FRF MEASUREMENTS ERRORS CAUSED BY
THE USE OF INERTIA MASS SHAKERS
T.Olbrecbts, P.Sas, D.Vandepitte
Katholieke Universiteit Leuven
Faculty of Engineering, Department of Mechanical Engineering
Division Production Engineering, Machine Design and Automation
Celestijnenlaan 3OOB, B-3001 Leuven, Belgium
WWW: http://www.mech.kuleuven.ac.be/pma/pma.html
ABSTRACT.
Response transducers and excitation systems change
structural behaviour. Therefore one should take into
account this influence when interpreting the results. It is
however common practice to assume this influence to
be small, a practice that can lead to serious errors as
shown here.
The loading effect of accelerometers is well known.
Accelerometers add mass to the tested structure, which
will result in a shift of the resonances to lower
frequencies. A second loading effect is the addition of
damping. Since all accelerometers have to be physically
connected to their amplifiers, cables hang around the
stmcture which results in an increase of the damping.
Less obvious is the loading of the excitation system.
Excitation systems introduce unwanted forces and
moments at the excitation location. Unfortunately it is
not easy nor feasible to measure those forces and
moments for each FRF measurement. Threedimensional force transducers are not always available
and measuring moment.s is not feasible. As a
consequence, this loading effect is often assumed to be
negligible or even thought to be non-existent.
Experiments on a simple structure and simulation
showed the opposite. Connecting excitation systems to
the structure can result in contradictory changes of the
dynamic behaviour.
Following paragraphs discuss the results of three tests
on an identical structure. The first test is done with
hammer excitation, in the second one an electrodynamic
shaker excited the stmcture through a flexible stinger
and the third one was performed with a rigidly
connected inertial shaker. Numerical simuations have
been performed to generate physical insight and to
A modal tat is successful only when the
loading of
the test structure by measurement
instrumentation is minimal. Unintentional load effects
caused by accelerometers, shakers, suspension can
disturb the measurements. Cancelling out dynamic
loading is not always possible. In practice one often
~SSU~WS the loading effects to be small without
checking them.
This paper discusses the dynamic loading effects
different excitation methods have on the dynamic
behaviour of tested structures. Comnparison of a modal
test with different types of excitation systems and finite
element models reveal differences in the dynamic
behaviour. This paper discusses the fundamentals of the
loading effects behind inertial shaker excitation.
Analytical models are used to enhance the
understanding of those dynamic rffects.
NOMENCLATURE
Mcgl
: Mass matrix at centre of gravity
FX%F,,FZ
Mx,M,,Mz
: Forces at excitation point
: Moments at excitation point
1.
Introduction
Most often the determination of the dynamic behaviour
of a structure starts with the measurement of frequency
or impulse response functions (FRF’s or IRF’s).
Generally an excitation system introduces one or more
forces into the stmcture and transducers measure the
responses at different locations on the structure.
188
show which effects have to be taken into account when
using rigidly connected inenial shakers.
2. Excitation systems
There are two large groups of excitation systems:
impact and shaker excitation systems. [l] When no
parts of the excitation system are fixed to the measured
structure, there is no unintentional loading on the
stmctore. A well known example of a non-contact
excitation system is hammer excitation.
2.1. Impact excitation systems
Impacting the structure with a hammer (figure I) is an
often used excitation method. The force input of the
hammer on the structure is measured with a force cell
that is connected to the hammer. With hammer
Figure 1 : Hammer excitation
excitation, no force cell is fixed to the structure. This
means that there is no loading of the stmcture due to the
fixation of excitation equipment on the input location.
2.2. Shaker excitation systems
With contact excitation systems, the connection
between shaker and test stmctwes loads the stmcture.
This can be very critical when the mass of the
excitation system is not negligible with respect to the
mass of the tested stmctore. Not only the translational
inertia are important but also the rotational inertia of the
exciter system influence the dynamic behaviour of the
test structure in a dramatic way. In most applications
the excitation system is supposed to deliver a
unidirectional external force F, (figure 2) along the
measurement axis of the force transducer. This
assumption is not exact. Forces and moments in all
directions (F,,F,,M,,M,,M,) need to be assessed. These
loads do not depend on the characteristics of the shaker
only, they also depend on the type and magnitude of
deformation the structure is expected to exhibit.
