Forced-vibration methods

An instrument for the measurement of heat buildup in vulcanised rubber by a forced vibration method. 

Before considering particular test methods, it is useful to survey the principles and terms used in dynamic testing. There are basically two classes of dynamic motion, free vibration in which the test piece is set into oscillation and the amplitude allowed to decay due to damping in the system, and forced vibration in which the oscillation is maintained by external means. These are illustrated in Figure 9.1 together with a subdivision of forced vibration in which the test piece is subjected to a series of half-cycles. The two classes could be sub-divided in a number of ways, for example forced vibration machines may operate at resonance or away from resonance. Wave propagation (e.g. ultrasonics) is a form of forced vibration method and rebound resilience is a simple unforced method consisting of one half-cycle. The most common type of free vibration apparatus is the torsion pendulum. 

The forced vibration methods away from resonance can again be subdivided into those which apply deformation cycles and those which apply force cycles, the more usual being deformation cycles. An alternative form of test uses transient loading instead to continuous cycling. 

FTMA is a forced vibration test method based on direct measurement of stress and strain spectra. As with all forced vibration methods, FTMA is subject to spurious wave effects at high frequencies. The lower frequency limit is determined by transducers, signal conditioners, etc. The lower limit in this research was 35 Hz as determined by the inherent properties of the piezoelectric transducers. With different transducers (for example load cell for the force and LVDT for displacement measurements) and signal conditioners, FTMA should measure material properties down to much lower frequencies. 

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. 

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... 

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.

Free vibration and forced vibration methods have been employed to determine the respective data. Free vibration was common earlier in polymer blend studies, but forced vibration data is much more common today due to the availability of more sophisticated testing equipment. Free vibration methods include the torsion pendulum, the vibrating reed and the torsional braid analyzer. The torsion pendulum is comprised of an inertial source (disk or rod), which can freely vibrate and is attached to a specimen, which is rigidly fixed at one end. Upon angular deformation of the inertial source and releasing, a damped sinusoidal curve depicts the resultant deformation of the sample [18,19]. Tan S can be calculated from... 

Perhaps the most widely used method for engineering polymers is the direct forced-vibration method. The method has the great advantage that the frequency of the excitation can be changed at will without changing the specimen. Hence it is readily possible to determine the frequency dependence of complex modulus and loss factor over a wide range. 

In the forced-vibration methods described above it is necessary to monitor both load and displacement. If the measurements are performed at resonance, using the decay of free vibration, it is sufficient to measure one variable, load or displacement. However, this method has the drawback that data are obtained at one frequency only, the resonance frequency, which is a function of the dimensions of the specimen and its material properties. 

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