# To estimate modal characteristics from response

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Unformatted text preview: onse can be modeled as the response of the structure to an excitation signal that is a linear combination of impulsive and step signals. • • • When the excitation autospectrum is uniform, the autospectrum of the response signal is proportional to the square of the modulus of the frequency response function. Using the notation of a pole-zero model, the poles of the response spectrum are the poles of the frequency response, which are the parameters of the system resonances. If the autospectrum is not uniform, then the (5-39) +UC-SDRL-RJA CN-20-263-663/664 Revision: June 12, 2001 + excitation spectrum can be modeled as an analytic function, to a precision comparable to typical experimental error in the measurement of spectra. In this model, the excitation spectrum has poles that account for the nonuniformity of the spectrum amplitude. The response signal, therefore, can be modeled by a spectrum that contains zeros at the zeros of the excitation and the zeros of the frequency response, and contains poles at the poles of the excitation and at the poles of the frequency response. It is obviously important that the force spectrum should have no poles or zeros which coincide with poles of the frequency response. For transient inputs, such as an impact or step relaxation, the assumption of smooth excitation spectra is generally true, but for operating inputs or inputs generated by an exciter system, care must be taken to insure the input force spectrum is smooth. This is especially true for tests performed using a hydraulic or an electro-mechanical exciter, because the system being analyzed may "load" the exciter system (the structure’s impedance is so low that the desired force level cannot be achieved within the constraint of small motion), and this causes a nonuniformity in the input force spectrum. To determine the characteristics of the system from the response, it is necessary that the response have the same poles as the frequency response, or that the analysis process corrects for the zeros and poles of the excitation. If the force input spectrum has a zero in the frequency range of interest, the pole location measured from the response spectrum will not match that of the frequency response. This potential problem is demonstrated in Figure 5-12 for the typical case of shaker excitation. The top ﬁgure is the magnitude of the frequency response function. The middle ﬁgure is the auto power spectrum of the input and the lower ﬁgure is the auto power spectrum of the response. Note that the estimates of modal parameters that would be derived from the auto power spectrum of the response would be quite different from those derived from the frequency response function. (5-40) +UC-SDRL-RJA CN-20-263-663/664 Revision: June 12, 2001 + Figure 5-12. Input Spectrum Example Presently, there is a great deal of interest in determining modal parameters from measured response data taken on operating systems (for example: turbulent ﬂow over an airfoi...
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