Jtam-A4.dvi


JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

54, 1, pp. 27-39, Warsaw 2016
DOI: 10.15632/jtam-pl.54.1.27

ANALYSIS OF AN EXPERIMENTAL SETUP FOR STRUCTURAL

DAMPING IDENTIFICATION

OlafP.Hentschel,MariusBonhage, LarsPanning-von Scheidt, JörgWallaschek

Leibniz Universität Hannover, Institute of Dynamics and Vibration Research, Hannover, Germany

e-mail: hentschel@ids.uni-hannover.de; bonhage@ids.uni-hannover.de; panning@ids.uni-hannover.de;

wallaschek@ids.uni-hannover.de

Markus Denk, Pierre-Alain Masserey

ALSTOM Power, Steam Turbines and Generators, Baden, Switzerland; e-mail: markus.denk@power.alstom.com

In the present paper, an experimental setup for structural damping determination arising
from energy dissipations within the material is presented. The experimental setup is deve-
loped in such away that all unintended damping sources are eliminated. In this connection,
priority is also given to the reproducibility of the experimental data. In addition, a vacuum
chamber is developed to reduce the damping arising from the interaction with the surroun-
dingmedium. Furthermore, beam-shaped specimens are clamped in a suspended way, using
screws with an apex to fix the specimens in their nodes of vibration. Then, the influence
of test rig specific parameters on the damping value is analyzed. In this context, an ideal
setup of the test rig is identified to measure structural damping values arising from dissi-
pations within the material. Finally, a common model for material damping description is
parameterized using the experimental data.

Keywords: damping determination, material damping, vacuum chamber, impact excitation,
experimental setup

1. Introduction

In nearly all fields ofmechanical engineering, the avoidance ofHighCycleFatigue (HCF) failures
is of great importance. To reduce this risk, prediction and reduction of vibration amplitudes is
a primary objective. One of themost important parameters for amplitude prediction is structu-
ral damping. In turbomachinery blading applications, for example aerodynamic, frictional and
material damping are the most dominant dampingmechanisms. In this paper, the latter one is
in the focus of investigation.
During the last decades, the research mainly concentrated on the usage of nonlinear calcu-

lation tools to predict vibration amplitudes. Here, optimization of friction dampers in joints in
dynamic systems is a superior criterion. Such calculations require specification of contact para-
meters as well as structural parameters. From this, many authors use low established material
damping values to calculate transfer functions. Weiwei and Zili (2010) mention the material
damping as low, using it for numerical blade calculation by means of a 3-D numerical contact
model. Laborenz et al. (2010) also use a low material damping ratio ξ with 1.41 · 10−4 for es-
tablishing their eddy current approach. Using the damping ratio ξ and the eigenfrequency ω0,
the differential equation of a single degree of freedom (SDOF) system (displacement x) can be
written as follows

ẍ+2ξω0ẋ+ω
2
0x=0 (1.1)

Siewert and Stüer (2010) and Krack et al. (2012) only mention material damping as low and
important for their nonlinear calculations. Petrov andEwins (2006) use a collective loss factor η



28 O.P. Hentschel et al.

for aerodynamic andmaterial damping of 0.001. Regarding a linear SDOF-System it is possible
to formulate the loss factor η in terms of damping ration ξ

η=2ξ
√

1− ξ2 (1.2)

Resulting from the tendency to utilize blisks (blade integrated disks) to cut assembly costs
and increase engine efficiency, the structural damping arising from the material is the most
reasonable energy dissipation process. Therefore, quantification of mechanical damping (due to
effects inside the material) is of essential relevance to predict and reduce vibration amplitudes
in terms of HCF. Dealing with such low values, precise damping determination requires an
appropriate experimental setup. To quantifymaterial damping, an adequate experimental setup
is elementary. For this purpose, a double reed cantilever beam is recommendedas a test specimen
by Gibson and Plunkett (1977), Granick and Stern (1965) as well as by Gudmundson and
Wüthrich (1986). Thedisadvantage of using such a specimen is the necessity of frequency tuning
with additional masses.
Regarding theadequate experimental setup, all otherdamping sources like frictional damping

