Wavelet analysis for identification of damping ratios and natural frequencies

This study addresses the identification of damping ratios and natural frequencies in linear structural dynamic systems. A previously proposed method based on the Morlet wavelet transform of the system's response is investigated analytically. The method can be applied to single- or multi-degree of freedom, lightly or heavily damped systems. It utilizes a relationship between natural frequency, damping ratio and the continuous Morlet wavelet transform of the system response. It is found that the validity of the relationship depends on the scaling factor a, translation factor b, and the frequency parameter ω0 of the Morlet wavelet transform. A general guideline of choosing a, b, and ω0 is provided in this paper. Both numerical and experimental results verify the theoretical analysis.