Resonance Devices with Forced Oscillations

Compound Resonance Devices with Forced Oscillations 

Reference has already been made in Chapter 5 to the exploitation of a resonance oscillation of a moving apparatus element in the measurement of dynamic viscoelastic properties, commonly used in characteristic impedance determinations. This principle is frequently employed for measurements on soft solids and will now be described in more detail. 

A simple illustration is shown in Fig. 6-5 an electromagnetic drive causes periodic shearing of two discs with shear sandwich geometry. The complex ratio of driving force to velocity is the same as that given in equations 21 to 23 of Chapter 5  

At the resonance frequency, ojq, the imaginary term vanishes and the force and velocity are in phase the force and displacement are out of phase by 90, and this 

Resonance apparatus for dynamic measurements on soft solids. (Dillon, Prettyman, and Hall. ) 

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Compound Resonance Devices with Forced Oscillations... 

One s intuition is to seek a mechanism for a resonant interaction (hence, the term draw resonance ) between some forcing disturbance and the viscoelastic time scale of the polymer melt. This approach is misplaced experiments with a variety of polymers clearly show that the characteristic period for the diameter oscillations is uncorrelated from any characteristic relaxation time of the polymer, but the period does correlate quite well with the residence time on the spinline. In fact, draw resonance can occur even for a Newtonian fluid Figure 11.2 shows periodic tension variations in the steady drawing of a filament of com symp, a Newtonian liquid, at a draw ratio of 26. (The takeup device was a roll from which the liquid... 

The frequency range of the forced-oscillation resonance devices described in this section is generally from 10 to a few thousand Hz. It should be emphasized that we are still dealing with situations where the dimensions of the sample (thickness in the case of shear, length for torsion or extension, etc.) are small compared with the wavelength of an elastic wave corresponding to the type of deformation used. Thus, the inertia of the sample itself does not enter into the calculations. 

Forced resonance devices are better suited for lower elasticity samples like dilute polymer solutions. A mass is oscillated sinusoidally to the resonant frequency of the sample-apparatus combination. The resonant frequency with and without the sample and the energy used to drive at resonance allow calculation of G and G". These devices operate at around 1000Hz. Since both measurements are made on the oscillator, it can be conveniently immersed into a lab beaker or even process equipment as discussed in Section 8.6 (Nametre, 1990). Several different stiffness lumps have been mounted on one shaft to allow G and G" to be determined at several frequencies in one loading (Ferry, 1980 Knudsen et al., 1992). 

The resonance method is useful when the data are required at only one frequency or at a small number of frequencies. In a typical device used to measure the dynamic tensile storage modulus, the rod, which has a circular or rectangular cross section, is hung by threads at nodal points. An oscillating force is applied at one end of the rod by means of a piezolectric transducer. The response is detected at the other end by a capacitive transducer. To achieve that, it is very convenient to paint the extremities of the rod in front of the transducers with cooloidal silver or another conductive paint. 

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