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Unformatted text preview: ng to be underestimated. Overestimates amplitude at antiresonances. • • H v Technique: Best estimate of amplitude at resonances. Causes damping to be estimated best. Best estimate of amplitude at antiresonances. Phase characteristics not altered. • • • 5.2.3.1 Multiple Input Force Analysis/Evaluation
Of the variety of situations that can cause difﬁculties in the computation of the frequency response functions, the highest potential for trouble is the case of coherent inputs. If two of the inputs are fully coherent at one of the analysis frequencies, then there are no unique frequency response functions associated with those inputs at that analysis frequency. Unfortunately, there (529) +UCSDRLRJA CN20263663/664 Revision: June 12, 2001 + are a number of situations where the input cross spectrum matrix [GFF] may be singular at speciﬁc frequencies or frequency intervals. When this happens, the inverse of [GFF] will not exist and Equation (5.28) cannot be used to solve for the frequency response function at those frequencies or in those frequency intervals. First, one of the input autospectra may be zero in amplitude over some frequency interval. When this occurs, then all of the cross spectra in the same row and column in the input cross spectrum matrix [GFF] will also be zero over that frequency interval. Consequently, the input cross spectrum matrix [GFF] will be singular over that frequency interval. Second, two or more of the input signals may be fully coherent over some frequency interval. Although the signals used as inputs to the exciter systems must be uncorrelated random inputs, the response of the structure at resonance, combined with the inability to completely isolate the exciter systems from this response results in the ordinary or conditioned partial coherence functions with values other than zero, particularly, at the system poles. For example, for the two input case, as long as the coherence function between the inputs is not unity at these frequencies, Equation (5.28) can be solved uniquely for the frequency response functions. Note that the auto and cross spectra involved in the calculation of the multiple input case for the estimation of frequency response functions should be computed from analog time data that has been digitized simultaneously. If data is not processed in this manner, many more averages are required to reduce the variance on each individual auto and cross spectrum and the efﬁciency of the multiple input approach to the estimation of frequency response functions will not be as attractive. Finally, numerical problems, which cause the computation of the inverse to be inexact, may be present. This can happen when an autospectrum is near zero in amplitude, when the cross spectra have large dynamic range with respect to the precision of the computer, or when the matrix is illconditioned because of nearly redundant input signals. Due to the form of the equations that must be solved to compute frequency r...
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This note was uploaded on 09/29/2013 for the course MECHANICAL ME taught by Professor Regalla during the Fall '11 term at Birla Institute of Technology & Science, Pilani  Hyderabad.
 Fall '11
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