92 5. EXPERIMENTAL MODAL ANALYSIS
5.1.6 CLOSURE
Several intuitive experimental modal analysis tools have been described. SDOF frequency re-
sponse functions displayed in three ways, namely: (1) magnitude and phase components vs. fre-
quency; (2) real and imaginary components vs. frequency (also called co- and quad- functions);
and (3) polar real vs. imaginary components vs. frequency. All three display types provide intu-
itive, well-known means for estimation of modal frequency and damping parameters. Review
of FRFs associated with individual FRFs for actual MDOF systems offer some insights for es-
timation of modal frequency and damping parameters when modes are well separated (not the
case for the ISPE test article and other shell-type structures).
Global skyline functions offer some insight into the presence of multiple modes in a des-
ignated frequency band. However, such functions do not necessarily highlight the presence of
localized modes. A more comprehensive approach involving review of many or all measured
FRF response functions is a tedious, time-consuming endeavor.
5.2 PART 2: THE SIMULTANEOUS FREQUENCY DOMAIN
METHOD
5.2.1 INTRODUCTION
Difficulties encountered by NASA/MSFC on the Integrated Spacecraft Payload Element
(ISPE) modal survey in the fall of 2016 bring an important challenge to the forefront. Specifi-
cally, which estimated test modes are “authentic,” and which modes are due to “noise” associated
with measured FRFs? e present discussion on experimental modal analysis (EMA) focuses
on mathematical isolation of individual estimated test mode FRFs in a manner that is similar to
the concept developed by Mayes and Klenke [4]. While the presently discussed EMA approach
ought to be quite independent of the investigator’s choice of experimental modal analysis algo-
rithm, the results herein apply to methods that explicitly estimate the tested system’s state-space
plant matrix such as the Simultaneous Frequency Domain (SFD) method [5–7].
e latest version of SFD (SFD-2018) employs mathematical operations aimed at isolat-
ing individual candidate experimental modes without direct reliance on information associated
with the subject system’s TAM) mass matrix. e key to mathematical and visual isolation of
individual modes from measured data is the left-hand eigenvector. Virtually all modern experi-
mental modal analysis techniques produce estimates of (right-hand) eigenvectors and eigenval-
ues (modal frequency and damping). While techniques for estimation of left-hand eigenvec-
tors are well-known (e.g., the “real mode transpose times TAM mass matrix product” and the
Moore–Penrose pseudo-inverse [8]), they have been judged inadequate. e purest approach to
estimation of left-hand eigenvectors is a consequence specifically those techniques that estimate
the measured system’s plant or effective dynamic system matrix, such as SFD. Since a complete
set of raw experimental modes are identified consistent with the order of the estimated plant, the
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