Viscoelasticity forced vibration methods

Free vibration methods suffer from the disadvantage that the frequency of vibration depends on the stiffness of the specimen, which varies with temperature, so that forced vibration methods are to be preferred when the frequency and temperature dependence of viscoelastic behaviour are to be investigated. 

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.

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. 

The viscoelastic properties of the vulcanizates in the function of temperature were examined by means of the method of resonance-free, forced vibrations, using Rheovibron apparatus DDV-II-C at frequency of 110 Hz. The mobility of macromolecules and their fragments was examined by means of the nuclear magnetic resonance (NMR) method. 

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]. 

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