5.3. REFERENCES 105
frequency, magnitude, and phase components vs. frequency, and polar real vs. imaginary
components. Authenticity of an estimated mode is then judged on the basis of quality of
the plots.
2. e SDOF modal FRF is also formed from exact mathematical solution of the estimated
effective dynamic system. Graphical comparison of this result with the above left-handed
product information offers further means of authentic vs. junk” mode discrimination.
3. Finally, a coherence metric based on comparison of the results of “1” and “2” provides a
0–100% figure of merit for estimated experimental modes.
5.3 REFERENCES
[1] R. E. D., Bishop and G. M. L. Gladwell, An investigation into the theory of resonance
testing, Philosophical Transactions, Royal Society of London, Series A, 225(A-1055):241–
280, 1963. DOI: 10.1098/rsta.1963.0004. 85
[2] D. L. Brown and R. J. Allemang, e modern era of experimental modal analysis, Sound
and Vibration Magazine, January 2007. 85
[3] A. G. Piersol and T. L. Paez, Eds., Harris’ Shock and Vibration Handbook, 6th ed.,
McGraw-Hill, 2010. 85, 91
[4] R. Mayes and S. Klenke, e SMAC modal parameter extraction package, IMAC XVII,
1999. 92
[5] R. N. Coppolino, A simultaneous frequency domain technique for estimation of modal
parameters from measured data, SAE Paper 811046, 1981. DOI: 10.4271/811046. 92,
93
[6] R. N. Coppolino and R. C. Stroud, A global technique for estimation of modal param-
eters from measured data, SAE Paper 851926, 1985. DOI: 10.4271/851926. 93
[7] R. N. Coppolino, Efficient and enhanced options for experimental mode identification,
IMAC XXI, 2003. 92, 93
[8] R. Penrose, A generalized inverse for matrices, Proc. of the Cambridge Philosophical Society,
51:406–13, 1955. DOI: 10.1017/s0305004100030401. 92
[9] G. H. Golub and C. Reinsch, Singular value decomposition and least squares solutions,
Numerische Mathematik, 14:403–420, 1970. DOI: 10.1007/bf02163027. 93
[10] K. Miller, Complex linear least squares, SIAM Review, 15(4):706–726, 1973. DOI:
10.1137/1015094. 93
106 5. EXPERIMENTAL MODAL ANALYSIS
[11] Load analysis of spacecraft and payloads, NASA-STD-5002, 1996. 96
[12] Independent structural loads analysis, U.S. Air Force Space Command, SMC-S-004, 2008.
96
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