ASTM E756-05(2010)
(Test Method)Standard Test Method for Measuring Vibration-Damping Properties of Materials
Standard Test Method for Measuring Vibration-Damping Properties of Materials
SIGNIFICANCE AND USE
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, especially at resonance. This test method determines the properties of a damping material by indirect measurement 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.
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.
SCOPE
1.1 This test method measures the vibration-damping properties of materials: the loss factor, η, and Young's modulus, E, or the shear modulus, G. Accurate over a frequency range of 50 to 5000 Hz and over the useful temperature range of the material, this 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 cantilever beam test specimen configurations.
1.2 This standard does not purport to address all the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Designation: E756 − 05 (Reapproved 2010)
Standard Test Method for
Measuring Vibration-Damping Properties of Materials
This standard is issued under the fixed designation E756; 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 (´) indicates an editorial change since the last revision or reapproval.
This standard has been approved for use by agencies of the U.S. Department of Defense.
1. Scope 3.1.1 free-layer (extensional) damper—a treatment to con-
trol the vibration of a structural by bonding a layer of damping
1.1 This test method measures the vibration-damping prop-
material to the structure’s surface so that energy is dissipated
erties of materials: the loss factor, η, and Young’s modulus, E,
through cyclic deformation of the damping material, primarily
ortheshearmodulus, G.Accurateoverafrequencyrangeof50
in tension-compression.
to 5000 Hz and over the useful temperature range of the
3.1.2 constrained-layer (shear) damper—a treatment to
material, this method is useful in testing materials that have
control the vibration of a structure by bonding a layer of
application in structural vibration, building acoustics, and the
damping material between the structure’s surface and an
control of audible noise. Such materials include metals,
additional elastic layer (that is, the constraining layer), whose
enamels, ceramics, rubbers, plastics, reinforced epoxy
relativestiffnessisgreaterthanthatofthedampingmaterial,so
matrices, and woods that can be formed to cantilever beam test
that energy is dissipated through cyclic deformation of the
specimen configurations.
damping material, primarily in shear.
1.2 This standard does not purport to address all the safety
concerns, if any, associated with its use. It is the responsibility 3.2 Definitions of Terms Specific to This Standard:
of the user of this standard to establish appropriate safety and 3.2.1 glassy region of a damping material—a temperature
health practices and determine the applicability of regulatory region where a damping material is characterized by a rela-
limitations prior to use. tively high modulus and a loss factor that increases from
extremely low to moderate as temperature increases (see Fig.
2. Referenced Documents 1).
2.1 ASTM Standards: 3.2.2 rubbery region of a damping material—a temperature
region where a damping material is characterized by a rela-
E548 Guide for General Criteria Used for Evaluating Labo-
tively low modulus and a loss factor that decreases from
ratory Competence (Withdrawn 2002)
moderate to low as temperature increases (see Fig. 1).
2.2 ANSI Standard:
3.2.3 transition region of a damping material—a tempera-
S2.9 Nomenclature for Specifying Damping Properties of
ture region between the glassy region and the rubbery region
Materials
where a damping material is characterized by the loss factor
passing through a maximum and the modulus rapidly decreas-
3. Terminology
ing as temperature increases (see Fig. 1).
3.1 Definitions—Except for the terms listed below, ANSI
3.3 Symbols—The symbols used in the development of the
S2.9 defines the terms used in this test method.
equations in this method are as follows (other symbols will be
introduced and defined more conveniently in the text):
ThistestmethodisunderthejurisdictionofASTMCommitteeE33onBuilding
and Environmental Acoustics and is the direct responsibility of Subcommittee
E = Young’s modulus of uniform beam, Pa
E33.10 on Vibration.
η = loss factor of uniform beam, dimensionless
Current edition approved May 1, 2010. Published August 2010. Originally
approved in 1980. Last previous edition approved in 2005 as E756–05. DOI:
E = Young’s modulus of damping material, Pa
10.1520/E0756-05R10.
η = loss factor of damping material, dimensionless
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
G = shear modulus of damping material, Pa
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on
4. Summary of Method
the ASTM website.
