Volume 43 Issue 8
Aug.  2022
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LU Lian, REN Weixin, WANG Shidong. Structural Instantaneous Frequency Identification Based on the Fractional Fourier Transform[J]. Applied Mathematics and Mechanics, 2022, 43(8): 825-834. doi: 10.21656/1000-0887.420241
Citation: LU Lian, REN Weixin, WANG Shidong. Structural Instantaneous Frequency Identification Based on the Fractional Fourier Transform[J]. Applied Mathematics and Mechanics, 2022, 43(8): 825-834. doi: 10.21656/1000-0887.420241

Structural Instantaneous Frequency Identification Based on the Fractional Fourier Transform

doi: 10.21656/1000-0887.420241
  • Received Date: 2021-08-12
  • Accepted Date: 2021-12-01
  • Rev Recd Date: 2021-11-25
  • Available Online: 2022-06-30
  • Publish Date: 2022-08-01
  • To identify the instantaneous frequencies of time-varying signals, the theoretical relationship between the frequency and rotational angle α in a signal was derived based on the definition of the fractional Fourier transform. Then the fractional Fourier transform was interpreted to be essentially an algorithm combining the ordinary Fourier transform with the dilation and translation window. A general expression of the signal instantaneous frequency in the fractional Fourier domain was thereafter formulated so that the structural instantaneous frequency can be extracted accordingly. The feasibility and reliability of the proposed method were verified with a simulated nonlinear frequency modulation signal and a numerical example of a 3DOF damped time-varying structure system. The results show that, the results of the proposed method are in good agreement with the theoretical values, and the method has a certain degree of anti-noise capability. Subsequently, the proposed method is applicable to the identification of the instantaneous frequencies of time-varying structures.

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