The most used variant of contact excitation systems is
the electrodynamic shaker in combination with a stinger
Figure 2 : Test set-up with electrodynamic
shaker and stinger
(figure 2). A stinger connects the moving part of the
shaker with the stmcmre. This connection is stiff in the
excitation direction and flexible in the other directions.
This minimises force and moment inputs in the
directions other than the measured excitation direction
Z. When a displacement or a rotation is applied to the
stinger in the non-measured directions, the beam bends.
Unfortunately the design of such stingers needs some
experience. When performing tests on stmctures with
different stinger designs, it becomes clear that it is
impossible to completely eliminate the loading of the
measurement. Lee and Chou [2] modelled the influence
different stinger designs have on the measurements and
concluded that the use of improper stingers or test-setups will bias the test results. Also the parts that connect
the stinger with structure and shaker have to be
designed carefully. They often introduce phenomena
like non-linearities and rattling... Misalignment of the
shaker and the stinger will result in bad measurements.
A second excitation system that is often used, is the
inertial shaker set-up (figure 3). The internal design of
an inertial shaker is very similar to the design of a
normal shaker. For seismic shakers, the reference is not
the ground but rather the mass of the shaker itself [3].
The built-in electrodynamic system creates a relative
189
acceleration between the seismic mass and the head of
the shaker. When it is connected to an object, the shaker
creates internal forces between structure and shaker.
These forces excite the test structure.
It is possible to use inertia1 shakers with stingers. One
can suspend the inertia1 shaker in a flexible rig and
connect the shaker with the test structure through a
stinger. Often inertial shakers are rigidly connected to
the test structure without any flexible interconnection.
This results in a loading of the stmcture since inertial
shaker inertia are rather large. This means that
unwanted forces and moments act on the stmcture, with
both static and dynamic components (figure 3,
F,,F,,M,,M,,M,). Therefore measurements with inertia1
with stinger and inertial shaker excitation. Results
reveal important differences between the different tests
and show that loading can be very important.
3.1. Test structure
A simple structure was used (figure 4). The test
structure consists of a* aluminium rectangular frame,
size 800 x 600 mm with a thickness of 4 mm. Slightly
out of centre, there is a mass, size 160 x 160 mm and a
thickness of 20 mm. This mass is bolted onto the frame
with 4 spoke-like members (aluminium, width 20 mm,
thickness 4 mm), rectangular to the frame. The spokes
are glued to the mass.
The excitation point is located on the lower left corner
of the structure (figure 4:). Only out of plane motion is
considered. The input force excites the structure in a
direction perpendicular to the plane of the structure.
Accelerometers measure responses in the same
direction. The force cell was mounted in the force
transmission path next to the excitation point (figure 1,
2 and 3).
The shaker-with-stinger test and the inertial shaker test
took place with the excitation systems underneath the
structure (figure 1 and 2). The impact point of the
hammer excitation was on the opposite side. A stinger
with an approximate length of 100 mm and a diameter
of 1 mm connected the test stmctare to the shaker. In
the inertia1 shaker test, a connection piece joins the
shaker and the stmctare rigidly together. The
Figure 3 : Test set-up with inertia1 shaker
shakers need careful interpretation.
2.3. Force transducers
Force transducers measure the forces that enter the
structure during the measurement. They will be related
to the responses on different locations of the stmcture.
They are placed in the force transmission path (figure 1,
2 and 3). Unfortunately most of the force transducers
only measure the forces in one direction and can not
measure a complete set of 3 forces and 3 moments.
Often the forces that are not measured are thought to be
small and are neglected. This is not always true and as a
consequence the measurements are biased.
Figure 4 : Measured structure
connection part is cylindrical with a length of 4Omm
(force cell included) and a diameter of 15 mm. The
inertial shaker has a mass of 1.25 kg and the test
stmcture weighs 3 kg.
Measurements were done with a block size of 2048,
sampling frequency f,=l250 Hz. The measured
frequency band is from 0 up to 500 Hz resulting in a
frequency resolution of Af=O.6 Hz. Shaker tests are
3. Loading effects on experiments
A systematic series of tests have been performed to
enhance the understanding of the loading effect
excitation systems have on a test object. This paragraph
compares three tests on the same structure. Following
excitation systems are used: hammer excitation, shaker
190
performed with a burst random excitation sipnal (burst
length of 70%). The electrodynamic shakei- was a B&K
type 4710 shaker. A Gearing & Watson IV40 inertial
shaker was used in the inertial shaker test set-up.
3.2. Experimental results
Figures 5 and 6 show the results of the three tests with
different excitation systems.
