ASTM E756-05(2023)

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 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 reduct...
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 Hz 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.

General Information

• Status: Published
• Publication Date: 31-Oct-2023
• ICS: 91.120.20 - Acoustics in building. Sound insulation
• Technical Committee: E33 - Building and Environmental Acoustics
• Drafting Committee: E33.10 - Structural Acoustics and Vibration

Relations

• Replaces: ASTM E756-05(2017) - Standard Test Method for Measuring Vibration-Damping Properties of Materials
• Effective Date: 01-Nov-2023
• Referred By: ASTM E2963-22 - Standard Test Method for Laboratory Measurement of Acoustical Effectiveness of Ship Noise Treatments Laboratory Measurement of Acoustical Effectiveness for Marine Bulkhead and Deck Treatments
• Effective Date: 01-Nov-2023
• Referred By: ASTM C634-22 - Standard Terminology Relating to Building and Environmental Acoustics
• Effective Date: 01-Nov-2023

Overview

ASTM E756-05(2023): Standard Test Method for Measuring Vibration-Damping Properties of Materials is an internationally recognized method developed by ASTM International. The standard outlines procedures to measure important vibration-damping parameters, including loss factor (η), Young's modulus (E), and shear modulus (G), over a broad frequency range (50 Hz to 5000 Hz) and within the useful temperature range for the material in question. This test method plays a crucial role in applications involving the mitigation of structural vibration and noise, with direct relevance in engineering, construction, automotive, aerospace, and acoustics industries.

Key Topics

• Vibration-Damping Measurement: The standard provides guidance for indirect measurement of material damping properties using cantilever beam theory. This ensures the data obtained are independent of the geometry of the specimen, focusing on intrinsic material properties.
• Loss Factor and Modulus Determination: It specifies how to determine the loss factor (which quantifies damping effectiveness) and the modulus (stiffness) of various materials, both essential for predicting how materials will perform under dynamic loads.
• Material Types: The standard applies to a wide range of materials capable of being fabricated into cantilever beam configurations, including metals, enamels, ceramics, rubbers, plastics, reinforced epoxies, and wood.
• Testing Approach:
  • Use of uniform (self-supporting), single-side damped, double-side damped, or sandwich specimen configurations, adapted to material stiffness and intended use.
  • Performance of tests within an environmental chamber to ensure temperature control and assessment over a temperature range.
  • Use of non-contacting transducers (when possible) for excitation and response measurement to minimize external sources of damping.
• Data Reduction and Assumptions: Assumes materials behave according to linear viscoelastic theory under test conditions. The standard emphasizes the necessity of consistent force amplitude and careful specimen preparation for accurate measurements.

Applications

• Structural Vibration Control: Engineers use the test data to design damping treatments for mechanical structures, reducing unwanted resonance and extending product life.
• Acoustic Material Evaluation: Architects and building engineers rely on these measurements to select and design materials and assemblies that control sound transmission and minimize noise in buildings.
• Noise and Vibration Simulation: Provides validated input parameters for advanced modeling techniques (such as finite element analysis), enabling prediction of damping performance before physical prototypes are constructed.
• Material Development and Selection: Material developers and product designers leverage the results to compare the vibration-damping performance of new materials or formulations under controlled laboratory conditions.
• Quality Assurance and Compliance: Manufacturers employ the method to establish consistency in material properties, support research, and demonstrate compliance with industry or regulatory requirements.

Related Standards

• ANSI S2.9: Nomenclature for Specifying Damping Properties of Materials
• ASTM E548: Guide for General Criteria Used for Evaluating Laboratory Competence (referenced as a laboratory quality assurance guide)
• Other ASTM Acoustics and Vibration Standards: Standards addressing methods for sound attenuation, modal analysis, and noise measurement.

Practical Value

Implementing ASTM E756 enables the development of quieter, more reliable products and infrastructure by quantifying the vibration-damping properties of candidate materials. Accurate damping measurement is integral to the design, modeling, and quality control processes in industries where vibration reduction enhances performance, safety, or comfort.

Regular use of this standard ensures reproducible, objective comparisons of material performance, underpinned by internationally recognized testing methodologies. This builds confidence in material choice and system reliability while supporting regulatory and customer requirements in global markets.

Keywords: ASTM E756, vibration damping, loss factor, Young's modulus, shear modulus, structural acoustics, noise control, material testing, beam theory, acoustic materials, finite element analysis, vibration measurement.

