基于伪频响函数矩阵法的运行模态分析方法

Operational Modal Analysis Method Based on the Pseudo Frequency Response Function Matrix

基于传递率测量的伪频响函数法运行模态分析技术无需白噪声激励假设,具有强"谐波模态抑制"能力,但其模态识别结果依赖待分析伪频响函数的选取、稳定性欠佳。为解决该问题,建立了基于伪频响函数矩阵法的运行模态分析方法。该方法首先构造多参考测点、多参考工况的伪频响函数矩阵,然后基于伪频响函数矩阵采用最小二乘复频域法求解模态频率和阻尼比、基于传递率函数矩阵求解模态振型,最后通过建立相应的稳态图并结合以多参考测点平均的传递率函数矩阵第2阶奇异值的倒数为基础的模态指示函数来确定模态阶数与最终的模态结果。5自由度质量-弹簧-阻尼系统仿真结果及自由梁的运行模态试验结果均表明,提出方法既继承了基于伪频响函数法的运行模态分析方法的强"谐波模态抑制"能力,亦能有效解决伪频响函数法识别结果稳定性欠佳的问题、一定程度上提高模态识别精度,且更利于自动化。

The operational modal analysis(OMA) technique based on the pseudo frequency response function(PFRF) method by the use of transmissibility measurements does not require the white noise excitation assumption, and has strong ability of harmonic modes rejection. However, its modal identification results depend on the selection of the PFRF to be analyzed, the stability needs to be improved. To solve this issue, an OMA method based on the pseudo frequency response function matrix(PFRFM) method is proposed. Firstly, the PFRFM with multiple reference measurement points and multiple reference loading conditions is constructed.Subsequently, the least squares complex frequency domain method is applied to the PFRFM to extract the modal frequencies and damping ratios, the transmissibility matrices are used to extract the modal shapes. Finally, the number of modes and the final modal results are determined by combing the stabilization diagram with the modal indicator function that is built on the arithmetic mean of the reciprocal of the second singular values about the transmissibility matrices with different references. The results of simulations for a 5 DOF mass-spring-damping system and experiments for a free beam demonstrate that the proposed method not only inherits the strong ability of harmonic modes rejection, but also can effectively solve the problem of insufficient stability of identification results of the PFRF method, obtain higher precision modal results to a certain extent, and is more conducive to automation.