Smoothing Errors in Fourier Transform Based Modal Data Analysis

Many current multimodal curve-fitting algorithms for extracting modal parameters are based on the Fourier transform of structural vibration response to transient and random excitation. The use of the periodic Fourier transform to analyze basically nonperiodic data introduces spurious side lobes in the response spectra, which have the appearance of and may be mistaken for actual modes. A resolution error is also introduced by the Fourier analysis which produces distortion in the vibration response spectra and an over estimate of the damping extracted from such spectra by the conventional methods. Hanning smoothing is often used to suppress the spurious side lobes but only at the expense of increased resolution errors. Theory, describing the effect of Hanning smoothing on power and cross spectra, is presented. Effect of curve fitting unsmoothed and Hanning smoothed cross spectra is described and a method for correcting the damping extracted from such spectra is presented. Viscous damping ratios obtained by the above and other data analysis methods are compared.