DETERMINATION OF FREQUENCY-RESPONSE FUNCTIONS FROM RESPONSE MEASUREMENTS .2. REGENERATION OF FREQUENCY-RESPONSE FUNCTIONS FROM POLES AND ZEROS

This paper proposes a complete method to track changes in a frequency response function (FRF) which might be caused by a variety of reasons such as the development of local material damage. The changes are trac ked in response measurements, without the necessity of measuring the f orcing function, but would allow better estimates to be made of this f orcing function by an inverse filtering process (as compared with assu ming that the FRF is unchanged). The changes in the FRF are obtained i n terms of the poles and zeros rather than the more common pole/residu e model, using a cepstral curve fitting process as described in a comp anion paper. The effect of out-of-band modes on the in-band FRF, durin g such development, is investigated. It is found that they basically d etermine the slope of the FRF and that a magnitude equaliser in the fo rm of a group of phantom zeros' may be applied unchanged over a range of FRF variation. This magnitude equaliser may be determined either fr om a finite element model or from initial measurements of the FRF wher e the force is measured. Such measurements might be made under somewha t different conditions, such as on a stationary machine, after which t he process described here could be used to update the FRF estimate und er operating conditions. The method used to track the changes in the p oles and zeros (via the cepstrum) loses information on scaling, and so three scaling methods are introduced and compared. It is next discuss ed how to combine the tracked in-band poles and zeros with the magnitu de equaliser to regenerate a revised FRF as changes proceed. A free-fr ee beam was chosen as the object of study. A slot was cut in the middl e of the beam with depth varying in steps up to more than half the thi ckness to simulate the gradual development of changes in natural frequ encies up to 10 per cent. The position of the slot was chosen so that only the symmetric modes changed in frequency, while the antisymmetric modes remained unchanged, and the method was able to reproduce the mo dified FRFs fully. (C) 1996 Academic Press Limited.