ordampingdueto the surroundingmediumhave tobeminimized inorder to identify thematerial
damping only (seeGranick andStern, 1965; Gibert et al., 2012). Therefore,measurements under
vacuum are recommended.
For the identification of damping values, Plunkett (1959) gives an overview of possible me-

thods for single degree of freedom systems, which can be classified in time and in frequency
domain approaches. Concerning multi degree of freedom systems, the Rational Fractional Po-
lynomial method based on a parameter fit in the frequency domain is presented by Richardson
and Formenti (1982). Moreover, the Least-Squares Complex Exponential method is described
by He and Fu (2001). This method is classified using time domain methods. Furthermore, Bert
(1973) offers an overview of methods for modeling, experimental determination and parameter
identification of material damping.Within this work, the method presented by Hentschel et al.
(2015) is used for damping determination.
The objective of the present work is the development of an experimental setup for material

damping determination, which serves the requirements for accuracy especially for expected low
damping values. The reproducibility of the experimental data is a superior criterion within the
development of the experimental setup. The experimental setup including the vacuum chamber
and the specimen clamping mechanism is presented, documenting the constructional effort ta-
ken to minimize sources of unintended damping, as frictional damping within joints. Then the
specimen excitation using a voice coil actuator and the data acquisition process are described.
An automated impact excitation is used to enable the possibility of excitation in the vacuum
chamber and to satisfy the criterion of reproducibility. Amethod for determining damping valu-
es including a short-term Fourier transform using resampling is briefly presented (see Hentschel
et al., 2015). The used test rig, in combinationwith the analysismethod, offers the possibility to
identify the decay curve of onemode shape in order to calculate the damping values. From this,
decay fitting is used (see Rice et al., 2007 and Siewert et al., 2010). Then further experimental
results are presented, which investigate in addition to the influence of ambient pressure also
the influence of the clamping conditions on the determined specimen specific damping value of
stainless steel. Using themeasured data, a commonmodel formaterial damping description (see
Lazan, 1968 and Szwedowicz et al., 2008) is parameterized. Conclusions are given at the end.

2. Experimental setup

Based on a common frequency range for turbine blades, the experimental setup is developed.
Using a specific specimen length, plate-type specimens aremanufactured for the frequency range
of interest, corresponding to the mode shape of interest.



Analysis of an experimental setup for structural damping identification 29

2.1. Specimen clamping

The specimens which are used for thematerial damping tests are beamswith defined eigen-
frequencies. The sample geometry (width and thickness) is selected in such a way that a wide
gap between the eigenfrequencies of the test specimens is present. To reduce the influence of
parasitic damping (i.e. frictional damping due to clamping), the specimens are clamped in a
suspendedway in their nodes of vibration (Fig. 1) corresponding to themode shape of interest.
Boltswith an apex (Fig. 1) are used to fix the specimensdependingon the analyzedmode shape.
This allows an evaluation of “free”modes andprevents rigid bodymode shapes. In addition, the
clampingmechanism design leaves a wide frequency gap between the specimen eigenfrequencies
and those of the system consisting of the clamping device and the specimen (Fig. 1).

Fig. 1. Mode shapes of the clampingmechanism and the apex formed clamping screw

This avoids potential interactions between the specimen and clamping and helps one to eli-
minate unintended damping sources in the clamping mechanism. In Table 1, the normalized
frequencies of interest fs,i (representing a common eigenfrequency range of turbine blades) cho-
sen concerning the specimen and the nearest normalized eigenfrequencies of the system fsy,l,i
and fsy,u,i are shown.

