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ASTM E756-05 (Reapproved 2017)

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ASTM E756-05 (Reapproved 2017)

Designation E756 − 05 Reapproved 2017Standard Test Method forMeasuring Vibration-Damping Properties of Materials1This standard is issued under the fixed designation E756; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript 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. Scope1.1 This test method measures the vibration-damping prop-erties of materials the loss factor, η, and Young’s modulus, E,or the shear modulus, G.Accurate over a frequency range of 50to 5000 Hz and over the useful temperature range of thematerial, this method is useful in testing materials that haveapplication in structural vibration, building acoustics, and thecontrol of audible noise. Such materials include metals,enamels, ceramics, rubbers, plastics, reinforced epoxymatrices, and woods that can be formed to cantilever beam testspecimen configurations.1.2 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety, health, and environmental practices and deter-mine the applicability of regulatory limitations prior to use.1.3 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade TBT Committee.2. Referenced Documents2.1 ASTM Standards2E548 Guide for General Criteria Used for Evaluating Labo-ratory Competence Withdrawn 200232.2 ANSI StandardS2.9 Nomenclature for Specifying Damping Properties ofMaterials43. Terminology3.1 DefinitionsExcept for the terms listed below, ANSIS2.9 defines the terms used in this test method.3.1.1 free-layer extensional dampera treatment to con-trol the vibration of a structural by bonding a layer of dampingmaterial to the structure’s surface so that energy is dissipatedthrough cyclic deformation of the damping material, primarilyin tension-compression.3.1.2 constrained-layer shear dampera treatment tocontrol the vibration of a structure by bonding a layer ofdamping material between the structure’s surface and anadditional elastic layer that is, the constraining layer, whoserelative stiffness is greater than that of the damping material, sothat energy is dissipated through cyclic deformation of thedamping material, primarily in shear.3.2 Definitions of Terms Specific to This Standard3.2.1 glassy region of a damping materiala temperatureregion where a damping material is characterized by a rela-tively high modulus and a loss factor that increases fromextremely low to moderate as temperature increases see Fig.1.3.2.2 rubbery region of a damping materiala temperatureregion where a damping material is characterized by a rela-tively low modulus and a loss factor that decreases frommoderate to low as temperature increases see Fig. 1.3.2.3 transition region of a damping materiala tempera-ture region between the glassy region and the rubbery regionwhere a damping material is characterized by the loss factorpassing through a maximum and the modulus rapidly decreas-ing as temperature increases see Fig. 1.3.3 SymbolsThe symbols used in the development of theequations in this method are as follows other symbols will beintroduced and defined more conveniently in the text1This test method is under the jurisdiction ofASTM Committee E33 on Buildingand Environmental Acoustics and is the direct responsibility of SubcommitteeE33.10 on Structural Acoustics and Vibration.Current edition approved Sept. 1, 2017. Published December 2017. Originallyapproved in 1980. Last previous edition approved in 2010 as E756 – 05 2010.DOI 10.1520/E0756-05R17.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3The last approved version of this historical standard is referenced onwww.astm.org.4Available 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 StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade TBT Committee.1E Young’s modulus of uniform beam, Paη loss factor of uniform beam, dimensionlessE1 Young’s modulus of damping material, Paη1 loss factor of damping material, dimensionlessG1 shear modulus of damping material, Pa4. Summary of Method4.1 The configuration of the cantilever beam test specimenis selected based on the type of damping material to be testedand the damping properties that are desired. Fig. 2 shows fourdifferent test specimens used to investigate extensional andshear damping properties of materials over a broad range ofmodulus values.4.1.1 Self-supporting damping materials are evaluated byforming a single, uniform test beam Fig. 2a from the dampingmaterial itself.4.1.2 Non–self-supporting damping materials are evaluatedfor their extensional damping properties in a two-step process.First, a self-supporting, uniform metal beam, called the basebeam or bare beam, must be tested to determine its resonantfrequencies over the temperature range of interest. Second, thedamping material is applied to the base beam to form a dampedcomposite beam using one of two test specimen configurationsFig. 2borFig. 2c. The damped composite beam is tested toobtain its resonant frequencies, and corresponding compositeloss factors over the temperature range of interest. The damp-ing properties of the material are calculated using the stiffnessof the base beam, calculated from the results of the base beamtests see 10.2.1, and the results of the composite beam testssee 10.2.2 and 10.2.3.4.1.3 The process to obtain the shear damping properties ofnon-self-supporting damping materials is similar to the twostep process described above but requires two identical basebeams to be tested and the composite beam to be formed usingthe sandwich specimen configuration Fig. 2d.4.2 Once the test beam configuration has been selected andthe test specimen has been prepared, the test specimen isclamped in a fixture and placed in an environmental chamber.Two transducers are used in the measurement, one to apply anexcitation force to cause the test beam to vibrate, and one tomeasure the response of the test beam to the applied force. Bymeasuring several resonances of the vibrating beam, the effectof frequency on the material’s damping properties can beestablished. By operating the test fixture inside an environmen-tal chamber, the effects of temperature on the material proper-ties are investigated.4.3 To fully evaluate some non-self-supporting dampingmaterials from the glassy region through the transition regionto the rubbery region may require two tests, one using one ofthe specimen configurations Fig. 2borFig. 