Closely spaced modes identification through modified frequency domain decomposition

In practical engineering, power spectral density is always used to identify structural dynamic properties by picking peak points. However, the peaks in the spectral curve are not easy to be determined sometimes. A lot of peaks in the curve would cause some peaks close, which induces the closely spaced modes. The damping ratio is another reason to generate closely spaced modes, because the damping can make some peaks merge together. This paper proposes an innovative method to identify the closely spaced modes. First, the formulation is derived to reveal the components of the closely spaced modes in the power spectral density based on frequency domain decomposition. Then singular vector comparison is presented to determine whether there are closely spaced modes or not, where an angle criterion between two vectors is proposed. Finally, a numerical example is used to validate the effectiveness of the proposed method. The results show that the angle criterion can find the independent and dependent modes. For the close peak points in the spectral curve, the angle can determine that the points are single or closely spaced modes. Therefore, the proposed method to identify the closely spaced modes is efficient.