ASTM E756-98
(Test Method)Standard Test Method for Measuring Vibration-Damping Properties of Materials
Standard Test Method for Measuring Vibration-Damping Properties of Materials
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1.1 This test method measures the vibration-damping properties of materials, including loss factor, [eta], Young's modulus, E, and shear modulus, G. Accurate over a frequency range of 50 to 5 kHz and over the useful temperature range of the material, this test method is useful in testing materials that have application in structural vibration, building acoustics, and the control of audible noise. Such materials include metals, enamels, ceramics, rubbers, plastics, reinforced epoxy matrices, and woods that can be formed to the test specimen configurations.
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Designation: E 756 – 98
Standard Test Method for
Measuring Vibration-Damping Properties of Materials
This standard is issued under the fixed designation E 756; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope additional elastic layer (that is, the constraining layer), whose
relative stiffness is greater than that of the damping material, so
1.1 This test method measures the vibration-damping prop-
that energy is dissipated through cyclic deformation of the
erties of materials: the loss factor, h, and Young’s modulus, E,
damping material, primarily in shear.
or the shear modulus, G. Accurate over a frequency range of 50
3.2 Definitions of Terms Specific to This Standard:
to 5000 Hz and over the useful temperature range of the
3.2.1 glassy region of a damping material—a temperature
material, this method is useful in testing materials that have
region where a damping material is characterized by a rela-
application in structural vibration, building acoustics, and the
tively high modulus and a loss factor that increases from
control of audible noise. Such materials include metals, enam-
extremely low to moderate as temperature increases (see Fig.
els, ceramics, rubbers, plastics, reinforced epoxy matrices, and
1).
woods that can be formed to cantilever beam test specimen
3.2.2 rubbery region of a damping material—a temperature
configurations.
region where a damping material is characterized by a rela-
1.2 This standard does not purport to address all the safety
tively low modulus and a loss factor that decreases from
concerns, if any, associated with its use. It is the responsibility
moderate to low as temperature increases (see Fig. 1).
of the user of this standard to establish appropriate safety and
3.2.3 transition region of a damping material—a tempera-
health practices and determine the applicability of regulatory
ture region between the glassy region and the rubbery region
limitations prior to use.
where a damping material is characterized by the loss factor
2. Referenced Documents passing through a maximum and the modulus rapidly decreas-
ing as temperature increases (see Fig. 1).
2.1 ASTM Standard:
3.3 Symbols—The symbols used in the development of the
E 548 Guide for General Criteria Used for Evaluating Labo-
equations in this method are as follows (other symbols will be
ratory Competence
introduced and defined more conveniently in the text):
2.2 ANSI Standard:
S2.9 Nomenclature for Specifying Damping Properties of
Materials
E = Young’s modulus of uniform beam, Pa
h = loss factor of uniform beam, dimensionless
3. Terminology
E = Young’s modulus of damping material, Pa
3.1 Definitions—Except for the terms listed below, ANSI
h = loss factor of damping material, dimensionless
S2.9 defines the terms used in this test method.
G = shear modulus of damping material, Pa
3.1.1 free-layer (extensional) damper—a treatment to con-
4. Summary of Method
trol the vibration of a structural by bonding a layer of damping
material to the structure’s surface so that energy is dissipated
4.1 The configuration of the cantilever beam test specimen
through cyclic deformation of the damping material, primarily
is selected based on the type of damping material to be tested
in tension-compression.
and the damping properties that are desired. Fig. 2 shows four
3.1.2 constrained-layer (shear) damper—a treatment to
different test specimens used to investigate extensional and
control the vibration of a structure by bonding a layer of
shear damping properties of materials over a broad range of
damping material between the structure’s surface and an
modulus values.
4.1.1 Self-supporting damping materials are evaluated by
forming a single, uniform test beam (Fig. 2a) from the damping
This test method is under the jurisdiction of ASTM Committee E-33 on
material itself.
Environmental Acoustics and is the direct responsibility of Subcommittee E33.03 on
4.1.2 Non–self-supporting damping materials are evaluated
Sound Transmission.
Current edition approved September 10, 1998. Published November 1998.
for their extensional damping properties in a two-step process.
Originally published as E 756–80. Last Previous edition E 756–93.