Table 1.Normalized frequencies

Next lower Normalized Next upper
Specimen normalized eigenfrequency normalized

eigenfrequency of interest eigenfrequency

1 fsy,l,a =0.031 fs,a =0.106 fsy,u,a =0.182

2 fsy,l,b =0.087 fs,b =0.32 fsy,u,b =0.511

3 fsy,l,c =0.9 fs,c =1 fsy,u,c =1.08

2.2. Excitation and measurement

Specimensare excitedbya force impact generatedbyavoice coil actuator. In this connection,
an automated test sequence with a high reproducibility of the excitation force is realized. Based
on this, a mechanical coupling of the structure and the excitation mechanism is avoided, which
eliminates a potential source for data distortion. The voice coil actuator is operating in current
mode. In this context, it is possible to control the acceleration of the actuator. A force sensor
is used to monitor the behavior of the impact. Due to the used electrical device for specimen
excitation, a high reproducibility of the impact force is realizable (see Fig. 2). Figure 2 shows in
addition the relation of the preset current to the measured impact force.

The vibration ismeasured by a laserDoppler vibrometer. An opticalmeasurement technique
is used to avoid a coupling between structure and sensor, whichmay induce additional uninten-



30 O.P. Hentschel et al.

Fig. 2. Measured force with several executions of the excitation (left) and corresponding coil current
(right)

Fig. 3. Experimental setup (schematic)

ded damping. In Fig. 3, the schematic experimental setup is shown, also illustrating necessary
supply and control units.

2.3. Vacuum chamber

The vacuum chamber is used to eliminate damping caused by the surroundingmedium.The
chamber is developed in two main design steps (Fig. 4). The first design step is focused on
the ability to facilitate the whole experimental setup in the chamber. The specimen clamping
and also the excitation mechanism are bolted to the bottom of the chamber. An electrical feed-
-through for the excitationmechanism and awindow for vibrationmeasurement are considered.
On the basis of the first design step, the position of the flange, the flange height, the flange
diameter and the wall thickness of the chamber are changed. This is ensured by frequency
optimization with respect to a wide frequency range of interest (common eigenfrequency range
of turbine blades). Being designed for vacuum conditions, a potential coupling of the specimen
and the structure (via the remaining air in the chamber) is eliminated due to the performed
frequency optimization. In this way, precise detection of the influence of the surrounding air
on the damping value is also possible. Furthermore, additional masses are applicable on the
chamber cap, to ensure a shift of the eigenfrequency range of the vacuum chamber. This enables
a high variability of the analyzable eigenfrequencies of interest.

It is possible to define the optimization problem by maximizing the gap between the eigen-
frequencies of the chamber and the eigenfrequencies of interest (representative eigenfrequency
range for turbine blades). In Fig. 5, the frequency gaps are graphically presented.

The optimization variable Opt has to be calculated using the three frequency gaps (∆fa,
∆fb, ∆fc). In this context, it has to be ensured that the frequency gaps reach their maximal



Analysis of an experimental setup for structural damping identification 31

Fig. 4. Design steps of the vacuum chamber

Fig. 5. Frequency gaps of the specimen and the vacuum chamber (bold: eigenfrequency range of the
chamber), top: chamber without additional masses, bottom: chamber with additional masses

magnitudes. Furthermore, the magnitudes of ∆fb and ∆fc should be equal. As a consequence,
the optimization variable can be defined as follows

Opt = e∆fa+h(∆fb,∆fc) (2.1)

The factor e represents aweight factor concerning thefirst frequencygap.To satisfy the criterion
ofmaximal and equalmagnitudes of the factors∆fb and∆fc, the functionh(∆fb,∆fc) is defined

h(∆fb,∆fc)= a|cos(α)∆fb− sin(α)∆fc|σ(sin(α)∆fc− cos(α)∆fb)

+ b|cos(α)∆fb− sin(α)∆fc|σ(cos(α)∆fb− sin(α)∆fc)− c(sin(α)∆fb+cos(α)∆fc)

(2.2)

The factors a, b, c and α are additional weight factors concerning the two frequency gaps ∆fb
and ∆fc. The several weight factors are used to ensure a high variability of the optimization
process. Out of this, it is possible to repeat the optimization by changing the weighting factors
to give e.g. priority to another frequency gap.
The influences of these factors on the frequency gaps are summarized in Table 2 and Fig. 6.

