This article compares four test methods for measuring damping properties of materials using piezoelectric transducers: the Central Impedance Method, Modified Oberst Method, Seismic Response Method, and simply supported beam method. Experiments were conducted on aluminum beams and ECCS-PET layers under controlled temperature conditions. Results for damping loss factor and Young's modulus obtained from each method were compared to study variability. The Central Impedance Method showed the lowest statistical dispersion. Non-resonant simply supported beam method allows characterization of materials at very low frequencies without size limitations of resonant methods.

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Materials and Design 32 (2011) 2423–2428
Contents lists available at ScienceDirect
Materials and Design
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Technical Report
Comparison of four test methods to measure damping properties of materials
by using piezoelectric transducers
Roberto Pereira a, Jorge P. Arenas a,⇑, Ernesto Zumelzu b
a
Institute of Acoustics, Univ. Austral de Chile, PO Box 567, Valdivia, Chile
b
Institute of Materials and Thermo-Mechanic Processes, Univ. Austral de Chile, PO Box 567, Valdivia, Chile
a r t i c l e i n f o a b s t r a c t
Article history: This article presents the experimental results of damping loss factor and Young’s modulus obtained for
Received 26 September 2010 stiff and flexible materials through the use of four different methodologies: the Central Impedance
Accepted 27 November 2010 Method, the Modified Oberst Method, the Seismic Response Method, and the simply supported beam
Available online 4 December 2010
method. The first three methods are based on the ASTM standard but using different experimental setting
and different Frequency Response Functions. The fourth method corresponds to a non-resonant tech-
nique used in the characterization of materials at very low frequencies. In this work, the results of damp-
ing loss factor and Young’s modulus obtained through these four methods are compared, the variability of
results is studied and the sensitivity of each technique when facing controlled temperature variations is
verified.
Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Damping loss factor is defined as the ratio between the energy
dissipated within the damping layer and the energy stored in the
The study of structural properties in materials is becoming whole structure, per cycle of vibration [1]. Use of constrained
more and more important in different disciplines of engineering and unconstrained damping material layers has been a helpful tool
and mechanical design [1]. A number of investigations have been for structural designers concerned with mitigating stress or dis-
carried out to modify the molecular structure of materials aimed placement amplitude in vibrating systems. In addition, some re-
at enhancing their internal damping without altering their other search has been specifically aimed to optimize the damping of
physical constants. These kinds of improvements involve develop- these layers [5].
ing adequate methods to measure damping loss factor [2]. The methodology established by ASTM [6] corresponds to a
Stiffness and damping are some of the most important design standardized test to measure loss factor and Young’s Modulus in
criteria for mechanical components and systems. Frequently, materials. This test is based on the analysis of peaks in the Fre-
performance of a component or a structure is determined by com- quency Response Function (FRF) measured without interfering
bination of its stiffness and damping. This is particularly evident with the system being analyzed. Consequently, this method im-
when designing the dynamic characteristics of modern machines plies the use of some specialized measurement instruments that
since their increased speed and power, combined with lighter could make the experimental setup highly expensive.
structures, may result in intense resonances and in the develop- On the other hand, there is a variety of different contacting
ment of self-excited vibrations [3]. measuring approaches that can be employed for characterizing
In general, materials selection and component design are two materials by resonance and non-resonance tests. Moreover, use
parallel streams followed when a mechanical component is de- of piezoelectric transducers is quite common in some of these
signed. Firstly, a tentative material is chosen and data for it are tests, where accelerometers and force sensors are by far the most
assembled either from data sheets or from data books. In design, traditional and widely used piezoelectric sensors employed in
a choice of material can determine the price of a product and pro- modal testing [7]. Thus, carrying out tests using this type of trans-
duction paths. Later, a more detailed specification of the design and ducers becomes an alternative worthy to be analyzed.
