ASTM E756-05(2017)
(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
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 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 beyond the linear region, the data analysis will not be applicable. For linear beam behavior, the peak displacement from rest for a composite beam should be less than the thickness of the base beam (See Appendix X2.3).
5.3.2 The amplitude of the force signal applied to the excitation transducer is maintained constant with frequency. If the force amplitude cannot be kept constant, then the response of the beam must be divided by the force amplitude. The ratio of response to force (referred to as the compliance or receptance) presented as a function of frequency must then be used for evaluating the damping.
5.3.3 Da...
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 of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.
1.3 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
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This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E756 − 05 (Reapproved 2017)
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 2.2 ANSI Standard:
S2.9 Nomenclature for Specifying Damping Properties of
1.1 This test method measures the vibration-damping prop-
Materials
erties of materials: the loss factor, η, and Young’s modulus, E,
ortheshearmodulus, G.Accurateoverafrequencyrangeof50
3. Terminology
to 5000 Hz and over the useful temperature range of the
3.1 Definitions—Except for the terms listed below, ANSI
material, this method is useful in testing materials that have
S2.9 defines the terms used in this test method.
application in structural vibration, building acoustics, and the
3.1.1 free-layer (extensional) damper—a treatment to con-
control of audible noise. Such materials include metals,
trol the vibration of a structural by bonding a layer of damping
enamels, ceramics, rubbers, plastics, reinforced epoxy
material to the structure’s surface so that energy is dissipated
matrices, and woods that can be formed to cantilever beam test
through cyclic deformation of the damping material, primarily
specimen configurations.
in tension-compression.
1.2 This standard does not purport to address all of the
3.1.2 constrained-layer (shear) damper—a treatment to
safety concerns, if any, associated with its use. It is the
control the vibration of a structure by bonding a layer of
responsibility of the user of this standard to establish appro-
damping material between the structure’s surface and an
priate safety, health, and environmental practices and deter-
additional elastic layer (that is, the constraining layer), whose
mine the applicability of regulatory limitations prior to use.
relativestiffnessisgreaterthanthatofthedampingmaterial,so
that energy is dissipated through cyclic deformation of the
1.3 This international standard was developed in accor-
dance with internationally recognized principles on standard- damping material, primarily in shear.
ization established in the Decision on Principles for the
3.2 Definitions of Terms Specific to This Standard:
Development of International Standards, Guides and Recom-
3.2.1 glassy region of a damping material—a temperature
mendations issued by the World Trade Organization Technical
region where a damping material is characterized by a rela-
Barriers to Trade (TBT) Committee.
tively high modulus and a loss factor that increases from
extremely low to moderate as temperature increases (see Fig.
2. Referenced Documents
1).
3.2.2 rubbery region of a damping material—a temperature
2.1 ASTM Standards:
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).
3.2.3 transition region of a damping material—a tempera-
ture region between the glassy region and the rubbery region
where a damping material is characterized by the loss factor
ThistestmethodisunderthejurisdictionofASTMCommitteeE33onBuilding
passing through a maximum and the modulus rapidly decreas-
and Environmental Acoustics and is the direct responsibility of Subcommittee
ing as temperature increases (see Fig. 1).
E33.10 on Structural Acoustics and Vibration.
Current edition approved Sept. 1, 2017. Published December 2017. Originally
3.3 Symbols—The symbols used in the development of the
approved in 1980. Last previous edition approved in 2010 as E756 – 05 (2010).
equations in this method are as follows (other symbols will be
DOI: 10.1520/E0756-05R17.
introduced and defined more conveniently in the text):
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
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
the ASTM website.
3 4
The last approved version of this historical standard is referenced on Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
www.astm.org. 4th Floor, New York, NY 10036, http://www.ansi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E756 − 05 (2017)
4.1.2 Non–self-supporting damping materials are evaluated
for their extensional damping properties in a two-step process.
First, a self-supporting, uniform metal beam, called the base
beam or bare beam, must be tested to determine its resonant
frequencies over the temperature range of interest. Second, the
dampingmaterialisappliedtothebasebeamtoformadamped
composite beam using one of two test specimen configurations
(Fig. 2bor Fig. 2c). The damped composite beam is tested to
obtain its resonant frequencies, and corresponding composite
loss factors over the temperature range of interest. The damp-
ing properties of the material are calculated using the stiffness
of the base beam, calculated from the results of the base beam
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
FIG. 1 Variation of Modulus and Material Loss Factor with
beams to be tested and the composite beam to be formed using
Temperature
(Frequency held constant) the sandwich specimen configuration (Fig. 2d).
