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Testing Brief Measuring Dynamic Properties of Elastomersbetween 400 Hz. and 10,000 Hz.IntroductionMeasuring the dynamic properties o elastomeric materials in the range o 400 Hz. to 10,000 Hz. is importantbecause this is a signi cant range in human hearing. Elastomers are o ten used to control or reduce vibrational re-quencies in this range.

Te analysis o small amplitude vibrations in de ormed viscoelastic solids (Morman and Nagtegaal (1983), MormanKao, Nagtegaal (1981) [3,4] is applicable to rubber support mounts, automotive door seals [2] and vibration isola-tion gaskets. Use o these capabilities in analysis so tware such as ABAQUS or MSC.MARC requires the equilib-

rium large strain material properties and thdynamic material properties. An outlineor the experimental determination o thedynamic material properties at vibrationrequencies between 400 Hz. and 10,000Hz. using a wave propagation approach isprovided herein.

Dynamic PropertiesTe dynamic material properties o interest

are the storage modulus and loss moduluso the material when subjected to a sinu-soidal vibration superimposed on a meanstrain. Te storage modulus and the lossmodulus are the real and imaginary parts othe dynamic modulus [1]. In this case, orinput into the analysis so tware, we are in-terested in the di erential dynamic modulusdescribed by Nolle [5] as ollows:

“Di erential dynamic modulus re ers to dynamic modulus determined rom a sample upon which a static de orma-tion is imposed along the same coordinate as the dynamic de ormation. Because the di erential dynamic modulus a complicated unction o static strain or many rubbers, it is best to regard the sample at any particular static de ormation as a distinct material rom the standpoint o dynamic modulus measurements. … Te di erential dynamicmodulus cannot be identi ed with the slope o the quasi-static stress-strain curve except at very low requency.”In this discussion, dynamic modulus will be measured as di erential dynamic modulus. Te dynamic modulus measurements are not simply a unction o requency and there ore need to be made at mean strain levels appropriate tothe application.

Figure 1, Storage Modulus Measurements for 1 Material using both Low Frequency and High Frequency techniques to generate data over a wide Frequency Range

Laser SurfaceVelocimeter

Accelerometer

DynamicShaker

TemperatureChamber

Test Specimen

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Measuring Dynamic Properties at Frequencies from 400Hz. to 10,000 Hz. As vibration requencies exceed 400 Hz., the dynamic vibration wavelength becomes too small to be considered very large comparedto the specimen length. As such, one needs to consider the e ect o the wave traveling through the specimen. Te mass o the specimenbecomes signi cant (Figure 2). A method to measure the dynamicproperties in the range o 400 Hz. to 20,000 Hz. is to per orm wave propagation experiments [5]. In these experiments, the rate o travel and the attenuation o the wave amplitude o a traveling wavein a long thin strip o elastomer are measured.

Te experimental procedure is to stretch a long strip o elastomer tothe mean strain level o interest and allow it to reach an equilibriumcondition. Te specimen needs to be very narrow such that the width and thickness are very small relative to the dynamic vibration wavelength yet very long such that a high requency traveling wavedoesn’t reach the end and refect back into the measurement. A

small sinusoidal dynamic vibration o short duration is introducedat one end o the long specimen so as to produce a longitudinaltraveling wave. An accelerometer is used to measure the vibrationat the source and a velocity sensor is used to measure the amplitudeo the wave as it travels past a point which is a known distance along the specimen. From this a phase relationship between the source andthe point and an amplitude relationship between the source and thepoint is determined. Te same dynamic vibration is again introducedand the phase relationship and amplitude relationship to a di erent point is determined.Given relative measurements at two known points along the specimen, the phase and amplitude relationship be-tween the two points becomes known. From the phase o the wave between points a known distance apart, the wavelengthλ can be calculated. Te speed c o the longitudinal wave is given by:

c = λ

where is the vibration requency. I the density (ρ) o the material is known, rom basic wave equations the dy-namic modulus can be calculated as ollows:

Dynamic Modulus E*=ρc 2

Te storage modulus and the loss modulus corresponding to the dynamic modulus may be determined using the

amplitude attenuation measurements [5]. Te advantage o the wave propagation experiment is that high requencydynamic properties can be measured directly. Te disadvantage is that the amplitudes or this type o experimentalapparatus tend to be very small. Because the amplitudes are very small, they are relatively insensitive to the absovalue o dynamic strain. Tis may not be critical because high requency vibrations in engineering application areo ten very small. Experimental Methods

At Axel Products, a commercial laser sur ace velocimeter is used to measure the velocity on the specimen sur ace.Tis non-contacting method allows or the use o an environmental chamber such that the material properties can

∞

k

m

k

m

k

m

k

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Figure 2, High Frequency Material Representationincluding Mass Effects

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Axel Products, Inc.2255 S Industrial

Ann Arbor MI 48104Tel: 734 994 8308Fax: 734 994 8309info@axelproducts.com

For more information, visit www.axelproducts.com. Axel Products provides physical testing services or engineers and analysts. Te ocus ison the characterization o nonlinear materials such as elastomers and plastics.

Data rom the Axel laboratory is o ten used to develop material models in nite elementanalysis codes such as ABAQUS, MSC.Marc, ANSYS and LS-Dyna.

0 2000 4000 6000 8000 10000

S t o r a g e

M o

d u

l u s

( M P a

)

Frequency (Hz)

Figure 3, Storage Modulus Measurements for 1 Material using both Low Frequency and High Frequency techniques to generate data over a wide Frequency Range

be determined between temperatures o ap-proximately -40C to 150C. Te test speci-men is ideally very long (> 400 mm) butshorter specimens ( >175 mm) have beenused with modest success.

References1. J D. Ferry, Viscoelastic Properties o Polymers, 3rth ed. (Wiley, New York, 1980)

2. Y Gur and K N Morman, Jr., AnalyticalPrediction o Sound ransmission Trough Automotive Door Seal Systems, Presentedat Te Tird Joint Meeting o the Acousti-cal Society o America and the AcousticalSociety o Japan, Honolulu, Hawaii, De-

cember 2-6, 1996

3. K N Morman, Jr., and J C Nagtegaal,Finite Element Analysis o Sinusoidal Small-Amplitude Vibrations in De ormed Viscoelastic Solids. Part I. Teoretical Development, International Journal or Numerical Methods in Engineering, Vol. 19, pp.1079-1103 (1983)

4. K N Morman, Jr., B.G. Kao and J C Nagtegaal, “ Finite Element Analysis o Viscoelastic Elastomeric StructureVibrating about Non-Linear Statically Stressed Con gurations”, SAE Paper 811309 (1981)

5. A W. Nolle, “Methods or Measuring Dynamic Mechanical Properties o Rubber-Like Materials,” J. Appl. Phys.19, 753 (1948)