of the material is required. At this point it may be necessary to get Particular studies of contacting measuring approaches for
detailed material properties from possible suppliers or to conduct characterizing materials are abundant in the technical literature,
experimental tests [4]. but comparative studies have not been reported. This work aims
to fill in this gap by presenting a comparison of four methodologies
⇑ Corresponding author. Tel.: +56 63 221012; fax: +56 63 221013. to estimate the characteristics of damping and stiffness in
E-mail address: jparenas@uach.cl (J.P. Arenas). materials. For the purpose of comparable results among different
0261-3069/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.matdes.2010.11.070

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2424 R. Pereira et al. / Materials and Design 32 (2011) 2423–2428
methods, all of the tests were performed under similar controlled
conditions.
2. Theoretical review
2.1. ASTM methodology
In general, all resonant methods use the ASTM standard [6]. Fig. 2. Central Impedance Method (CIM).
This standard establishes a methodology based on the measure-
ment of Frequency Response Functions (FRF) of clamped-free beam
(uniform or composite) to determine the loss factor g, Young’s
modulus E, shear loss factor gShear and shear modulus G of an
absorbing material under test.
For a uniform beam of length l, density q and thickness H, the
loss factor g of a given mode n, at the resonance frequency fn can
be calculated by
Dfn
g¼ ; ð1Þ Fig. 3. Modified Oberst Method (MOM).
fn
where Dfn is the half power bandwidth of mode n. The system loss
factor is approximately equal to twice the critical damping ratio of a
vibrating system at resonance. The Young’s modulus is determined
from
2 4
12ql fn
E¼ ; ð2Þ
H C2
2
n
where Cn is a coefficient associated to mode n. In the case of an
Oberst beam (see Fig. 1) or a beam composed of a base beam and Fig. 4. Seismic Response Method (SRM).
a layer of absorbing material of density q1 and thickness H1, the
Young’s modulus E1 of the absorbing material associated to mode Different from previous methods, SRM [10] is based on the appli-
c of the Oberst beam, at resonance frequency fc, is obtained from cation of a forced motion s(t) at one end of the beam and measuring
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the displacement response r(t) at the opposing end, as shown in
E Fig. 4. Then, the FRF to be analyzed in this method is R/S, where R
E1 ¼ ða À bÞ þ ða À bÞ2 À 4T 2 ð1 À aÞ ; ð3Þ
2T 3 and S are the Fourier transform of r(t) and s(t), respectively.
Both MOM and SRM require the use of a laser vibrometer or
where a = (fc/fn)2(1 + DT), b = 4 + 6T + 4T2, T = H1/H, and D = q1/q.
some non-contact measuring method so as to avoid physical con-
The corresponding loss factor g1 of mode c is
3 tact with the system.
2
ð1 þ MT Þ 1 þ 4MT þ 6MT 2 þ 4MT 3 þ M 2 T 4
g1 ¼ gc 4 5; ð4Þ 2.3. Non-resonant method
ðMTÞ 3 þ 6T þ 4T 2 þ 2MT 3 þ M2 T 4
One of the disadvantages of the resonant methods is that rela-
where M = E1/E and gc is the loss factor of the composite beam com-
tively large beams must be used to force resonant modes to appear
puted from Eq. (1).
in the low frequency region for the characterization of materials in
low frequency. This produces a series of practical difficulties,
2.2. Resonant methods
mainly when making the experimental setup. The methodology
proposed by Zaveri and Olesen [11], based on the theory stated
The Central Impedance Method (CIM), the Modified Oberst
by Timoshenko [12], and here referred to as SSM, requires a beam
Method (MOM) and the Seismic Response Method (SRM) are all
of longitude l, width b, thickness h, and density q, which is simply
resonant methods.
supported at both ends. This beam is excited by a harmonic force
The CIM [8] uses contact transducers and is based in the analy-
p(t) = P0sin xt at its center, which produces a displacement re-
sis of the FRF defined as X/F, where X is the Fourier transform of the
sponse h(t) = H0sin(xt + u), which is measured at the same point
displacement signal x(t) measured at the beam center, produced by
where the force is applied, as shown in Fig. 5.
