Forced vibration measurement methods

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. 

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.)...

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]. 

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

There are several possible approaches to the measurement of dynamic properties using forced oscillation of the test piece and the methods can be classified in various ways. The first distinction is between forced vibration at or near resonance and forced vibration away from resonance, with measurements at frequencies away from resonance being by far the most common. 

The measurement method described in this article is an embodiment of the non-resonance, direct-force-excitation approach that subjects a double-lap shear sample of damping polymer to force from a vibration shaker. In concept this approach can be applied irrespective of whether the material is in a rubbery, glassy, or intermediate state. Each material specimen is small in size and behaves as a damped spring over the entire frequency range. The small specimen size is in contrast with some alternate approaches in which the specimens have sufficiently large dimensions to be wave-bearing. 

Figure 6.34 presents the working principle of the vibrating capacitor method U is an opposite electromotive force that is inserted in the measurement circuit, Vdpc is the change in contact potential between the solid that forms the electrodes of capacitor C (previously denoted by Vrs), and R is an electrical resistance. 

Dynamic mechanical analysis is quite useful to observe the result of chemical reactions of polymer chains (e.g., transesterification) as evidenced by Figs. 3.12 and 3.13 [26]. The DMA method can be applied isothermally to determine crystallization kinetics (modulus versus time measurements) [13, 27] and reaction rate of thermosetting materials (e.g., epoxy) [28]. For reaction rate determination of liquid systems, the torsional braid analyzer is most appropriate as the braid can be saturated with the prepolymer liquid. A cellulose blotter could be used for the torsion pendulum, and a section of nylon hosiery could be used for forced vibration studies (both supports saturated with liquid prepolymer). 

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. 

Most of the force fields described in the literature and of interest for us involve potential constants derived more or less by trial-and-error techniques. Starting values for the constants were taken from various sources vibrational spectra, structural data of strain-free compounds (for reference parameters), microwave spectra (32) (rotational barriers), thermodynamic measurements (rotational barriers (33), nonbonded interactions (1)). As a consequence of the incomplete adjustment of force field parameters by trial-and-error methods, a multitude of force fields has emerged whose virtues and shortcomings are difficult to assess, and which depend on the demands of the various authors. In view of this, we shall not discuss numerical values of potential constants derived by trial-and-error methods but rather describe in some detail a least-squares procedure for the systematic optimisation of potential constants which has been developed by Lifson and Warshel some time ago (7 7). Other authors (34, 35) have used least-squares techniques for the optimisation of the parameters of nonbonded interactions from crystal data. Overend and Scherer had previously applied procedures of this kind for determining optimal force constants from vibrational spectroscopic data (36). 

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