Oscillatory tests - or mechanical vibrational spectroscopy

If we perform an oscillatory test by applying a sine-wave-shaped input of either stress or strain, we can then, using suitable electronic methods, easily resolve (i.e. separate) the resulting sinusoidal strain or stress output into a certain amoimt of solid-like response, which is in phase with the input, and a corresponding amount of liquid-like response which is n/2 (i.e. 90°) out of phase with the input, see figure 8. 

The solid-like component at any particular frequency is characterised by the storage modulus, G, and the liquid-like response is described by the complementary loss modulus, G . The units of both these moduli are pascals. The values of both these parameters vary with applied frequency, co, which is given by 2nf where/is the frequency in hertz (Hz). As all modern rheometers are weU able to handle the complicated mathematical calculations necessary for determining these moduli, we do not need to consider the calculation procedure here. 

Note that the G and G data produced by rheometers is sometimes reported in different ways, as for instance 

Note It is important to realise that there is no extra information in any of these other derived parameters compared with that which is contained in the basic G and G information. Hence, we shall only be using these basic G and G parameters. 

In the same way that instrument mechanical inertia can cause problems at short times in creep tests, so too can it cause difficulties at high frequencies in oscillatory tests, especially with respect to the G data. Even fluid inertia can become important at the latest highest frequencies of around 100 hertz. Fortunately, in good rheometers, these effects are dealt with in the software and the displayed results have had the inertial components eliminated, see figure 9 for a typical example of viscoelastic results corrected for inertia. 

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