a force f(t) having a Fourier transform F, which is also applied at the
For a frequency f, below the first resonance frequency, the loss
beam center. The principle is shown in Fig. 2.
factor g is calculated through the equation
MOM [9] uses the displacement z(t) at one of the bar’s end, pro-
duced by a forced displacement y(t) at the bar center (see Fig. 3). tan u
g¼ 2f 2
; ð5Þ
Then, the FRF used in this method is Z/Y, where Z and Y correspond 1 þ H0 2pcos lbhq
P
0
u
to the Fourier transform of z(t) and y(t), respectively.
and Young’s modulus E is calculated through
3
2l P0
E¼ cos u þ 2p2 f 2 lbhq ; ð6Þ
Ip4 H0
where I is the cross-sectional moment of inertia of the beam.
As this method does not use resonances, ASTM standard is not
Fig. 1. Oberst beam. applicable in this case. In this way, according to what was stated

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R. Pereira et al. / Materials and Design 32 (2011) 2423–2428 2425
was joined to this beam through a thin double adhesive. To obtain
resonances in different frequencies, several aluminum beams and
ECCS–PET layers of different lengths were considered. These spec-
imens are summarized in Table 1.
The width of all samples is 18.8 mm. The aluminum used has a
thickness of 2.5 mm and a density of 2927.402 kg/m3. The ECCS–
PET used has a width of 18.8 mm, a thickness of 0.15 mm and a
Fig. 5. Simply-supported beam Method (SSM).
density of 9447.083 kg/m3. Concerning the SSM, measurements
with different size beams were carried out with the purpose of ver-
ifying if overlapping of curves obtained from beams having differ-
ent length is produced.
Table 1
Samples under study.
3.2. Experimental setup
Method Sample type and length (cm) Number of samples
CIM and MOM Aluminum beams (32) 5
The different transducers used in this study are piezoelectric
Aluminum beams (25) 5
Aluminum beams (18) 5 (see Table 2). Measurements were carried out inside a tempera-
ECCS–PET layers (32) 5 ture-controlled chamber at T1 = 24 °C and T2 = 40 °C. Sample
ECCS–PET layers (25) 5 excitation was done, for resonant methods, through an electro-
ECCS–PET layers (18) 5 dynamic shaker BK 4810. For the SSM a shaker BK 4809 was
SRM Aluminum beams (16) 5 used, due to its better performance at low frequencies. White noise
Aluminum beams (12) 5 was used as excitation signal for all the experiments. The signal
Aluminum beams (9) 5
ECCS–PET layers (16) 5
was amplified by means of an amplifier BK 2718. Acquisition
ECCS–PET layers (12) 5 and further digital signal processing was done through a system
ECCS–PET layers (9) 5 Pulse BK 3560-C. Hanning windows were used in all cases and
SSM Aluminum beams (32) 5 FRF were calculated with a spectral resolution of 0.5 Hz. When nec-
Aluminum beams (25) 5 essary, the integration of the temporal signal was carried out with
ECCS–PET layers (32) 5 the Pulse system. Fig. 6 shows a general diagram of the measure-
ECCS–PET layers (25) 5
ment setup used.
4. Results and discussion
Table 2
Piezoelectric transducers: FS = force sensor, Ac = accelerometer.
4.1. Results of the base beam
Method Excitation Response
CIM FS BK 8230 Ac BK 4518-003 As an example of the variability detected in the results obtained
MOM Ac 4513-001 Ac BK 4518-003 through the resonant methods, Fig. 7 presents the results obtained
SRM Ac 4513-001 Ac BK 4518-003 through CIM. This method presented the lowest statistical disper-
SSM FS BK 8230 Ac BK 4518-003
sion in all trials.