First, a self-supporting, uniform metal beam, called the base
Annual Book of Standards, Vol 14.02.
beam or bare beam, must be tested to determine its resonant
Available from America National Standards Institute, 1430 Broadway, New
York, NY 10018. frequencies over the temperature range of interest. Second, the
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E 756
measure the response of the test beam to the applied force. By
measuring several resonances of the vibrating beam, the effect
of frequency on the material’s damping properties can be
established. By operating the test fixture inside an environmen-
tal chamber, the effects of temperature on the material proper-
ties are investigated.
4.3 To fully evaluate some non–self-supporting damping
materials from the glassy region through the transition region
to the rubbery region may require two tests, one using one of
the specimen configurations (Fig. 2b or 2c) and the second
using the sandwich specimen configuration (Fig. 2d) (See
Appendix X2.6).
5. Significance and Use
5.1 The material loss factor and modulus of damping
materials are useful in designing measures to control vibration
in structures and the sound that is radiated by those structures,
FIG. 1 Variation of Modulus and Material Loss Factor with
especially at resonance. This test method determines the
Temperature
(Frequency held constant)
properties of a damping material by indirect measurement
(Glassy, Transition, and Rubbery Regions shown)
using damped cantilever beam theory. By applying beam
theory, the resultant damping material properties are made
independent of the geometry of the test specimen used to
obtain them. These damping material properties can then be
used with mathematical models to design damping systems and
predict their performance prior to hardware fabrication. These
models include simple beam and plate analogies as well as
finite element analysis models.
5.2 This test method has been found to produce good results
when used for testing materials consisting of one homogeneous
layer. In some damping applications, a damping design may
consist of two or more layers with significantly different
characteristics. These complicated designs must have their
constituent layers tested separately if the predictions of the
mathematical models are to have the highest possible accuracy.
5.3 Assumptions:
5.3.1 All damping measurements are made in the linear
range, that is, the damping materials behave in accordance with
linear viscoelastic theory. If the applied force excites the beam
FIG. 2 Test Specimens
beyond the linear region, the data analysis will not be appli-
cable. For linear beam behavior, the peak displacement from
damping material is applied to the base beam to form a damped
rest for a composite beam should be less than the thickness of
composite beam using one of two test specimen configurations the base beam (See Appendix X2.3).
(Fig. 2b or 2c). The damped composite beam is tested to obtain
5.3.2 The amplitude of the force signal applied to the
its resonant frequencies, and corresponding composite loss excitation transducer is maintained constant with frequency. If
factors over the temperature range of interest. The damping
the force amplitude cannot be kept constant, then the response
properties of the material are calculated using the stiffness of of the beam must be divided by the force amplitude. The ratio
the base beam, calculated from the results of the base beam of response to force (referred to as the compliance or recep-
tests (see Section 10.2.1), and the results of the composite tance) presented as a function of frequency must then be used
beam tests (see Sections 10.2.2 and 10.2.3). for evaluating the damping.
4.1.3 The process to obtain the shear damping properties of 5.3.3 Data reduction for both test specimens 2b and 2c (Fig.
non–self-supporting damping materials is similar to the two 2) uses the classical analysis for beams but does not include the
step process described above but requires two identical base effects of the terms involving rotary inertia or shear deforma-
beams to be tested and the composite beam to be formed using tion. The analysis does assume that plane sections remain
the sandwich specimen configuration (Fig. 2d). plane; therefore, care must be taken not to use specimens with
4.2 Once the test beam configuration has been selected and a damping material thickness that is much greater (about four
the test specimen has been prepared, the test specimen is times) than that of the metal beam.
clamped in a fixture and placed in an environmental chamber. 5.3.4 The equations presented for computing the properties
Two transducers are used in the measurement, one to apply an of damping materials in shear (sandwich specimen 2d - see Fig.
excitation force to cause the test beam to vibrate, and one to 2) do not include the extensional terms for the damping layer.
E 756
This is an acceptable assumption when the modulus of the rate material property results can only be obtained by using the
damping layer is considerably (about ten times) lower than that test specimen configuration that is appropriate for the range of
of the metal. the modulus results.