(Glassy, Transition, and Rubbery Regions shown)
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
E = Young’s modulus of uniform beam, Pa
excitation force to cause the test beam to vibrate, and one to
η = loss factor of uniform beam, dimensionless
measure the response of the test beam to the applied force. By
E = Young’s modulus of damping material, Pa
1 measuring several resonances of the vibrating beam, the effect
η = loss factor of damping material, dimensionless
of frequency on the material’s damping properties can be
G = shear modulus of damping material, Pa
established.Byoperatingthetestfixtureinsideanenvironmen-
tal chamber, the effects of temperature on the material proper-
4. Summary of Method
ties are investigated.
4.1 The configuration of the cantilever beam test specimen
4.3 To fully evaluate some non-self-supporting damping
is selected based on the type of damping material to be tested
materials from the glassy region through the transition region
and the damping properties that are desired. Fig. 2 shows four
to the rubbery region may require two tests, one using one of
different test specimens used to investigate extensional and
the specimen configurations (Fig. 2bor Fig. 2c) and the second
shear damping properties of materials over a broad range of
using the sandwich specimen configuration (Fig. 2d) (See
modulus values.
Appendix X2.6).
4.1.1 Self-supporting damping materials are evaluated by
formingasingle,uniformtestbeam(Fig.2a)fromthedamping 5. Significance and Use
material itself.
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
models include simple beam and plate analogies as well as
finite element analysis models.
5.2 Thistestmethodhasbeenfoundtoproducegoodresults
whenusedfortestingmaterialsconsistingofonehomogeneous
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
FIG. 2 Test Specimens mathematicalmodelsaretohavethehighestpossibleaccuracy.
E756 − 05 (2017)
5.3 Assumptions: 5.4.1.3 For a sandwich specimen (see 10.2.4 and Fig. 2d),
theterm(f /f ) (2+DT)shouldbeequaltoorgreaterthan2.01.
5.3.1 All damping measurements are made in the linear
s n
5.4.1.4 The above limits are approximate. They depend on
range,thatis,thedampingmaterialsbehaveinaccordancewith
the thickness of the damping material relative to the base beam
linear viscoelastic theory. If the applied force excites the beam
and on the modulus of the base beam. However, when the
beyond the linear region, the data analysis will not be appli-
value of the terms in Sections 5.4.1.1, 5.4.1.2,or 5.4.1.3 are
cable. For linear beam behavior, the peak displacement from
near these limits the results should be evaluated carefully. The
rest for a composite beam should be less than the thickness of
ratiosinSections5.4.1.1,5.4.1.2,and5.4.1.3shouldbeusedto
the base beam (See Appendix X2.3).
judge the likelihood of error.
5.3.2 The amplitude of the force signal applied to the
5.4.2 TestspecimensFig.2bandFig.2careusuallyusedfor
excitation transducer is maintained constant with frequency. If
stiff materials with Young’s modulus greater than 100 MPa,
the force amplitude cannot be kept constant, then the response
where the properties are measured in the glassy and transition
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
5.3.3 Data reduction for both test specimens 2b and 2c (Fig.
valueof100MPaisgivenasaguideforbasebeamthicknesses
2)usestheclassicalanalysisforbeamsbutdoesnotincludethe
within the range listed in 8.4. The value will be higher for
effects of the terms involving rotary inertia or shear deforma-
thickerbeamsandlowerforthinnerbeams.Whenthe100MPa
tion. The analysis does assume that plane sections remain
guideline has been exceeded for a specific test specimen, the
plane; therefore, care must be taken not to use specimens with
test data may appear to be good, the reduced data may have
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-
ofdampingmaterialsinshear(sandwichspecimen2d-seeFig.
rate material property results can only be obtained by using the
2) do not include the extensional terms for the damping layer.
test specimen configuration that is appropriate for the range of
This is an acceptable assumption when the modulus of the
the modulus results.