With the aim of presenting the variability in the results ob-
tained from each methodology, Fig. 8 presents the summary of re-
in [11], the physical characteristics of a viscoelastic material are sults obtained through the three resonant methods. Ends of error
not possible to be obtained starting from the known data of a base bars correspond to the lowest and highest measured values,
beam. respectively, whereas the point where the graphics intersects these
lines corresponds to the median of the group of measured values.
3. Experimental procedure Unlike the average, median of a data set is not too sensitive to ex-
treme values; therefore it was chosen as a descriptive value.
3.1. Materials Concerning aluminum loss factor g, results in the wider fre-
quency range, the lowest variability and the highest correspon-
The materials used in this study are an aluminum sample and dence with those presented in the literature [14] corresponded to
an ECCS–PET, which is a thin and flexible polymer–metal com- the results measured through CIM. Fig. 8 shows that the results ob-
monly used in the food industry for food conservation [13]. In this tained by MOM and SRM present a higher dispersion and higher
case, the aluminum was used as a base beam and the ECCS–PET values, mainly at low frequencies.
Fig. 6. General measurement setup. (A) BK Pulse 3560-C, (B) BK 2718 amplifier, (C) BK shaker, (D) response piezoelectric transducer, (E) excitation piezoelectric
transducer, (F) personal computer. (C–E) and the location of the transducers depend on each method.

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2426 R. Pereira et al. / Materials and Design 32 (2011) 2423–2428
0.07 ied. However, these results converge into physically right values
when the loss factor is computed and diverge for Young’s modulus
0.06 as the frequency increases. In this case, limit values are acceptable
and tend to coincide with those obtained through SRM.
0.05 The increase of temperature during measurements reveals
changes in the values of the loss factor and Young’s modulus calcu-
Loss factor η
0.04 lated by means of each method, although a uniform tendency is not
observed. Concerning CIM, an increase in g values is observed in
0.03
general.
On the other hand, the results obtained by the non-resonant
0.02
test SSM are shown in Fig. 9. The results show the usual frequency
dependences of the dynamic properties associated to typical metal
0.01
or stiff structural materials, as presented in [15,16].
Here the tendency is clear and loss factor values slightly de-
0
crease as temperature rises. Almost no variation in values is ob-
0 500 1000 1500 2000 2500 served for Young’s modulus. These effects show the temperature-
Frequency (Hz) frequency dependence for a solid in which there is dense and reg-
ular packing of molecules. It is a fact that an increase in frequency
Fig. 7. Values of g obtained through CIM, T: 24 °C. Ã: l = 32 cm, m = 1; +: l = 25 cm, has an equivalent effect on the damping and stiffness as a decrease
m = 1; s: l = 18 cm, m = 1; h: l = 32 cm, m = 3; Â: l = 25 cm, m = 3; 4: l = 32 cm,
in temperature, and vice versa [1,17].
m = 5; : l = 18 cm, m = 3; }: l = 25 cm, m = 5 (m: excited mode).
4.2. Results of the PET layer
In contrast, regarding the results obtained for Young’s modulus,
SRM values are the closest to those presented in [14]. CIM presents Fig. 10 presents the summary of results for the PET layer ob-
a high variability and high values at low frequencies. Above tained through the three resonant methods. We observe that mea-
500 Hz, these values become stable and are close to those reported surements of loss factor carried out at 24 °C are quite similar when
in the literature. MOM gives clear information only in the first using MOM and SIM. Information is limited up to approximately
resonances present in the measured FRF, which implies a charac- 330 Hz. The increase in temperature makes information given by
terization covering a more limited frequency range. SSM gives FRF clearer and makes ASTM standard applicable [6]. In this way,
dissimilar results depending on the length of the beam being stud- information up to 850 Hz is obtained (see Fig. 10). Despite the
0.45 0.45
0.4 0.4
0.35 0.35
0.3 0.3
Loss factor η
Loss factor η
0.25 0.25
0.2 0.2
0.15 0.15
0.1 0.1
0.05 0.05
0 0
0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500
Frequency (Hz) Frequency (Hz)
11 11
x 10 x 10
20 20
18 18
Young´s modulus E (Pa)
Young´s modulus E (Pa)
16 16
14 14
12 12
10 10
8 8
6 6
4 4
2 2
0 0
0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500
Frequency (Hz) Frequency (Hz)
Fig. 8. Comparison of g and E values obtained through three resonant methodologies. 5: SRM. : MOM, h: CIM. Plots to the left: 24 °C; plots to the right: 40 °C.

