Nonresonant forced vibration

Dynamic techniques are used to determine storage and loss moduli, G and G respectively, and the loss tangent, tan 5. Some instmments are sensitive enough for the study of Hquids and can be used to measure the dynamic viscosity T 7 Measurements are made as a function of temperature, time, or frequency, and results can be used to determine transitions and chemical reactions as well as the properties noted above. Dynamic mechanical techniques for sohds can be grouped into three main areas free vibration, resonance-forced vibrations, and nonresonance-forced vibrations. Dynamic techniques have been described in detail (242,251,255,266,269—279). A number of instmments are Hsted in Table 8. Related ASTM standards are Hsted in Table 9. 

Fig. 46. Schematic diagram of a dynamic mechanical analy2er based on the nonresonance-forced vibration principle (Rheovibron-type).

This test method employs nonresonant forced vibration techniques for determining the complex viscosity (see below) and viscoelastic characteristics of thermoplastic resins as a function of frequency, strain amplitude, temperature, and time. A wide range of frequencies can be used, typically from 0.01 to 100 Hz. 

Dynamic viscoelastic measurements are useful in studying the structure of polymers, because these mechanical properties are sensitive to glass transition, crystallinity, cross-linking, filling systems (filler or plasticizer), molecular aggregation, and phase separation. To determine dynamic viscoelastic properties, such as storage modulus, loss modulus, and tan, various methods have been proposed, and recently many types of instruments are commercially available. Typical methods to measure the dynamic viscoelasticity are classified into three categories damped free vibration, resonance free vibration, and nonresonance forced vibration. These methods are standardized by the international standard ISO 6721 [3]. 

In nonresonance forced vibration methods, either a sinusoidal deformation or load is applied to the specimen, and the response of either the force or deformation is detected, respectively. The storage modulus ( ), loss modulus ( "), and the phase angle (S) between the deformation and force are calculated. The tensile, flexural, and shear modes are generally used, and most of the commercially available apparatuses use nonresonance forced vibration... 

Figure 9 shows an example of a nonresonance forced vibration apparatus. A sinusoidal deformation is applied to the specimen, and the amplitude of the deformation is measured using a strain transducer, and the magnitude of the response force is measured using a stress transducer. If the deformation and force are recorded on a recorder, the output data are as shown in Fig. lOA. 

Fig. 10 Output data from the nonresonance forced vibration method. (A) Relationship between sinusoidal force and deformation for a viscoelastic body. (B) Dynamic stress-strain hysteresis loop for a viscoelastic body.

BS 903 PA24 Guide to the determination of dynamic properties of rubbers DIN 53513 Determination of the viscoelastic properties of elastomers on exposure to forced vibration at nonresonant frequencies... 

Free vibration methods such as the torsion pendulum are covered by ISO 4663 and are limited to cry low strains and frequencies, and are in much less frequent use these days than the forced vibration nonresonant systems on which this chapter will focus. The early Du Pont DMA and German Myrenne used input energy to maintain the resonant oscillation amplitude, but the main limitations were variable frequency according to the sample size (which had to be glassy or plastic) or one frequency only (1 Hz) respectively. 

A comprehensive review of measurement techniques is presented by Capps (167), who also gives data for the complex Young s modulus for a range of polymers. This data includes the rubbery, transition, and glassy regions, and parameters for time-temperature superposition (eq. 45). The measiuement techniques fall broadly into three categories wave propagation methods, resonance methods, and forced-vibration nonresonance methods. The resonance and forced-vibration... 

Forced-Vibration Nonresonance Methods, in the forced, nonresonant method (183,188) sensors are used to measure the drive force and resulting displacement at one end of the sample. The complex modulus (shear or Young s) is determined from the amplitude ratio and relative phase of the force to the displacement. There are similarities between the resonance and nonresonance techniques. The complex modulus is measured over a limited frequency range at a number of fixed temperatures, and the time-temperature superposition principle is used... 

Fig. 7. Schematic diagram for the single cantilever beam apparatus for measurement of the complex Young s modulus. (A forced vibration nonresonance method.)...

Forced nonresonant DM testing is covered by ISO 6721 5, 2856,4664 ASTM D2231 and DIN 53513, and this chapter will particularly look at the variation of properties as the temperature, stress amplitude, or frequency of vibration is varied in a wide range of test geometries so that almost any nonfluid material can be loaded and measured. 

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