The last approved version of this historical standard is referenced on
4.1 The configuration of the cantilever beam test specimen
www.astm.org.
is selected based on the type of damping material to be tested
Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
4th Floor, New York, NY 10036, http://www.ansi.org. and the damping properties that are desired. Fig. 2 shows four
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E756 − 05 (2010)
tests (see 10.2.1), and the results of the composite beam tests
(see 10.2.2 and 10.2.3).
4.1.3 The process to obtain the shear damping properties of
non-self-supporting damping materials is similar to the two
step process described above but requires two identical base
beams to be tested and the composite beam to be formed using
the sandwich specimen configuration (Fig. 2d).
4.2 Once the test beam configuration has been selected and
the test specimen has been prepared, the test specimen is
clamped in a fixture and placed in an environmental chamber.
Two transducers are used in the measurement, one to apply an
excitation force to cause the test beam to vibrate, and one to
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.Byoperatingthetestfixtureinsideanenvironmen-
FIG. 1 Variation of Modulus and Material Loss Factor with tal chamber, the effects of temperature on the material proper-
Temperature
ties are investigated.
(Frequency held constant)
4.3 To fully evaluate some non-self-supporting damping
(Glassy, Transition, and Rubbery Regions shown)
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. 2bor Fig. 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,
especially at resonance. This test method determines the
properties of a damping material by indirect measurement
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
usedwithmathematicalmodelstodesigndampingsystemsand
predict their performance prior to hardware fabrication. These
FIG. 2 Test Specimens
models include simple beam and plate analogies as well as
finite element analysis models.
5.2 Thistestmethodhasbeenfoundtoproducegoodresults
different test specimens used to investigate extensional and
whenusedfortestingmaterialsconsistingofonehomogeneous
shear damping properties of materials over a broad range of
layer. In some damping applications, a damping design may
modulus values.
consist of two or more layers with significantly different
4.1.1 Self-supporting damping materials are evaluated by
characteristics. These complicated designs must have their
formingasingle,uniformtestbeam(Fig.2a)fromthedamping
constituent layers tested separately if the predictions of the
material itself.
mathematicalmodelsaretohavethehighestpossibleaccuracy.
4.1.2 Non–self-supporting damping materials are evaluated
for their extensional damping properties in a two-step process. 5.3 Assumptions:
First, a self-supporting, uniform metal beam, called the base 5.3.1 All damping measurements are made in the linear
beam or bare beam, must be tested to determine its resonant range,thatis,thedampingmaterialsbehaveinaccordancewith
frequencies over the temperature range of interest. Second, the linear viscoelastic theory. If the applied force excites the beam
dampingmaterialisappliedtothebasebeamtoformadamped beyond the linear region, the data analysis will not be appli-
composite beam using one of two test specimen configurations cable. For linear beam behavior, the peak displacement from
(Fig. 2bor Fig. 2c). The damped composite beam is tested to rest for a composite beam should be less than the thickness of
obtain its resonant frequencies, and corresponding composite the base beam (See Appendix X2.3).
loss factors over the temperature range of interest. The damp- 5.3.2 The amplitude of the force signal applied to the
ing properties of the material are calculated using the stiffness excitation transducer is maintained constant with frequency. If
of the base beam, calculated from the results of the base beam the force amplitude cannot be kept constant, then the response
E756 − 05 (2010)
of the beam must be divided by the force amplitude. The ratio regions of such materials. These materials usually are of the
of response to force (referred to as the compliance or recep- free-layertypeoftreatment,suchasenamelsandloadedvinyls.
tance) presented as a function of frequency must then be used The sandwich beam technique usually is used for soft vis-
for evaluating the damping. coelastic materials with shear moduli less than 100 MPa. The
valueof100MPaisgivenasaguideforbasebeamthicknesses
5.3.3 Data reduction for both test specimens 2b and 2c (Fig.
2)usestheclassicalanalysisforbeamsbutdoesnotincludethe within the range listed in 8.4. The value will be higher for
thickerbeamsandlowerforthinnerbeams.Whenthe100MPa
effects of the terms involving rotary inertia or shear deforma-
tion. The analysis does assume that plane sections remain guideline has been exceeded for a specific test specimen, the
test data may appear to be good, the reduced data may have
plane; therefore, care must be taken not to use specimens with
a damping material thickness that is much greater (about four little scatter and may appear to be self-consistent.Although the
times) than that of the metal beam. composite beam test data are accurate in this modulus range,
5.3.4 The equations presented for computing the properties the calculated material properties are generally wrong. Accu-
rate material property results can only be obtained by using the
ofdampingmaterialsinshear(sandwichspecimen2d-seeFig.