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.
5.4.6 Consider known aging limits on both the damping and
smallmeasurementerrorsresultinlargeerrorsinthecalculated
adhesive materials before preserving samples for aging tests.
properties. To prevent such conditions from occurring, it is
recommended that:
6. Apparatus
5.4.1.1 For a specimen mounted on one side of a base beam
(see 10.2.2 and Fig. 2b), the term (f /f ) (1 + DT) should be
6.1 The apparatus con
...
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E756 − 05 (Reapproved 2017)
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 2.2 ANSI Standard:
S2.9 Nomenclature for Specifying Damping Properties of
1.1 This test method measures the vibration-damping prop-
Materials
erties of materials: the loss factor, η, and Young’s modulus, E,
or the shear modulus, G. Accurate over a frequency range of 50
3. Terminology
to 5000 Hz and over the useful temperature range of the
3.1 Definitions—Except for the terms listed below, ANSI
material, this method is useful in testing materials that have
S2.9 defines the terms used in this test method.
application in structural vibration, building acoustics, and the
3.1.1 free-layer (extensional) damper—a treatment to con-
control of audible noise. Such materials include metals,
trol the vibration of a structural by bonding a layer of damping
enamels, ceramics, rubbers, plastics, reinforced epoxy
material to the structure’s surface so that energy is dissipated
matrices, and woods that can be formed to cantilever beam test
through cyclic deformation of the damping material, primarily
specimen configurations.
in tension-compression.
1.2 This standard does not purport to address all of the
3.1.2 constrained-layer (shear) damper—a treatment to
safety concerns, if any, associated with its use. It is the
control the vibration of a structure by bonding a layer of
responsibility of the user of this standard to establish appro-
damping material between the structure’s surface and an
priate safety, health, and environmental practices and deter-
additional elastic layer (that is, the constraining layer), whose
mine the applicability of regulatory limitations prior to use.
relative stiffness is greater than that of the damping material, so
1.3 This international standard was developed in accor- that energy is dissipated through cyclic deformation of the
damping material, primarily in shear.
dance with internationally recognized principles on standard-
ization established in the Decision on Principles for the
3.2 Definitions of Terms Specific to This Standard:
Development of International Standards, Guides and Recom-
3.2.1 glassy region of a damping material—a temperature
mendations issued by the World Trade Organization Technical
region where a damping material is characterized by a rela-
Barriers to Trade (TBT) Committee.
tively high modulus and a loss factor that increases from
extremely low to moderate as temperature increases (see Fig.
2. Referenced Documents
1).
3.2.2 rubbery region of a damping material—a temperature
2.1 ASTM Standards:
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).
3.2.3 transition region of a damping material—a tempera-
ture region between the glassy region and the rubbery region
where a damping material is characterized by the loss factor
This test method is under the jurisdiction of ASTM Committee E33 on Building
passing through a maximum and the modulus rapidly decreas-
and Environmental Acoustics and is the direct responsibility of Subcommittee
ing as temperature increases (see Fig. 1).
E33.10 on Structural Acoustics and Vibration.
Current edition approved Sept. 1, 2017. Published December 2017. Originally
3.3 Symbols—The symbols used in the development of the
approved in 1980. Last previous edition approved in 2010 as E756 – 05 (2010).
equations in this method are as follows (other symbols will be
DOI: 10.1520/E0756-05R17.
2 introduced and defined more conveniently in the text):
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
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
the ASTM website.
3 4
The last approved version of this historical standard is referenced on Available from American National Standards Institute (ANSI), 25 W. 43rd St.,
www.astm.org. 4th Floor, New York, NY 10036, http://www.ansi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E756 − 05 (2017)
4.1.2 Non–self-supporting damping materials are evaluated
for their extensional damping properties in a two-step process.
First, a self-supporting, uniform metal beam, called the base
beam or bare beam, must be tested to determine its resonant
frequencies over the temperature range of interest. Second, the
damping material is applied to the base beam to form a damped
composite beam using one of two test specimen configurations
(Fig. 2b or Fig. 2c). The damped composite beam is tested to
obtain its resonant frequencies, and corresponding composite
loss factors over the temperature range of interest. The damp-
ing properties of the material are calculated using the stiffness
of the base beam, calculated from the results of the base beam
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
FIG. 1 Variation of Modulus and Material Loss Factor with
beams to be tested and the composite beam to be formed using
Temperature
the sandwich specimen configuration (Fig. 2d).