The hammer excitation is considered to be the
reference, because loading effects are minimal. Figures
5 and 6 show that resonance frequencies, measured with
the
shaker-stinger
combination, shift to lower
frequencies. Frequency shifts are small. They are in the
order of 3 to 4Hz. Frequency shifts tend to increase
with increasing frequency. Also damping changes. The
shift of resonance frequencies is caused by the inertia of
the stinger-structure connection piece. The effect of the
translational inertia underneath the force ceil (figure 2)
in the direction normal to the plane of the stmcture is
measured by the force cell and is treated as an external
‘o-x
I ‘,
10
20
30
40
fr.,::“, ,“ZP
70
80
90
0
Figure 6 : FRF results of tests (second frequency band)
significant and one expects resonance frequencies to
shift to much lower frequencies. Apparently this does
not happen. So other phenomena are acting upon the
structure.
Since it is sure that the inertia of the system increases,
the increase of the resonance frequencies can only be
caused by an increase of the stiffness of the complete
system. Simulations confilm this to be true. In fact, the
lower resonances tend to shift to lower frequencies.
Beyond a certain thmshold frequency resonance
frequencies shift to higher frequencies.
Unfortunately the quality of the inertial shaker FRF’s
degrade under 30Hz which makes comparison of the
inertial shaker test FRF’s with the hammer test FRF’s
impossible under 30Hz. But simulations (see next
paragraph) confirm the observation that low resonance
frequencies decrease while high rescmance frequencies
increase.
I
100
Figure 5 : FRF results of tests (first frequency band)
force acting on the structure. The resulting reaction
forces and moments of the translational inertia in the
plane and the rotational inertia of this connection piece
together with the force cell are not measured and are
not taken into account in the FRF calculation.
Comparison of the inertial shaker test with the hammer
test shows that resonance frequencies shift to higher
frequencies (figure 5 and 6). These results seem to be
contradictory. It is a general rule that when adding
inertia to a stmchue, resonance frequencies decrease.
As the shaker is rigidly connected to the structure, the
complete inertia that is connected to the measured
structure is much higher than in the shaker-stinger case.
The added translational and rotational inertia are
4. Finite element simulations
4.1. The finite element model
A complete set of 3 forces and 3 moments act on the
structure at the interface between shaker and structure.
Although all these forces and moments are external,
only one force is treated as an external force. As a
consequence, the non-measured forces and moments
have to be considered as internal forces and moments.
Inertia of the shaker should be considered as a part of
the stmcture. Comparison of the test structure model
with a second model where the shaker is connected onto
191
the shaker-structure connection are small, all the
internal forces and moments at the shaker-structure
connection are. caused by the inertia of this mass
element.
4.2. Analytical results
Previous models, with and without the shaker model
included, are run in a normal modes analysis.
Comparison of the resonance frequencies of those two
models reveal the loading effect an inertial shaker has
on a test stmctore. Table 1 shows the results of both
configurations.
structure model
the structure, will demonstrate significant loading
effects with the inertial shaker.
The model of the test structure is implemented in
MSUNASTRAN
and consists of about 1500 shell
elements of one square cm each. The shaker-structure
connection piece, force cell included, is modelled with
5 bar elements (figure 7 node IOl=>node 5). These
elements have the properties of a brass bar with a
diameter of 15 mm. At the shaker end of the connection
piece (node 5), a rigid bar element connects the last
node (node 5) with a node (node 6) placed at the centre
of gravity of the seismic mass. In this node 6 a mass
element represents the inertia of the shaker. The mass
matrix for this element contains mass and inertia terms.
0 0 0 0
0
m,
0 mv
0 0 0
0 1
Table 1 : Results of normal mode analysis
Table I proves that the connection of the shaker to the
test structure results in a downward shift of the
resonance frequencies of the first two modes. This mass
effect is expected. After adding inertia, resonance
frequencies shift to lower frequencies. Figure 8 shows
the mode shapes of the two configurations for the first
mode. Global mode shapes are almost identical, but in
the vicinity of the shaker there is a clear difference in
the deformation shape.