Standards Content (Sample)

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 2023)
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
3. Terminology
50 Hz 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
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
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 Nov. 1, 2023. Published December 2023. Originally
3.3 Symbols—The symbols used in the development of the
approved in 1980. Last previous edition approved in 2017 as E756 – 05 (2017).
equations in this method are as follows (other symbols will be
DOI: 10.1520/E0756-05R23.
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 [e-mail]. 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 (2023)
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
(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. 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.
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 (2023)
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 5.4.1.1, 5.4.1.2, or 5.4.1.3 are near these
cable. For linear beam behavior, the peak displacement from
limits the results should be evaluated carefully. The ratios in
rest for a composite beam should be less than the thickness of
5.4.1.1, 5.4.1.2, and 5.4.1.3 should be used to judge the
the base beam (See X2.3).
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
rate material property results can only be obtained by using the
Fig. 2) do not include the extensional terms for the damping
test specimen configuration that is appropriate for the range of
layer. This is an acceptable assumption when the modulus of
the modulus results.
the damping layer is considerably (about ten times) lower than
5.4.3 Applying an effective damping material on a metal
that 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 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, that is,
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 beam
(see 10.2.2 and Fig. 2b), the term (f /f ) (1 + DT) should be
6.1 The apparatus consists of a rigid test fixture to hold the
c n
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) mentation for generating the excitation signal and measuring
m n
should be equal to or greater than 1.01. the response signal. Typical setups are shown in Figs. 3 and 4.
E756 − 05 (2023)
6.2.1 To check the rigidity and clamping action of the
fixture, test a bare steel beam as a uniform specimen (see 8.1.1)
using the procedure in Section 9 and calculate the material
properties using the equations in 10.2.1. If Young’s modulus is
not 2.07 E+11 Pa (30 E+6 psi) and the loss factor is not
approximately 0.002 to 0.001 for modes 1 and 2 and 0.001 or
less for the higher modes, then there is a problem in the fixture
or somewhere else in the measurement system (see X2.2).
6.2.2 It is often useful to provide vibration isolation of the
test fixture to reduce the influence of external vibrations which
may be a source of measurement coherence problems.
6.2.3 Fig. 3 shows a test fixture with a vertical orientation of
the specimen beam. The location of the clamp may be either at
the top with the specimen extending downward, as shown in
Fig. 3, or at the bottom with the specimen extending upward.
Horizontal orientation of the beam is also commonly employed
(see Fig. 4).
6.3 Environmental Chamber—An environmental chamber
is used for controlling the temperature of the test fixture and
specimen. As an option, the chamber may also be controlled for
other environmental factors such as vacuum or humidity.
Environmental chambers often are equipped with a rotating fan
for equalizing the temperature throughout the chamber. If it is
found that the fan is a source of external vibration in the test
FIG. 3 Block Diagram of Experimental Set-Up Using Separate beam, the fan may be switched off during data acquisition
Excitation and Response Channels and a Sinusoidal Excitation
provided it is conclusively shown that doing so does not affect
Signal
the test temperature or temperature distribution within the
specimen. If the temperature of the chamber and the specimen
are not stable, no measurement data may be acquired.
6.4 Transducers—Two transducers are utilized. One trans-
ducer applies the excitation force, and the other measures the
response of the beam. Because it is necessary to minimize all
sources of damping except that of the material to be
investigated, it is preferable to use transducers of the noncon-
tacting type. Usually the excitation force is applied using an
electromagnetic, noncontacting transducer (for example, ta-
chometer pickup) and sometimes response is measured using
the same type of transducer. When using stainless steel,
aluminum, or nonferrous beams, small bits of magnetic mate-
rial may be fastened adhesively to the base beam side of the
specimen to achieve specimen excitation and measurable
response.
6.4.1 At higher frequencies, where noncontacting transduc-
ers lack the sensitivity necessary for measurements, subminia-
ture transducers (less than 0.5 g) (that is, accelerometers, strain
gages, and so on) may be attached to the beam. Before using a
contacting transducer, it must be demonstrated, using the
process described in 6.2.1, that the transducer is not a signifi-
cant source of damping that would contaminate the measure-
ments. The data obtained with these contacting transducers
FIG. 4 Block Diagram of Experimental Set-Up Using a Two- must be identified and a comment cautioning the reader about