2) do not include the extensional terms for the damping layer. test specimen configuration that is appropriate for the range of
the modulus results.
This is an acceptable assumption when the modulus of the
dampinglayerisconsiderably(abouttentimes)lowerthanthat
5.4.3 Applying an effective damping material on a metal
of the metal.
beam usually results in a well-damped response and a signal-
5.3.5 The equations for computing the damping properties to-noise ratio that is not very high.Therefore, it is important to
from sandwich beam tests (specimen 2d–see Fig. 2) were
select an appropriate thickness of damping material to obtain
developed and solved using sinusoidal expansion for the mode measurable amounts of damping. Start with a 1:1 thickness
shapes of vibration. For sandwich composite beams, this
ratio of the damping material to the metal beam for test
approximation is acceptable only at the higher modes, and it
specimens Fig. 2b and Fig. 2c and a 1:10 thickness ratio of the
has been the practice to ignore the first mode results. For the
damping material to one of the sandwich beams (Fig. 2d).
other specimen configurations (specimens 2a, 2b, and 2c) the
Conversely, extremely low damping in the system should be
first mode results may be used.
avoided because the differences between the damped and
5.3.6 Assume the loss factor (η) of the metal beam to be undamped system will be small. If the thickness of the
zero. damping material cannot easily be changed to obtain the
thickness ratios mentioned above, consider changing the thick-
NOTE 1—This is a well-founded assumption since steel and aluminum
ness of the base beam (see 8.4).
materials have loss factors of approximately 0.001 or less, which is
significantly lower than those of the composite beams.
5.4.4 Read and follow all material application directions.
When applicable, allow sufficient time for curing of both the
5.4 Precautions:
damping material and any adhesive used to bond the material
5.4.1 With the exception of the uniform test specimen, the
to the base beam.
beam test technique is based on the measured differences
5.4.5 Learnaboutthecharacteristicsofanyadhesiveusedto
between the damped (composite) and undamped (base) beams.
bond the damping material to the base beam. The adhesive’s
When small differences of large numbers are involved, the
stiffness and its application thickness can affect the damping of
equations for calculating the material properties are ill-
the composite beam and be a source of error (see 8.3).
conditioned and have a high error magnification factor, i.e.
smallmeasurementerrorsresultinlargeerrorsinthecalculated 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 10.2.2 and Fig. 2b), the term (f /f ) (1 + DT) should be
c n
6.1 The apparatus consists of a rigid test fixture to hold the
equal to or greater than 1.01.
test specimen, an environmental chamber to control
5.4.1.2 For a specimen mounted on two sides of a base
temperature, two vibration transducers, and appropriate instru-
beam (see 10.2.3 and Fig. 2c), the term (f /f )(1+2DT)
m n
mentation for generating the excitation signal and measuring
should be equal to or greater than 1.01.
the response signal. Typical setups are shown in Figs. 3 and 4.
5.4.1.3 For a sandwich specimen (see 10.2.4 and Fig. 2d),
6.2 TestFixture—Thetestfixtureconsistsofamassive,rigid
theterm(f /f ) (2+DT)shouldbeequaltoorgreaterthan2.01.
s n
structure which provides a clamp for the root end of the beam
5.4.1.4 The above limits are approximate. They depend on
and mounting support for the transducers.
the thickness of the damping material relative to the base beam
and on the modulus of the base beam. However, when the
6.2.1 To check the rigidity and clamping action of the
value of the terms in Sections 5.4.1.1, 5.4.1.2,or 5.4.1.3 are fixture,testabaresteelbeamasauniformspecimen(see8.1.1)
near these limits the results should be evaluated carefully. The
using the procedure in Section 9 and calculate the material
ratiosinSe
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