Table 2. Influences of the different weight factors

Factor Influence

a weight factor concerning the magnitude of∆fc
b weight factor concerning the magnitude of∆fb
c symmetric weight factor concerning∆fb and∆fc
α weight factor concerning the relationship between ∆fb and∆fc

The optimization is carried out by performing modal analysis using the finite element pro-
gramANSYSand its sub-problemapproximationmethod (seeANSYS, 2009). The optimization
process is presented in detail in Fig. 7.
Using the defined scalar optimization variable and the optimization process presented in

Fig. 7, the ideal chambergeometrywithahighmagnitudeof the frequencygaps is calculated.The



32 O.P. Hentschel et al.

Fig. 6.Weight factors and their influences

Fig. 7. Design steps of the vacuum chamber

Fig. 8. Measured natural frequencies of the vacuum chamber

different eigenfrequenciesmeasured for themanufactured chamberwithout additionalmasses are
shown in Fig. 8.

It shall be pointed out that the requested frequency gaps are reached. Figure 9 shows the
vacuum chamber with the integrated experimental setup.

Being equipped with a vacuum pump, low chamber pressures can be reached (see Fig. 10)
andmaintained during testing.



Analysis of an experimental setup for structural damping identification 33

Fig. 9. Experimental setup: 1 – vacuum chamber, 2 – vibration desk, 3 – voice coil actuator,
4 – specimen, 5 – clamping device

Fig. 10. Pressure-time dependency

3. Damping determination

Themethodology of deriving damping values includes a Short-Term Fourier transformwith an
integrated Resampling (STFR) of the signal. The used methodology for damping identification
was already presented byHentschel et al. (2015). In this paper, only a short overview of the used
methodology will be given. Using the mentioned STFR method, it is possible to get adequate
information concerning vibration amplitude and eigenfrequency. This method is limited only to
structures excited by a force impact (realized with the experimental setup). Here, the decaying
signal xu[w], which is necessary for damping evaluation, is measured by a laser Doppler vibro-
meter. This signal can be specified by the following data sequence withNw values regarding the
signal parts u

xu[w] =

{

x(t=(uNw +w)T0) for 0¬w¬Nw−1

0 otherwise
(3.1)

wherew represents the signal point andT0 the sampling time.The signal is equidistantly divided
into

U =
NS

NW
−1 (3.2)

parts, and it is analyzed stepwise.NS represents the number of all data values. In the next step,
a Discrete Fourier Transform (DFT) is applied

Xu[k] =
Nw−1
∑

w=0

x((uNw +w)T0)e
−j2π kw

Nw (3.3)



34 O.P. Hentschel et al.

where k describes the spectral line number. In the following, the measured signal is extracted
with respect to themode shape of interest. Using this formulation, the frequency resolution∆ωf
reads

∆ωf =
2π

T0Nw
(3.4)

By analyzing weakly damped systems, the amplitude is underestimated at the eigenfrequency.
To avoid this problem, resampling of the signal is performed. The goal in this context is the
identification of the required sample rate in such a way that the frequency resolution ∆ωf,n is
equal to an integer numberedmultiple g of the eigenfrequency of interest ωd,int.

ωd,int = g∆ωf,n (3.5)

To satisfy the required sample rate corresponding to the criteria in Eq. (3.5), real numbered
alternation d of the sample rate T0 is necessary

∆ωf,n =
2π

T0,nNw
=
2π

dT0Nw
(3.6)

As the eigenfrequency is unknown (due to production tolerances), optimization (such as the
Nelder-Mead algorithm, Nelder andMead, 1965) of the resampling factor d is necessary. In this
respect, theachievement of themaximal amplitudeat eigenfrequency represents theoptimization
criterion.
After calculating the eigenfrequency, the modal amplitude for each part of the decay curve

can be identified.Dividing the decay curve into several parts, it is possible to calculate the decay
coefficient as a function of the mean amplitude.