Channel Spectrum Analyzer and Random Noise Excitation Signal
possible effects (damping and stiffness, especially due to the
wiring required by contacting transducers) from this approach
must be included in the report.
6.2 Test Fixture—The test fixture consists of a massive, rigid 6.4.2 Fig. 3 shows the arrangement of the transducers with
structure which provides a clamp for the root end of the beam the pick-up transducer near the root and the exciter transducer
and mounting support for the transducers. near the free end. The locations of the transducers may be
E756 − 05 (2023)
NOTE 3—This test specimen configuration is often called the modified
reversed, as shown in Fig. 4. The locations should be selected
Oberst beam.
to obtain the best signal-to-noise ratio.
8.1.4 Test specimen 2d, sandwich specimen, is used for
6.5 Instrumentation—The minimum instrumentation re-
determining the damping properties of soft materials that will
quirements for this test is two channels for vibration data
(excitation and response) and one channel for temperature data. be subjected to shear deformation in their application. A metal
6.5.1 Fig. 3 shows separate excitation and response signal spacer of the same thickness as the damping material must be
instrumentation channels. Alternatively, a two-channel spec-
added in the root section between the two base beams of the
trum analyzer (for example, based on the Fast Fourier Trans-
test specimen (see Fig. 2d). The spacer must be bonded in place
form algorithm) may be used (see Fig. 4).
with a stiff, structural adhesive system.The dimensions and the
6.5.2 The instrumentation may generate either a sinusoidal
resonant frequencies of the two base beams must match.
or random noise excitation signal.
Successful results have been obtained when the free lengths
6.5.3 It is recommended that the waveforms in both excita-
match within 60.5 mm, the thickness values match within
tion and response channels be monitored. If separate excitation
60.05 mm. For other beam dimensions that are not used in the
and response channels are used, as shown in Fig. 3, a
data reduction calculations, follow good engineering practice
two-channel oscilloscope can perform this function. Two-
when determining the adequacy of the match. For the resonant
channel spectrum analyzers usually have a similar waveform
frequencies, for each mode used in the calculations, the
display function.
frequencies must match to within 1.0 % of the lower measured
frequency value of the two beams. (See X2.1.2.)
7. Sampling
8.2 All test specimens are to have well-defined roots, that is,
7.1 The damping material test specimen shall be represen-
the end section of the beam to be clamped in the test fixture
tative of the bulk quantity of material from which the specimen
is taken. Where adhesive bonding is employed, care must be (see Fig. 2). The root section should have a length of 25 mm to
taken to minimize lot-to-lot variability of the adhesive’s 40 mm and have a height above the top surface of the beam and
chemical and physical properties.
a height below the bottom surface of the beam that are each at
least equal to the thickness of the composite beam. The
8. Test Specimen Preparation
presence of these roots is essential for generating useful and
meaningful data for most measurements because they give the
8.1 Select the configuration of the test specimen based on
the type of damping material to be tested and the damping best simulation of the cantilever boundary condition when the
properties that are desired. The techniques required for prepa- beam is clamped in the rigid test fixture. These roots can be
ration of the damping material test specimen often are depen- either integrally machined as part of the beam, welded to the
dent on the physical characteristics of the material itself. To beam, or bonded to the beam with a stiff, structural adhesive
prepare a damped composite beam may require various tech-
system (See X2.1).
niques such as spray coating, spatula application, or adhesive
8.3 Follow the damping material supplier’s recommenda-
bonding of a precut sample. Four test specimen configurations
tions in the selection and application of an adhesive. Lacking
are given in Fig. 2 and their use is described as follows:
such recommendations, the following should be considered:
8.1.1 Test specimen 2a, uniform beam, is used for measur-
The damping material is usually bonded to the metal beam
ing the damping properties of self-supporting materials. This
using a structural grade (versus a contact type) adhesive which
configuration is also used for testing the metal base beam or
should have a modulus much higher (about ten times) than that
beams that form the supporting structure in the other three
of the damping material. The thickness of the adhesive layer
specimen configurations.
must be kept to a minimum (less than 0.05 mm), and small in
8.1.2 Test specimen 2b, damped one side, is used to evaluate
comparison with that of the damping material. If these two
the properties of stiff damping materials when subjected to
extensional deformation. rules are not met, deformation may occur in the adhesive layer
instead of the damping layer and erroneous data will result.
NOTE 2—This is the test specimen configuration that was used by Dr. H.
Note that in some cases the damping material is of the
Oberst. (1) It is often called the Oberst beam or Oberst bar. The general
method of measuring damping using a vibrating cantilever beam is self-adhesive type.