From the third mode on, all resonance frequencies of
the model with the shaker shift to higher frequencies
compared to the model without shaker. As mentioned in
previous paragraph, this seems to be contradictory. The
M,,
0
0
0
0
I_
0
0
0
0
0
0
Izz
This mass ma1 trix does not contain the mass inertia m,
which causes the force that is measured by the force
cell. This force is treated as an external force and is not
modelled. Assuming that rotations and translations at
Output Set: Mode 1 14.48793 Hz
’ Output Set: Mode 2 14.80328 Hz
Figure 8 : Comparison of modes (left hand side without shaker, right hand side with shaker)
192
\<.”
c-*
Output Set: Mode 7 52.26723 Hz
- Output Set: Mode 6 48.09956 Hz
Figure 9 : Comparison of modes (left hand side without shaker, right hand side with shaker)
addition of inertia should result in a decrease of the
resonance frequencies. An increase can only be caused
by an increase of the stiffness. This is what happens.
Figure 9 shows the mode shapes of the fifth mode. The
two mode shapes are equivalent but one can see that in
i
output set: Mode 16 176.2481 HZ
higher the resonance frequencies, the higher the
reaction forces and moments will be. Beyond a certain
frequency, the shaker’s centre of gravity can be
considered as a constrained point in space. From then
on the bending stiffness of the shaker-structure
connection device plays a, major role in the dynamic
behaviour of the test stmcture. This connection device
causes the stmctore to behave stiffer at higher
frequencies. The detail in figure 10 shows how the
seismic mass keeps its position and orientation in space.
The reaction forces and moments to translation and
rotation result in the bending of the shaker-structure
connection piece. Note th:at the mass can move along
the excitation direction because the mass m, is 0 kg.
Correlation of modes on both systems depends on
displacements at the shakw location. Figure 1 I shows
mode shapes where the displacements in the excitation
point are relatively small. Difference in resonance
frequency is small too.
Figure 12 shows mode shapes with large displacements
at the excitation point. Consequently the shift in
resonance frequencies is higher than it is for the modes
that are characterised by small displacements.
/
Figure 10 : Detail shaker-structure connection
bending
the model with the shaker, the excitation point is
constrained. In fact the seismic mass induces reaction
forces and moments to all angular accelerations and to
all translational accelerations in the plane of the test
structure at the excitation location.
To some extent the seismic mass will try to stay at a
fixed point and to keep a fixed orientation in space. The
k
Output Set: Mode 8 68.74868 Hz
* Output Set: Mode 9 69.49683 Hz
Figure 11 : Comparison of modes (left hand side without shaker, right hand side with shaker)
193
k< O”+p”+%?+: MO& 15 166.5851 HZ
Outpti
Set: Mode 16 176.2481 Hz
Figure 12 : Comparison of modes (left hand side without shaker, right hand side with shaker)
changes and measurements are biased. These loading
effects are often thought to be small and negligible
because the measurement of all forces and moments is
not possible.
Three tests have been performed with hammer
excitation, shaker-with-stinger excitation and inertial
shaker excitation. All tests give different results and
prove that loading effects can be important. A careful
interpretation of test results is needed.
Finite element models enhance the understanding of
those loading effects. Inertial shakers not only add mass
to the struchwe, but can also increase the stiffness of the
complete system. At low frequencies, the mass effect
shifts resonances to lower frequencies. At higher
frequencies the stiffness effect increases the resonance
frequencies. The shaker-structure connection device
plays a major role in this increase of the stiffness.
This paper proves that results of dynamic behaviour
measurements with inertial shakers need a careful
interpretation of test results.
5. Correlation of analytical and experimental
determined mode shapes
Figure 13 shows the MAC matrix of the analytically
and experimentally determined mode shapes for the test
struchue with the inertial shaker. MAC values are high.
This confirms that the FE model is representative for
the real situation. The FE model provides ample
physical insight in deformation patterns close to the
shaker.
MAC
7. References
[I] W.Heylen, PSas, P.Vanherck, P.Bielen, “
O
n
instrumentation for experimental modal analysis”,
Proceedings ISMA 18, L,euven, September, 1993
Figure 13 : Correlation of experimental and analytical
modeshapes
(cpa=analytical shapes, cpb=experimental shapes)
“The effects of stingers on
receptance function measurements”, Transactions
[2] J.-C.Lee, Y.-F. Chou,
of the ASME, Vol. 118, April, 1996, p. 220-226
[3] W.Heylen, S.Lammens, P.Sas, “Modal analysis
theory and testing”, June, 1995, p.B.1.7
6. Conclusions
Experiments for the determination of dynamic
behaviour use excitation systems to introduce force
inputs. By connecting excitation systems to the test
struchwe,
the dynamic behaviour of the structure
194