4. Experimental results

In this Section, the influence of experimental setup specific parameters on the damping value is
analyzed. For this purpose, an optimal setup of the test rig is identified, using the achievement of
a minimal damping value as a criterion for test rig adjustment. In addition, the reproducibility
of the measured data is also analyzed whereby the experimental setup is reassembled prior to
each measurement. The measurements are realized four times per configuration. The tests are
performed using beams with a reduced eigenfrequency for the 2-nd bending fs,c (see Table 1).
As a result of this investigation, a quantification of the identified damping value concerning its
quality is expected.
The first analyzed parameter is the ambient pressure. In Fig. 11, the normalized damping

(ratio of the measured loss factor and the maximum measured loss factor) value versus the
normalized displacement (ratio of the measured displacement and the maximum measured di-
splacement) calculated from the measured velocity is shown.
To eliminate any possibility of an aerodynamic coupling between the vacuum chamber and

the specimen, damping values are measured with and without the chamber cap under ambient
conditions.Comparing thenormalizeddampingcoursewithandwithout thechamber cap (shown
inFig. 11), it canbe seen, that there is no influenceof the chamber cap on themeasureddamping
value. Additionally, a decrease of the normalized damping value with decreasing pressure is
visible.With regard to theambientpressureconditions, thedampingdecreases to17%.Themean
standard deviation is in a range of about 0.02% of themeasured damping value at themaximal
amplitude with respect to the analyzed configuration. Herewith, an adequate reproducibility
can be obtained. Due to the used scaling factor, the influence of normalized amplitude on the
damping value cannot be recognized.



Analysis of an experimental setup for structural damping identification 35

Fig. 11. Normalized damping as a function of normalized amplitude and pressure

The next analyzed parameter is the torque of the screws with the apex (see Fig. 1). This
analysis is performed at 0.08mbar (vacuum conditions). Five different torque magnitudes are
analyzed. The normalized damping value versus the normalized amplitude is shown in Fig. 12.

Fig. 12. Normalized damping as a function of normalized amplitude and torque

Based on this analysis, an amplitude-dependent damping value can be identified. Here, the
damping value increases with the increasing amplitude. The maximal damping is measurable
at the lowest torque (hand-tight). Under these conditions, the specimen is not completely fixed
in its nodes of vibration, starting to rattle after the force impact. Frictional and impact effects
are present and responsible for additional energy dissipations. In this respect, higher damping
values are measurable. With an increasing torque magnitude, the damping value decreases to
the lowest damping value at a torque magnitude of about 6Nm. Assuming that the lowest
measurable damping value course represents the energy dissipation due to dissipationwithin the
material, the specimen-specific material damping value is measurable under these conditions.
By a further increase of the torque value, the damping increases too. In this context, the apex
geometry is discussed. The point of contact is plasticized, and the damaged apex lies flat on
the specimen. Through these measurements, a mean standard deviation of about 0.03% of the
measured damping value at the maximal amplitude with respect to the analyzed configuration
is identifiable.
To check the influence of the apex variation on the damping value, different apex geometries

are analyzed. From this, three different apex geometries are used (see Fig. 13), whereby the apex
radius r is varied.
For specimen clamping, a torque of 6Nm (identified before) is used. The tests are performed

at 0.08mbar (vacuum conditions). In Fig. 14, the influence of this variation on the damping
value is presented.



36 O.P. Hentschel et al.

Fig. 13. Apex geometry

Fig. 14. Normalized damping as a function of normalized amplitude and apex geometry

The damping value increases with the increasing apex radius. This effect leads to an additio-
nal frictional damping within the contact area. Here, the lowest damping is identifiable at the
lowest apex radius (approximately 0mm). For these configurations, also a low standard devia-
tion (0.028% of the measured damping value at the maximal amplitude) is identifiable. This is
the basis for proving the adequate reproducibility of the measured values.