(Frequency held constant)
(Glassy, Transition, and Rubbery Regions shown)
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
E = Young’s modulus of uniform beam, Pa
excitation force to cause the test beam to vibrate, and one to
η = loss factor of uniform beam, dimensionless
measure the response of the test beam to the applied force. By
E = Young’s modulus of damping material, Pa
measuring several resonances of the vibrating beam, the effect
η = loss factor of damping material, dimensionless
of frequency on the material’s damping properties can be
G = shear modulus of damping material, Pa
established. By operating the test fixture inside an environmen-
tal chamber, the effects of temperature on the material proper-
4. Summary of Method
ties are investigated.
4.1 The configuration of the cantilever beam test specimen
4.3 To fully evaluate some non-self-supporting damping
is selected based on the type of damping material to be tested
materials from the glassy region through the transition region
and the damping properties that are desired. Fig. 2 shows four
to the rubbery region may require two tests, one using one of
different test specimens used to investigate extensional and
the specimen configurations (Fig. 2b or Fig. 2c) and the second
shear damping properties of materials over a broad range of
using the sandwich specimen configuration (Fig. 2d) (See
modulus values.
Appendix X2.6).
4.1.1 Self-supporting damping materials are evaluated by
forming a single, uniform test beam (Fig. 2a) from the damping 5. Significance and Use
material itself.
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
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
FIG. 2 Test Specimens mathematical models are to have the highest possible accuracy.
E756 − 05 (2017)
5.3 Assumptions: 5.4.1.3 For a sandwich specimen (see 10.2.4 and Fig. 2d),
the term (f /f ) (2 + DT) should be equal to or greater than 2.01.
5.3.1 All damping measurements are made in the linear
s n
5.4.1.4 The above limits are approximate. They depend on
range, that is, the damping materials behave in accordance with
the thickness of the damping material relative to the base beam
linear viscoelastic theory. If the applied force excites the beam
and on the modulus of the base beam. However, when the
beyond the linear region, the data analysis will not be appli-
value of the terms in Sections 5.4.1.1, 5.4.1.2, or 5.4.1.3 are
cable. For linear beam behavior, the peak displacement from
near these limits the results should be evaluated carefully. The
rest for a composite beam should be less than the thickness of
ratios in Sections 5.4.1.1, 5.4.1.2, and 5.4.1.3 should be used to
the base beam (See Appendix X2.3).
judge the likelihood of error.
5.3.2 The amplitude of the force signal applied to the
5.4.2 Test specimens Fig. 2b and Fig. 2c are usually used for
excitation transducer is maintained constant with frequency. If
stiff materials with Young’s modulus greater than 100 MPa,
the force amplitude cannot be kept constant, then the response
where the properties are measured in the glassy and transition
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-layer type of treatment, such as enamels and loaded vinyls.
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
5.3.3 Data reduction for both test specimens 2b and 2c (Fig.
value of 100 MPa is given as a guide for base beam thicknesses
2) uses the classical analysis for beams but does not include the
within the range listed in 8.4. The value will be higher for
effects of the terms involving rotary inertia or shear deforma-
thicker beams and lower for thinner beams. When the 100 MPa
tion. The analysis does assume that plane sections remain
guideline has been exceeded for a specific test specimen, the
plane; therefore, care must be taken not to use specimens with
test data may appear to be good, the reduced data may have
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-
of damping materials in shear (sandwich specimen 2d - see Fig.
rate material property results can only be obtained by using the
2) do not include the extensional terms for the damping layer.
test specimen configuration that is appropriate for the range of
This is an acceptable assumption when the modulus of the
the modulus results.
damping layer is considerably (about ten times) lower than that
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
materials have loss factors of approximately 0.001 or less, which is ness of the base beam (see 8.4).
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 Learn about the characteristics of any adhesive used to
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.
5.4.6 Consider known aging limits on both the damping and
small measurement errors result in large errors in the calculated
adhesive materials before preserving samples for aging tests.
properties. To prevent such conditions from occurring, it is
recommended that:
6. Apparatus
5.4.1.1 For a specimen mounted on one side of a base bea
...
