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**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 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_{c}/f_{n})^{2}(1 + DT) should be equal 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_{m}/f_{n})^{2}(1 + 2DT) should be equal to or greater than 1.01.

5.4.1.3 For a sandwich specimen (see 10.2.4 and Fig. 2d), the term (f_{s}/f_{n})^{2}(2 + DT) should be equal to or greater than 2.01.

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 above, consider changing the thickness of the base beam (see 8.4).

5.4.4 Read and follow all material application directions. When applicable, allow sufficient time for curing of both the damping material and any adhesive used to bond the material to the base beam.

5.4.5 Learn about the characteristics of any adhesive used to bond the damping material to the base beam. The adhesive's stiffness and its application thickness can affect the damping of the composite beam and be a source of error (see 8.3).

5.4.6 Consider known aging limits on both the damping and adhesive materials before preserving samples for aging tests.

**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, 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.*

**2. Referenced Documents** *(purchase separately)* The documents listed below are referenced within the subject standard but are not provided as part of the standard.

**ASTM Standards**

E548 Guide for General Criteria Used for Evaluating Laboratory Competence

**ICS Code**

ICS Number Code 91.120.20 (Acoustics in buildings. Sound insulation)

**UNSPSC Code**

UNSPSC Code 30141601(Acoustical insulation)

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**DOI:** 10.1520/E0756-05R17

**Citation Format**

ASTM E756-05(2017), Standard Test Method for Measuring Vibration-Damping Properties of Materials, ASTM International, West Conshohocken, PA, 2017, www.astm.org

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