Based on this analysis, it can be seen that a sufficient adjustment of the experimental setup
is necessary for sufficient structural damping identification arising from thematerial. InTable 3,
the adjustment of different parameters regarding the experimental setup is summarized.

Table 3.Adjustment of the experimental setup

Parameter Magnitude

Pressure 0.08mbar

Clamping torque 6Nm

Apex radius ≈ 0mm

5. Model verification

To demonstrate further utilization of the experimental data, the measured values are used to
parameterize a common model for material damping description. For this purpose, the test
rig is adjusted with respect to the data presented in Table 3. It now becomes obvious that
the measured normalized damping values correspond to the lowest measured values made in
previous investigations (see Fig. 14, Fig. 12 and Fig. 11). These damping values, which arise



Analysis of an experimental setup for structural damping identification 37

from dissipations within thematerial, are used for parameterization. In this connection, a static
hysteresis model is utilized which was already recommended by Lazan (1968)

ΨS =
∆WS

2πUS
=
1

2πUS

VS
∫

V=0

∆Wloc dV =
1

2πUS

VS
∫

V=0

Jσn dV (5.1)

InEq. (5.1),ΨS,∆WS,US andVS represent the specimen-specific loss coefficient, the entire loss,
the potential energy and the entire volume of the specimen. In this context, the local energy
dissipation ∆Wloc is describable as a function of the local stress σ weighted by two material
constants J and n. Analyzing the stress distribution by the Finite Element approach within
the specimen, the parameters can be identified. From this, the least squares method is used
to identify the magnitudes on the basis of the experimental data. In Fig. 15, the course of the
normalized damping with respect to the maximal local stress σmax is presented.

Fig. 15. Parameterization of a commonmodel for material damping description

It is to be mentioned that the maximal local stress σmax within the specimen corresponds
to the measured amplitude. The magnitude of the maximal local stress is identified using the
Finite Element approach. Finally, it can be seen that the experimental data presented in Fig. 15
are describable in a suitable way using the static hysteresis model presented by Lazan (1968).
In this context, the coefficient of determination has a magnitude of R2 =0.94.

6. Conclusions

In the present paper, an experimental setup for specimen-specificmaterial damping determina-
tion is developed. A design optimization with respect to the natural frequencies of a vacuum
chamber and a frequency range of interest are performed. It could be shown that requested
frequency gaps are achieved to avoid possible aerodynamic coupling between test specimen and
vacuum chamber. In addition, test specimens are clamped in their nodes of vibration to avoid
unintended frictional damping.Theclampingdevice is also frequencyoptimized to avoid possible
structural coupling. Moreover, a method for damping determination is discussed briefly. Sub-
sequently, several parameters influencing the measured specimen-specific damping value using
the analyzed setup are identified. It can be shown that a defined magnitude of the clamping
torque as well as a defined geometry of the clamping apex is important to identify an accurate
damping value. In this connection, an adjustment of the experimental setup is presented. In
this context, the lowest identifiable damping value is used as a criterion for the adjustment of
the experimental setup. Additionally, it can be shown that an adequate reproducibility of the



38 O.P. Hentschel et al.

measured values is realizable. Finally, amodel formaterial dampingdescription is parameterized
on the basis of the measured material-specific damping values.

Using the developed experimental setup, it is possible to identify influential parameters on
structural damping values arising from dissipations within thematerial. Based on this, develop-
ment and parameterization of material damping models is realizable. It should be mentioned,
that the analyzable respectively excitable frequency range is limited by the impact force.