This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E756 − 05 (Reapproved 2010) E756 − 05 (Reapproved 2017)
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
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 of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
1.3 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
E548 Guide for General Criteria Used for Evaluating Laboratory Competence (Withdrawn 2002)
2.2 ANSI Standard:
S2.9 Nomenclature for Specifying Damping Properties of Materials
3. Terminology
3.1 Definitions—Except for the terms listed below, ANSI S2.9 defines the terms used in this test method.
3.1.1 free-layer (extensional) damper—a treatment to control the vibration of a structural by bonding a layer of damping
material to the structure’s surface so that energy is dissipated through cyclic deformation of the damping material, primarily in
tension-compression.
3.1.2 constrained-layer (shear) damper—a treatment to control the vibration of a structure by bonding a layer of damping
material between the structure’s surface and an additional elastic layer (that is, the constraining layer), whose relative stiffness is
greater than that of the damping material, so that energy is dissipated through cyclic deformation of the damping material, primarily
in shear.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 glassy region of a damping material—a temperature region where a damping material is characterized by a relatively high
modulus and a loss factor that increases from extremely low to moderate as temperature increases (see Fig. 1).
3.2.2 rubbery region of a damping material—a temperature region where a damping material is characterized by a relatively
low modulus and a loss factor that decreases from moderate to low as temperature increases (see Fig. 1).
This test method is under the jurisdiction of ASTM Committee E33 on Building and Environmental Acoustics and is the direct responsibility of Subcommittee E33.10
on Structural Acoustics and Vibration.
Current edition approved May 1, 2010Sept. 1, 2017. Published August 2010December 2017. Originally approved in 1980. Last previous edition approved in 20052010
as E756E756 – 05 (2010).–05. DOI: 10.1520/E0756-05R10.10.1520/E0756-05R17.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or 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 the ASTM website.
The last approved version of this historical standard is referenced on www.astm.org.
Available from American National Standards Institute (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036, http://www.ansi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E756 − 05 (2017)
FIG. 1 Variation of Modulus and Material Loss Factor with
Temperature
(Frequency held constant)
(Glassy, Transition, and Rubbery Regions shown)
3.2.3 transition region of a damping material—a temperature region between the glassy region and the rubbery region where
a damping material is characterized by the loss factor passing through a maximum and the modulus rapidly decreasing as
temperature increases (see Fig. 1).
3.3 Symbols—The symbols used in the development of the equations in this method are as follows (other symbols will be
introduced and defined more conveniently in the text):
E = Young’s modulus of uniform beam, Pa
η = loss factor of uniform beam, dimensionless
E = Young’s modulus of damping material, Pa
η = loss factor of damping material, dimensionless
G = shear modulus of damping material, Pa
4. Summary of Method
4.1 The configuration of the cantilever beam test specimen is selected based on the type of damping material to be tested and
the damping properties that are desired. Fig. 2 shows four different test specimens used to investigate extensional and shear
damping properties of materials over a broad range of modulus values.
4.1.1 Self-supporting damping materials are evaluated by forming a single, uniform test beam (Fig. 2a) from the damping
material itself.
FIG. 2 Test Specimens
E756 − 05 (2017)
4.1.2 Non–self-supporting damping materials are evaluated for their extensional damping properties in a two-step process. First,
a self-supporting, uniform metal beam, called the base beam or bare beam, must be tested to determine its resonant frequencies
over the temperature range of interest. Second, the damping material is applied to the base beam to form a damped composite beam
using one of two test specimen configurations (Fig. 2b or Fig. 2c). The damped composite beam is tested to obtain its resonant
frequencies, and corresponding composite loss factors over the temperature range of interest. The damping properties of the
material are calculated using the stiffness of the base beam, calculated from the results of the base beam 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. By operating
the test fixture inside an environmental chamber, the effects of temperature on the material properties 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 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 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 beyond the linear region, the data analysis will not be applicable. For
linear beam behavior, the peak displacement from rest for a composite beam should be less than the thickness of the base beam
(See Appendix X2.3).