sometimes referred to as the Oberst beam test.
8.4 The metal used for the base beam is usually steel or
8.1.3 Test specimen 2c, damped two sides, has material
aluminum. Base beam dimensions found to be successful are a
coated on both sides of the base beam. The properties are
width of 10 mm, a free length of 180 mm to 250 mm, and a
determined under extensional deformation. This configuration
thickness of 1 mm to 3 mm. Other base beam dimensions may
allows for simplification in the equations relating to 8.1.2. It
be selected based on the desired frequency range of the
also helps to minimize curling of the composite beam during
measurements and the characteristics of the damping material
changing temperature conditions due to differences in thermal
to be tested. The width of the beam is not a factor in the
expansion.
equations for calculating the material properties. However,
when selecting the width of the beam, care should be taken to
5 avoid making the beam susceptible to torsional vibrations (see
The boldface numbers in parenthesis refer to the list of references at the end of
this test method. assumptions in 5.3.3).
E756 − 05 (2023)
8.5 The thickness of the damping material may vary, de-
pending on the specific properties of the material and the
temperatures and frequencies of interest.
9. Procedure
9.1 Mount the beam in a heavy, rigid fixture providing
clamping force around the root of the beam to simulate a fixed
end, cantilever boundary condition.
9.2 Place the test fixture, including the beam specimen,
inside an environmental chamber.
9.3 Position the transducers on or around the specimen as
appropriate for the type of transducer. (Noncontacting type
transducers are often placed approximately 1 mm away from
the specimen.) Typical setups are shown in Figs. 3 and 4.
9.4 Set the environmental chamber to the desired tempera-
ture. Vibration response measurements must be performed at
intervals over a wide range of temperatures. Temperature
increments of 5 °C or 10 °C between data acquisition tempera-
tures are common.
9.4.1 The beginning and end points of the temperature range
are dependent on the damping material being tested and must
FIG. 5 Typical Frequency Response Spectrum of an Undamped
Beam
be determined by monitoring the loss factor results for the
damped composite beam. The range is adequate when the
upper and lower slopes, as well as the peak of the loss factor
curve, have been well defined by the measurements (see Fig.
1).
9.4.2 To ensure that the test specimen is in full thermal
equilibrium during testing, adequate soak time is needed after
each new temperature is reached. The specimen-fixture system
is considered to be in full thermal equilibrium when the
temperature of the entire specimen-fixture system does not
differ from the desired test temperature by more than 60.6 °C.
The soak time depends on the thermal mass of the specimen-
fixture system. When determining the soak time it is recom-
mended that the minimum soak time not be less than 30 min
(see X2.8).
9.5 At each data acquisition temperature, excite the test
specimen by applying either a sinusoidal or random signal to
the excitation transducer by means of a power amplifier.
FIG. 6 Variation of Resonance Frequency with Temperature for
Measure the response of the beam using the second transducer.
the Indicated Bending Modes of a Damped Cantilever Beam
When using swept sinusoidal excitation, it is recommended
that a manually controlled sweep be used rather than an
automatically controlled sweep. This is because a high sweep
rate can cause considerable errors in the response spectrum, value of the response curve is 3 dB less (the 3 dB down points)
and a manual sweep allows better control for adapting to the than the value at resonance. The frequency difference between
circumstances of the measurement. Fig. 5 shows a typical the upper 3 dB down point and the lower 3 dB down point is
frequency response spectrum at a fixed temperature. the half-power bandwidth of the mode. The modal loss factor
9.5.1 Measure several resonant modes of the beam for each (η) is the ratio of the half-power bandwidth to the resonant
data acquisition temperature. Figs. 6 and 7 show examples of frequency (See the loss factor calculation in 10.2.1 for the
the variation with temperature in the resonance frequency and uniform beam).
loss factor of a damped composite beam. Four or more modes 9.5.3 Methods other than the half-power bandwidth method
are commonly measured starting with mode 2. Mode 1 is may be used for measuring the modal damping of the test
usually not measured (see 5.3.5). specimen provided it can be shown that the other methods give
9.5.2 Use the half-power bandwidth method to measure the the same results for moderately damped specimens. Examples
damping of the composite beam. Using the response curve of other possible methods are modal curve fitting (2), Nyquist
from each mode, measure the resonant frequency and the plots (3), dynamic stiffness methods (4) or the “n dB”
frequencies above and below the resonant frequency where the bandwidth method (5) (described below).
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10. Calculation
10.1 For all types of test specimens the calculation of the
damping material properties requires the resonant frequency of
each mode, the half-power bandwidth (3 dB down points) or
modal loss factor of each mode, the geometric properties of the
beam, and the densities of the material
...