Spider DSA User’s Manual
186
Note that the coherence can also be stated as the product of an FRF with its
inverse function. That is, if H
xy
measures a process going from input, x, to output,
y, H
yx
characterizes the same process, but treats y as the input and x as the output.
=
This product definition indicates the coherence represents an “energy round trip”
or a reflection through the process. We apply G
xx
to H
xy
and get G
xy
at the output.
Then we conjugate G
xy
(to flip it or reflect x(t) in time) and pass it through H
yx.
In
a perfect world, this would result in exactly G
xx
as the output of H
yx
.
If the system is linear and none of our measurements are contaminated by noise,
the trip is perfect, and we get back everything we put in. That is, the coherence
will be exactly 1.0. If the system is non-linear or if extraneous noise has been
interjected, the round-trip will be less efficient and the coherence will be less than
one (but never more).
Thus, the coherence is always between 0 and 1. A coherence of 1.0 means the
output is perfectly explained by the input (i.e. the system is linear). A coherence of
0 means the output and input are unrelated. Values in-between state the fraction
of measured output power explained by the measured input power and a linear
process. Experienced analysts always use the coherence measurement to quantify
the quality of an FRF measurement at every frequency.
Shock Response Spectrum
The Shock Response Spectrum (SRS) is an entirely different type of spectral
measurement. It is used access the damage potential of a transient event such as a
package drop or an earthquake. The SRS was first proposed by Dr. Maurice Biot
in 1932. The SRS is not the spectrum of the pulse. (The FFT provides this.) The
SRS is not a linear operator as the FFT is. That is, an SRS does not uniquely define
a single waveform. Many very different transient time-histories can produce the
same SRS.
What the Shock Response Spectrum is, is the representative response of a class of
simple structures to the given transient acceleration time-history. This response is
provided by simulating a group of spring-mass-damper systems sitting on a
common rigid base that is forced to move with the measured acceleration of the
subject shock pulse. Each single degree-of-freedom (SDOF) spring-mass-damper
has a different natural frequency; they all have the same damping factor. The
spectrum is formed by plotting the extreme motion (acceleration) experienced by
each mass against its resonance frequency.
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