Curve fitting of frequency response functions by use of pole-zero models

摘要

Resonance frequencies and modal shapes are obtained analytically for simple structures and by the finite element method, for example, for complex structures. The each resonances are expressed by single-degree-of-freedom (SDOF) systems and measured damping values are added to each SDOF's. By this resonant circuit model, however, responses of the anti-resonances are determined by the parameters of the resonance type SDOF's. Whether this way of handling the damping is accurate enough or not in order to represent the damping characteristics of a real structure is very important. On the application-oriented point of view, there is a trend in recent years that the characteristics of anti-resonances are used as well as those of the resonances for the loss factor measurement. The half-power-width method can be applied for both the resonance and anti-resonances. However, it is impossible to simultaneously obtain the loss factors at both resonances and anti-resonances by applying the curve fitting method, which is based on the above-mentioned resonant circuit model. For this reason, the pole-zero model was proposed for the curve fitting method and new error functions were also proposed. The application of the proposed method to measured frequency response functions of various materials were very successful. This is a report on a series of related studies.