# gff ik cross power spectrum between inputs i and

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Unformatted text preview: inputs is correlated with the other input(s). [ Λ ] represents the eigenvalues of the [GFF] matrix. If any of the eigenvalues of the [GFF] matrix are zero or insigniﬁcant, then the [GFF] matrix is singular. Therefore, for a three input test, the [GFF] matrix should have three eigenvalues. (The number of eigenvalues is the number of uncorrelated inputs). This concept is shown graphically in Figure 5-8 for the auto power spectra for a three input case. It is difﬁcult to determine if the inputs are mutually correlated from these plots. Figure 5-9 shows the principal force plots for the same case. At the frequencies where the third principal/virtual force drops (lowest curve), this indicates that the inputs are mutually correlated at those frequencies. This is not apparent from Figure 5-8. (5-32) +UC-SDRL-RJA CN-20-263-663/664 Revision: June 12, 2001 + 10 -4 Gxx : 1z,1z 10 -5 Magnitude 10 -6 10 -7 10 -8 0 50 100 150 200 250 Frequency, Hz 300 350 400 10 -4 Gxx : 2z,2z 10 -5 Magnitude 10 -6 10 -7 10 -8 0 50 100 150 200 250 Frequency, Hz 300 350 400 10 -4 Gxx : 3z,3z 10 -5 Magnitude 10 -6 10 -7 10 -8 0 50 100 150 200 250 Frequency, Hz 300 350 400 Figure 5-8. AutoPower Spectrum of Input Forces (5-33) +UC-SDRL-RJA CN-20-263-663/664 Revision: June 12, 2001 + 10 -4 Principal Force Analysis 10 -5 Magnitude 10 -6 10 -7 10 -8 10 -9 0 50 100 150 200 250 Frequency, Hz 300 350 400 Figure 5-9. Principal (Virtual) Force Spectrum Optimum Number Of Inputs The location and number of inputs has a direct effect on the quality of frequency response functions that are estimated. This is an area that has not been researched completely and is still being reviewed. It is clear that beyond some number of inputs, the return from the investment of more equipment, in the form of inputs, is not warranted. Some considerations are: • Two at symmetric locations. Frequency response functions can be added or subtracted to enhance in phase or out of phase modes. To excite as many modes as possible in one test conﬁguration. • (5-34) +UC-SDRL-RJA CN-20-263-663/664 Revision: June 12, 2001 + • • Two vertical and one horizontal on a car. One on each wing and one on each horizontal stabilizer, all symmetric, on an aircraft structure. • To excite "operating" conditions. 5.3 Excitation Excitation includes any form of input that is used to create a response in a mechanical system. This can include environmental or operational inputs as well as the controlled force input(s) that are used in a vibration or modal analysis test. In general, the following discussion will be limited to the force inputs that can be measured and/or controlled in some rigorous way. With respect to frequency response function measurements to be used in experimental modal analysis, the excitation normally is applied using shakers or with impact devices (hammers). For those excitation signals that require the use of a shaker, Figure 5-10 shows a typical test conﬁguration; Figure 5-11 shows a typical test conﬁ...
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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.

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