2c and the secondusing the sandwich specimen configuration Fig. 2d SeeAppendix X2.6.5. Significance and Use5.1 The material loss factor and modulus of dampingmaterials are useful in designing measures to control vibrationin structures and the sound that is radiated by those structures,especially at resonance. This test method determines theproperties of a damping material by indirect measurementusing damped cantilever beam theory. By applying beamtheory, the resultant damping material properties are madeindependent of the geometry of the test specimen used toobtain them. These damping material properties can then beused with mathematical models to design damping systems andpredict their performance prior to hardware fabrication. Thesemodels include simple beam and plate analogies as well asfinite element analysis models.5.2 This test method has been found to produce good resultswhen used for testing materials consisting of one homogeneouslayer. In some damping applications, a damping design mayconsist of two or more layers with significantly differentcharacteristics. These complicated designs must have theirconstituent layers tested separately if the predictions of themathematical models are to have the highest possible accuracy.FIG. 1 Variation of Modulus and Material Loss Factor withTemperatureFrequency held constantGlassy, Transition, and Rubbery Regions shownFIG. 2 Test SpecimensE756 − 05 201725.3 Assumptions5.3.1 All damping measurements are made in the linearrange, that is, the damping materials behave in accordance withlinear viscoelastic theory. If the applied force excites the beambeyond the linear region, the data analysis will not be appli-cable. For linear beam behavior, the peak displacement fromrest for a composite beam should be less than the thickness ofthe base beam See Appendix X2.3.5.3.2 The amplitude of the force signal applied to theexcitation transducer is maintained constant with frequency. Ifthe force amplitude cannot be kept constant, then the responseof the beam must be divided by the force amplitude. The ratioof response to force referred to as the compliance or recep-tance presented as a function of frequency must then be usedfor 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 theeffects of the terms involving rotary inertia or shear deforma-tion. The analysis does assume that plane sections remainplane; therefore, care must be taken not to use specimens witha damping material thickness that is much greater about fourtimes than that of the metal beam.5.3.4 The equations presented for computing the propertiesof 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 thedamping layer is considerably about ten times lower than thatof the metal.5.3.5 The equations for computing the damping propertiesfrom sandwich beam tests specimen 2d–see Fig. 2 weredeveloped and solved using sinusoidal expansion for the modeshapes of vibration. For sandwich composite beams, thisapproximation is acceptable only at the higher modes, and ithas been the practice to ignore the first mode results. For theother specimen configurations specimens 2a, 2b, and 2c thefirst mode results may be used.5.3.6 Assume the loss factor η of the metal beam to bezero.NOTE 1This is a well-founded assumption since steel and aluminummaterials have loss factors of approximately 0.001 or less, which issignificantly lower than those of the composite beams.5.4 Precautions5.4.1 With the exception of the uniform test specimen, thebeam test technique is based on the measured differencesbetween the damped composite and undamped base beams.When small differences of large numbers are involved, theequations 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 calculatedproperties. To prevent such conditions from occurring, it isrecommended that5.4.1.1 For a specimen mounted on one side of a base beamsee 10.2.2 and Fig. 2b, the term fc/fn21 DT should beequal to or greater than 1.01.5.4.1.2 For a specimen mounted on two sides of a basebeam see 10.2.3 and Fig. 2c, the term fm/fn212DTshould 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 fs/fn22 DT should be equal to or greater than 2.01.5.4.1.4 The above limits are approximate. They depend onthe thickness of the damping material relative to the base beamand on the modulus of the base beam. However, when thevalue of the terms in Sections 5.4.1.1, 5.4.1.2,or5.4.1.3 arenear these limits the results should be evaluated carefully. Theratios in Sections 5.4.1.1, 5.4.1.2, and 5.4.1.3 should be used tojudge the likelihood of error.5.4.2 Test specimens Fig. 2b and Fig. 2c are usually used forstiff materials with Young’s modulus greater than 100 MPa,where the properties are measured in the glassy and transitionregions of such materials. These materials usually are of thefree-layer type of treatment, such as enamels and loaded vinyls.The sandwich beam technique usually is used for soft vis-coelastic materials with shear moduli less than 100 MPa. Thevalue of 100 MPa is given as a guide for base beam thicknesseswithin the range listed in 8.4. The value will be higher forthicker beams and lower for thinner beams. When the 100 MPaguideline has been exceeded for a specific test specimen, thetest data may appear to be good, the reduced data may havelittle scatter and may appear to be self-consistent. Although thecomposite beam test data are accurate in this modulus range,the calculated material properties are generally wrong. Accu-rate material property results can only be obtained by using thetest specimen configuration that is appropriate for the range ofthe modulus results.5.4.3 Applying an effective damping material on a metalbeam usually results in a well-damped response and a signal-to-noise ratio that is not very high. Therefore, it is important toselect an appropriate thickness of damping material to obtainmeasurable amounts of damping. Start with a 11 thicknessratio of the damping material to the metal beam for testspecimens Fig. 2b and Fig. 2c and a 110 thickness ratio of thedamping material to one of the sandwich beams Fig. 2d.Conversely, extremely low damping in the system should beavoided because the differences between the damped andundamped system will be small. If the thickness of thedamping material cannot easily be changed to obtain thethickness ratios mentioned above, consider changing the thick-ness 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 thedamping material and any adhesive used to bond the materialto the base beam.5.4.5 Learn about the characteristics of any adhesive used tobond the damping material to the base beam. The adhesive’sstiffness and its application thickness can affect the damping ofthe composite beam and be a source of error see 8.3.5.4.6 Consider known aging limits on both the damping andadhesive materials before preserving samples for aging tests.6. Apparatus6.1 The apparatus consists of a ri

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