Residue Estimation from Frequency Response Functions by Synthesized Signals

This paper deals with residue estimations from measured Frequency Response Functions (FRF) once nafural frequencies and damping ratios have been evaluated The residue vector or matrix (&pending on the number of the column or rows used in the FRF matrix for the identrJication procedure) can be achieved by means of functions synthesized with the modal parameters mentioned above. These functions are used in order to form (as in the last step of the Prony method) a rectangular matrix, whose order depends on the considered spectral lines and on the number of modes (or vice versa). This last matrix, with the vector (or matrix) of the measured frequency response functions, allows one to obtain the residue vector (or matrix). Impulse respome truncation at the end of the observation window gives rise to biased residues both in magnitude and in phase, when they are derived by fitting a frequency response function or when they are achieved by functions directly synthesized in the frequency domain. On the contrary, if the functions are synthesized in the time domain, the residues can be estimated without any bias.