Introduction to Acoustics

efore the trigger point occurs. This is called a pretrigger
delay.
Modern FFT analyzers provide very high-resolution
(24 bit) analog-to-digital converters (ADCs) and large
capture block sizes (64 kpoint typical). These characteristics
nullify the need to use weighting functions or
windows when performing an impact test. The preferred
analysis is conducted without weighting, also termed
using a rectangular window.
Two common time-domain windows that are used
in impact testing with older equipment are the force
and exponential windows. These windows are applied
to the signals after they are sampled but before the FFT is
applied to them in the analyzer. The force window is used
to remove noise from the force signal. Any nonzero data
following the impulse signal in the sampling window is
assumed to be measurement noise. The force window
preserves the samples in the vicinity of the impulse but
removes the noise from all other samples in the force
signal.
The exponential window is used to reduce leakage in
the spectrum of the response. The FFT analyzer assumes
that the signal is periodic in the transform window. This
is true of signals that are completely contained within
the transform window or cyclic signals that complete
an integer number of cycles within the transform window.
If a time signal is not periodic in the transform
window a smearing of its spectrum will occur when it
is transformed to the frequency domain. This is called
leakage. Leakage distorts the spectrum and makes it inaccurate.
If the response does not decay to zero before
the end of the sampling window, an exponential window
can add artificial damping to all modes of the structure.
This artificial damping must be removed by the subsequent
curve-fitting algorithm to obtain proper damping
factors.
It is important that the impact hammer provides
a pulse that is well matched to the frequency span of
the analysis. This is accomplished by fitting a striking
tip of appropriate stiffness to the hammer’s force
gauge. A soft tip produces a broad pulse time-history
with a narrow spectrum. A hard tip increases the force
spectrum bandwidth by applying a narrow pulse. The
spectrum of the force pulse has a lobed structure and
all tests are done using the spectral content of the first
lobe. Trial measurements are made to select a tip that
provides a force spectrum that falls off no more than
25 dB from the direct-current (DC) point to the selected
analysis bandwidth.
It is often difficult to strike at exactly the same place
and angle multiple times. For this reason, averaging is
Modal Analysis 28.2 Experimental Modal Testing 1131
less useful in an impact test than in other types of experimental
modal analysis. Many experienced practitioners
favor conducting tests with a single strike at each target
DOF. This precludes calculating a coherence function,
but that very useful causality measurement often tells
you more about your ability to hit the same place twice
than it does about structural nonlinearities or noise in
measurement. For this reason, it is imperative to inspect
every measurement set in the time domain before accepting
it. Most analyzers automate this type of acquisition,
giving you an accept/reject control.
28.2.3 Shaker Testing
Not all structures can be impact tested. Sometimes the
surface is too delicate. Sometimes the impact force has
too low an energy density over the entire frequency range
of interest. In this case, FRF measurements must be
made by attaching one or more shakers to the structure.
Since the FRF is a single input function, the shaker
should transmit only one component of force in line
with the main axis of the load cell. Often a structure
tends to rotate slightly when it is displaced along an
axis. To minimize the problem of forces being applied
in other directions, the shaker is generally connected
to the load cell through a slender rod called a stinger to
allow the structure to move freely in the other directions.
The stinger should have a strong axial stiffness but weak
bending and shear stiffnesses.
A variety of broadband excitation signals have been
developed for making shaker measurements with FFT
analyzers: transient, random, pseudo-random, burst random,
sine sweep (chirp). A true random signal is
synthesized with a random number generator. Since it is
nonperiodic in the sampling window, a Hanning window
must always be used to minimize leakage.
A pseudo-random signal is specially synthesized
by an FFT analyzer to coincide with the window parameters.
It is synthesized over the desired frequency
range and then passed through an inverse FFT algorithm
to obtain a random time-domain signal, converted
to an analog signal and used as the shaker excitation
signal. Since the excitation signal is periodic in the
sampling window, the acquired signals are leakage-free.
However pseudo-random excitation does not excite nonlinearities
differently between spectrum averages and
will not, therefore, remove nonlinearities from FRF
measurements.
Burst random excitation combines some advantages
of both random and pseudo random testing. Its signals
are leakage free and when used with spectrum averag-
Part H 28.2