5.3.2 The amplitude of the force signal applied to the excitation transducer is maintained constant with frequency. If the force
amplitude cannot be kept constant, then the response of the beam must be divided by the force amplitude. The ratio of response
to force (referred to as the compliance or receptance) presented as a function of frequency must then be used for evaluating the
damping.
5.3.3 Data reduction for both test specimens 2b and 2c (Fig. 2) uses the classical analysis for beams but does not include the
effects of the terms involving rotary inertia or shear deformation. The analysis does assume that plane sections remain plane;
therefore, care must be taken not to use specimens with a damping material thickness that is much greater (about four times) than
that of the metal beam.
5.3.4 The equations presented for computing the properties of damping materials in shear (sandwich specimen 2d - see Fig. 2)
do not include the extensional terms for the damping layer. This is an acceptable assumption when the modulus of the damping
layer is considerably (about ten times) lower than that of the metal.
5.3.5 The equations for computing the damping properties from sandwich beam tests (specimen 2d–see Fig. 2) were developed
and solved using sinusoidal expansion for the mode shapes of vibration. For sandwich composite beams, this approximation is
acceptable only at the higher modes, and it has been the practice to ignore the first mode results. For the other specimen
configurations (specimens 2a, 2b, and 2c) the first mode results may be used.
5.3.6 Assume the loss factor (η) of the metal beam to be zero.
NOTE 1—This is a well-founded assumption since steel and aluminum materials have loss factors of approximately 0.001 or less, which is significantly
lower than those of the composite beams.
5.4 Precautions:
5.4.1 With the exception of the uniform test specimen, the beam test technique is based on the measured differences between
the damped (composite) and undamped (base) beams. When small differences of large numbers are involved, the equations for
E756 − 05 (2017)
calculating the material properties are ill-conditioned and have a high error magnification factor, i.e. small measurement errors
result in large errors in the calculated properties. To prevent such conditions from occurring, it is recommended that:
5.4.1.1 For a specimen mounted on one side of a base beam (see 10.2.2 and Fig. 2b), the term (f /f ) (1 + DT) should be equal
c n
to or greater than 1.01.
5.4.1.2 For a specimen mounted on two sides of a base beam (see 10.2.3 and Fig. 2c), the term (f /f ) (1 + 2DT) should be equal
m n
to or greater than 1.01.
5.4.1.3 For a sandwich specimen (see 10.2.4 and Fig. 2d), the term (f /f ) (2 + DT) should be equal to or greater than 2.01.
s n
5.4.1.4 The above limits are approximate. They depend on the thickness of the damping material relative to the base beam and
on the modulus of the base beam. However, when the value of the terms in Sections 5.4.1.1, 5.4.1.2, or 5.4.1.3 are near these limits
the results should be evaluated carefully. The ratios in Sections 5.4.1.1, 5.4.1.2, and 5.4.1.3 should be used to judge the likelihood
of error.
5.4.2 Test specimens Fig. 2b and Fig. 2c are usually used for stiff materials with Young’s modulus greater than 100 MPa, where
the properties are measured in the glassy and transition regions of such materials. These materials usually are of the free-layer type
of treatment, such as enamels and loaded vinyls. The sandwich beam technique usually is used for soft viscoelastic materials with
shear moduli less than 100 MPa. The value of 100 MPa is given as a guide for base beam thicknesses within the range listed in
8.4. The value will be higher for thicker beams and lower for thinner beams. When the 100 MPa guideline has been exceeded for
a specific test specimen, the test data may appear to be good, the reduced data may have little scatter and may appear to be
self-consistent. Although the composite beam test data are accurate in this modulus range, the calculated material properties are
generally wrong. Accurate material property results can only be obtained by using the test specimen configuration that is
appropriate for the range of the modulus results.
5.4.3 Applying an effective damping material on a metal beam usually results in a well-damped response and a signal-to-noise
ratio that is not very high. Therefore, it is important to select an appropriate thickness of damping material to obtain measurable
amounts of damping. Start with a 1:1 thickness ratio of the damping material to the metal beam for test specimens Fig. 2b and
Fig. 2c and a 1:10 thickness ratio of the damping material to one of the sandwich beams (Fig. 2d). Conversely, extremely low
damping in the system should be avoided because the differences between the damped and undamped system will be small. If the
thickness of the damping material cannot easily be changed to obtain the thickness ratios mentioned
...
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