References

1. ANSYS Inc., 2009, Advanced Analysis Techniques Guide,ANSYS Inc., Release 12.0, Canonsburg

2. Bert C.W., 1973, Material damping: an introductory review of mathematical models measures
and experimental techniques, Journal of Sound and Vibration, 29, 129-153

3. Gibert C., Blanc L., Almeida P., Leblanca X., Oustyb J.P., Thouvereza F., Lâıné
J.-P., 2012, Modal tests and analysis of a radial impeller at rest: influence of surrounding air
on damping, Proceedings of ASME Turbo Expo 2012, Power for Land, Sea and Air, Copenhagen
Denmark, Paper GT2012-69577

4. Gibson R.F., Plunkett R., 1977, A forced-vibration technique for measurement of material
damping, Journal of Experimental Mechanics, 17, 297-302

5. Granick N., Stern J.E., 1965, Material damping of aluminum by a resonantdwell technique,
NASA Technical Note, National Aeronautics and Space Administration, Washington D.C., USA,
NASA TND-2893

6. GudmundsonP.,WüthrichC., 1986,DieWerkstoffdämpfungvonStählenbei hohenDehnungs-
amplituden, Materialwissenschaft und Werkstofftechnik, 17, 286-292,Weinheim, Germany

7. He J., Fu Z.F., 2001,Modal Analysis, Butterworth Heinemann, OxfordAuckland Boston Johan-
nesburgMelbourne NewDehli

8. Hentschel O.P., Panning-von Scheidt L., Wallaschek J., Denk M., 2015, Introduction
and evaluation of a damping determination method based on a short-term fourier transform and
resampling (STFR), Journal of Theoretical and Applied Mechanics, 53, 2, 395-407

9. Krack M., Panning L., Wallaschek J., Siewert C., Hartung A., 2012, Robust design of
friction interfaces of bladed disks with respect to parameter uncertainties, Proceedings of ASME
Turbo Expo 2012, Power for Land, Sea and Air, Copenhagen Denmark, Paper GT2010-68578

10. Laborenz J., Siewert C., Panning L.,Wallaschek J., GerberC.,Masserey P.A., 2010,
Eddy current damping: a concept study for steam turbine blading, Journal of Engineering for Gas
Turbines and Power, 132, 1-7

11. Lazan B., 1968, Damping of Materials and Members in Structural Mechanics, Pergamon Press,
Oxford London EdinburghNewYork Toronto Sydney Paris Braunschweig

12. PetrovE.P., EwinsD.J., 2006,Effects of damping and varying contact area at blade-disk joints
in forced response analysis of bladed disk assemblies, Journal of Turbomachinery, 128, 403-410

13. Plunkett R., 1959, Measurement of damping, [In:] Structural Damping, Ruzicka J. (Edit.),
ASME, 117-131, Atlantic City NJ USA

14. Rice T., Bell D., Singh G., 2007, Identification of the stability margin between safe operation
and the onset of blade flutter, Proceedings of ASME Turbo Expo 2007, Power for Land, Sea and
Air, Montreal Canada, Paper GT2007-27462

15. RichardsonM.H., FormentiD.L., 1982,Parameter estimation from frequency responsemeasu-
rements using rational fraction polynomials,Proceedings of the First International Modal Analysis
Conference, Orlando FL USA, 167-180



Analysis of an experimental setup for structural damping identification 39

16. Siewert C., Panning L., Gerber C., Masserey P.A., 2010, Numerical and experimental
damping prediction of a nonlinearly coupled low pressure steam turbine blading, Proceedings of
ASME Turbo Expo 2008, Power for Land, Sea and Air, Berlin Germany, Paper GT2010 51073

17. Siewert C., Stüer H., 2010, Forced response analysis ofmistuned turbine bladings,Proceedings
of ASME Turbo Expo 2010, Power for Land, Sea and Air, GlasgowUK, Paper GT2010-23782

18. Szwedowicz J., Secall-Wimmel T., Dnck-Kerst P., 2008, Damping performance of axial
turbine stageswith loosely assembled friction bolts, the non-linear dynamic assessment, Journal of
Engineering for Gas Turbines and Power, 130, 3, 1-14

19. Weiwei G., Zili X., 2010, 3D numerical friction contact model and its application to nonlinear
blade damping, Proceedings of ASME Turbo Expo 2010, Power for Land, Sea and Air, Glasgow
UK, Paper GT2010-22292

Manuscript received January 19, 2015; accepted for print June 12, 2015