解耦,从而同步求解结构的频响函数及对应的灵敏度。最后,以多自由度弹簧质量系统与GARTEUR桁架结构为研究对象进行数值仿真分析,验证多复域频响函数灵敏度分析方法的正确性。结果表明,相较于传统的实数域有限差分法,多复域方法具有更高的分析精度,且所提方法对参数摄动量减小引起的误差不敏感,该方法能够为复杂结构的频响函数灵敏度分析提供更加准确的结果。

Sensitivity analysis of frequency response functions(FRFs)is widely used in structural model updating,damage identification and vibration control.Based on the traditional original complex domain for structural frequency response analysis,a multi-complex domain-based sensitivity analysis method of FRFs was proposed.Firstly,a second complex domain for design parameter perturbation was constructed.Then,the equations of motion and sensitivity analysis in the multicomplex domain were extended and expressed by real-matrix formulas,the FRFs and corresponding sensitivities were calculated simultaneously.Finally,a multi-freedom spring-mass system and a GARTEUR truss were taken as examples to verify the accuracy of the proposed method.The results show that the proposed multi-complex domain sensitivity analysis method is more accurate than the classical finite difference method.The proposed method is insensitive to the perturbation size of the design parameter.The method provides more accurate results for the FRFs sensitivity analysis of complex structures.