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R. Pereira et al. / Materials and Design 32 (2011) 2423–2428 2427
10
x 10
7
1.2 6
Young´s modulus E (Pa)
1 5
Loss factor η
0.8 4
0.6 3
0.4 2
0.2 1
0 0
20 40 60 80 100 20 40 60 80 100
Frequency (Hz) Frequency (Hz)
Fig. 9. Comparison of g and E values obtained through the non-resonant method SSM. h: 24 °C. : 40 °C. Dotted line: l = 32 cm. Continuous line: l = 25 cm.
1.2 1.2
1 1
0.8 0.8
Loss factor η
Loss factor η
0.6 0.6
0.4 0.4
0.2 0.2
0 0
0 100 200 300 400 500 600 700 800 900 0 200 400 600 800 1000
Frequency (Hz) Frequency (Hz)
12 12
x 10 x 10
9 9
8 8
Young´s modulus E (Pa)
Young´s modulus E (Pa)
7 7
6 6
5 5
4 4
3 3
2 2
1 1
0 0
0 100 200 300 400 500 600 700 800 900 0 100 200 300 400 500 600 700 800 900
Frequency (Hz) Frequency (Hz)
Fig. 10. Comparison of g and E values for PET layer obtained through three resonant methodologies. 5: SRM. : MOM, h: CIM. Plots to the left: 24 °C; plots to the right: 40 °C.
existing dispersion, similarities are observed among the obtained difference between the bending stiffnesses of the layer and base
curves. In addition, for the three resonant methodologies we ob- beam. This difference must be sufficiently large in order to measure
serve that estimated loss factor values increase as temperature the bending stiffness of the layer with precision and repeatability,
rises. At high temperatures the material becomes soft and reaches which is not the case studied here (0.15 mm of the PET layer com-
a rubbery state. This fact has also been observed and discussed in pared to 2.5 mm of the base beam). These effects have been previ-
the technical literature [17]. ously discussed by Jones and Parin [18] and Pritz [19].
On the other hand, there is no coincidence in the values obtained Nonetheless, the increase in temperature produced, in all cases,
for Young’s modulus through the studied methods, so there is no a decrease in the measured values. This fact is typical for highly
clear tendency on its values. It is well known that some of the errors polymeric materials and it has been widely covered in the litera-
in the estimated values are related to the ratio of layer thickness to ture [17,20]. Thus, considering the structural influence of the PET
base beam thickness. The layer should be thick enough to cause a polymer on the behavior of the ECCS–PET composite, the values

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2428 R. Pereira et al. / Materials and Design 32 (2011) 2423–2428
obtained for both loss factor and Young’s modulus through the specific negative effects such as undesirable resonances, impacts
three resonant methods are reasonable enough. On the contrary, between vibrating parts, accelerated wear, noise generation, and
SSM did not give realistic results; hence they were not included harmful vibrations transmitted to human operators.
in this section. Nonetheless, more experimental studies are needed for a rigor-
ous validation of the methods.
5. Conclusions
Acknowledgment
This work has been aimed in the comparison of the results of
loss factor and Young’s modulus obtained through the application This work has been supported by CONICYT–FONDECYT No.
of four methodologies using piezoelectric transducers. 1070375, which is gratefully acknowledged.
The following conclusions can be drawn from the experiments:
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