5.4.3 Applying an effective damping material on a metal
5.3.5 The equations for computing the damping properties
beam usually results in a well-damped response and a signal-
from sandwich beam tests (specimen 2d - see Fig. 2) were
to-noise ratio that is not very high. Therefore, it is important to
developed and solved using sinusoidal expansion for the mode
select an appropriate thickness of damping material to obtain
shapes of vibration. For sandwich composite beams, this
measurable amounts of damping. Start with a 1:1 thickness
approximation is acceptable only at the higher modes, and it
ratio of the damping material to the metal beam for test
has been the practice to ignore the first mode results. For the
specimens 2b and 2c (Fig. 2) and a 1:10 thickness ratio of the
other specimen configurations (specimens 2a, 2b, and 2c) the
damping material to one of the sandwich beams (2d). Con-
first mode results may be used.
versely, extremely low damping in the system should be
5.3.6 Assume the loss factor (h) of the metal beam to be
avoided because the differences between the damped and
zero.
undamped system will be small. If the thickness of the
NOTE 1—This is a well-founded assumption since steel and aluminum
damping material cannot easily be changed to obtain the
materials have loss factors of approximately 0.001 or less, which is
thickness ratios mentioned above, consider changing the thick-
significantly lower than those of the composite beams.
ness of the base beam (see Section 8.4).
5.4.4 Read and follow all material application directions.
5.4 Precautions:
When applicable, allow sufficient time for curing of both the
5.4.1 With the exception of the uniform test specimen, the
damping material and any adhesive used to bond the material
beam test technique is based on the measured differences
to the base beam.
between the damped (composite) and undamped (base) beams.
5.4.5 Learn about the characteristics of any adhesive used to
When small differences of large numbers are involved, the
bond the damping material to the base beam. The adhesive’s
equations for calculating the material properties are ill-
stiffness and its application thickness can affect the damping of
conditioned and have a high error magnification factor, i.e.
the composite beam and be a source of error (see Section 8.3).
small measurement errors result in large errors in the calculated
5.4.6 Consider known aging limits on both the damping and
properties. To prevent such conditions from occurring, it is
adhesive materials before preserving samples for aging tests.
recommended that:
5.4.1.1 For a specimen mounted on one side of a base beam
6. Apparatus
(see Section 10.2.2 and Fig. 2b), the term (f /f ) (1 + DT)
c n
6.1 The apparatus consists of a rigid test fixture to hold the
should be equal to or greater than 1.01.
test specimen, an environmental chamber to control tempera-
5.4.1.2 For a specimen mounted on two sides of a base
ture, two vibration transducers, and appropriate instrumenta-
beam (see Section 10.2.3 and Fig. 2c), the term (f /f ) (1 +
m n
tion for generating the excitation signal and measuring the
2DT) should be equal to or greater than 1.01.
response signal. Typical setups are shown in Figs. 3 and 4.
5.4.1.3 For a sandwich specimen (see Section 10.2.4 and
6.2 Test Fixture—The test fixture consists of a massive,
Fig. 2d), the term (f /f ) (2 + DT) should be equal to or greater
s n
rigid structure which provides a clamp for the root end of the
than 2.01.
beam and mounting support for the transducers.
5.4.1.4 The above limits are approximate. They depend on
6.2.1 To check the rigidity and clamping action of the
the thickness of the damping material relative to the base beam
fixture, test a bare steel beam as a uniform specimen (see
and on the modulus of the base beam. However, when the
Section 8.1.1) using the procedure in section 9 and calculate
value of the terms in Sections 5.4.1.1, 5.4.1.2, or 5.4.1.3 are
the material properties using the equations in Section 10.2.1. If
near these limits the results should be evaluated carefully. The
Young’s modulus is not 2.07 E+11 Pa (30 E+6 psi) and the loss
ratios in Sections 5.4.1.1, 5.4.1.2, and 5.4.1.3 should be used to
factor is not approximately 0.002 to 0.001 for modes 1 and 2
judge the likelihood of error.
and 0.001 or less for the higher modes, then there is a problem
5.4.2 Test specimens 2b and 2c (Fig. 2), are usually used for
in the fixture or somewhere else in the measurement system
stiff materials with Young’s modulus greater than 100 MPa, (See Appendix X2.2).
where the properties are measured in the glassy and transition 6.2.2 It is often useful to provide vibration isolation of the
regions of such materials. These materials usually are of the test fixture to reduce the influence of external vibrations which
free-layer type of treatment, such as enamels and loaded vinyls. may be a source of measurement coherence problems.
The sandwich beam technique usually is used for soft vis- 6.2.3 Fig. 3 shows a
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