DETERMINATION OF FREQUENCY RESPONSE FUNCTIONS FROM RESPONSE MEASUREMENTS—II. REGENERATION OF FREQUENCY RESPONSE FROM POLES AND ZEROS

Abstract

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 tracked in response measurements, without the necessity of measuring the forcing function, but ould allow better estimates to be made of this forcing function by an inverse filtering process (as compared with assuming that the FRF is unchanged). The changes in the FRF are obtained in terms of the poles and zeros rather than the more common pole/residue model, using a cepstral curve fitting process as described in a companion paper. The effect of out-of-band modes on the in-band FRF, during such development, is investigated. It is found that they basically determinej the slope of the FRF and that a magnitude equaliser in the form of a group of ‘phantom zeros’ may be applied unchanged over a range of FRF variation. This magnitude equaliser may be determined either from a finite element model or from initial measurements of the FRF where the force is measured. Such measurements might be made under somewhat different conditions, such as on a stationary machine, after which the process described here could be used to update the FRF estimate under operating conditions. The method used to track the changes in the poles and zeros with the magnitude equaliser to regenerate a revised FRF as changes proceed. A free-free beam was chosen as the object of study. A slot was cut in the middle of the beam with depth varying in steps up to more that half the thickness to simulate the gradual development of changes in natural frequencies 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 modified FRFs fully.