In recent years, a number of modal identification methods based on continuous wavelet transform (CWT) have been developed. The time variation of the instantaneous amplitude and phase of each mode component within measured signals can be considered by time-frequency representation. In the time-frequency plane, wavelet analysis decomposes the measured signals into a series of curves called ridges which directly express the amplitude and phase of each mode component within the measured signals. Thus, by the extraction of ridges and the value of CWT along the ridges, modal parameters are identified from the measured signals. The measured signals are free-decay responses of mechanical structures which are processed by time-frequency transform. In this process, the challenge is to determine ridges exactly. When the frequency window of CWT includes closely spaced natural frequencies, the ridge is distorted and a pseudo mode is generated.
Existing methods for modal identification by CWT give correct results when the frequency window includes one natural frequency. Thus, it is necessary to build a theoretical basis for correctly determining closely spaced natural frequencies by considering the distortion of ridges and determining the reasonable bandwidth when the frequency window includes two closely spaced natural frequencies.
Ri Yong Ho, a researcher at the Science Engineering Institute, has proposed a formula for mathematically considering the distortion of characteristics of a ridge when the frequency window includes two close mode components, and conducted a numerical simulation on MATLAB to verify it.
The simulation verified the accuracy of the proposed formula.
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