基于Hilbert变换的模态密度获取研究

提出了在试验获取模态密度时引入Hilbert变换来提高精度的方法,使用两种方法在不同边界条件下对一块薄板的模态密度获取进行了试验研究,这两种方法分别是加速度原点频响函数虚部平均值法和引入Hilbert变换平均值法。并将两种方法的获取结果与数值计算结果进行了对比分析。结果表明,引入实测加速度原点频响函数的实部Hilbert变换求解模态密度时,平均样本数目增加了一倍,比仅用实测加速度原点频响函数的虚部计算的结果更接近于理论和数值计算结果。

Research on the extraction of modal density based on Hilbert transform

A method for improving accuracy of extracting modal density by including Hilbert transform of real part of acceleration frequency response function was proposed. Experimental studies on modal density of a thin plate were carried out with different boundary conditions. Modal densities were obtained by the imaginary part as well as the average of imaginary part and Hilbert transform of real part of acceleration frequency response function. The results obtained by the experiments were compared with the simulation results. It is shown that the number of samples is doubled when Hilbert transform of real part is included. Modal densities obtained by the average of imaginary part and Hilbert transform of real part are closer to the theory and simulation results.