88 5. EXPERIMENTAL MODAL ANALYSIS
FRF Display: Transmissibility 04-Aug-1998 9:27 PM
Magnitude
Magnitude
10
0
10
1
Phase (Deg)
0
Imaginary
0
-10
-20
Imaginary
20
0
-20
Real
20
0
-20
100
-100
0.5
0.9 1.11 0.9 1.11
1.51
Frequency (Hz)
0.9 1.1
-10 0
Real
10
1
Frequency (Hz)
0.9 1.11
Frequency (Hz)
Figure 5.4: SDOF transmissibility, TR.f / vs. f .
A closer examination of the SDOF acceleration FRF reveals some well-known properties
of this (as well as SDOF displacement and transmissibility FRF) response functions, as displayed
in Figure 5.5.
In particular, the red dot near the peak value of the FRF magnitude, imaginary com-
ponent, and polar plot is indicative of the natural frequency, f
n
. In addition, the frequency
spacing of peaks in the imaginary component, indicated by the green dots, facilitates estimation
of damping.
5.1.3 FREQUENCY RESPONSE CHARACTERISTICS OF LINEAR MDOF
SYSTEMS
Consider a structural dynamic system subjected to applied excitation forces,
Œ
M
f
Ru
g
C
Œ
B
f
Pu
g
C
Œ
K
f
u
g
D
Œ
e
f
F
e
g
: (5.10)
Employing the assumption of simple harmonic excitation and responses, in the same man-
ner as employed for SDOF systems, MDOF frequency response to each separate “unit” excita-
tion force is described as
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