Resonance vibration methods

Table 2 Equations for Dynamic Moduli from Free and Resonance Vibrations Method and specimen Modulus (dyn/cm2)...

Bond [Min. Eng. (London), 60(1), 63-64 (1968)] reviewed attempts to induce breakage without wastefuUy applying pressure and concluded that inherent practical limitations have been found for the following methods spinning particles, resonant vibration, electro-hydrauhe crushing, induction heating, sudden release of gas pressure, and chisel-effect breakers. For a review of more recent efforts, see edition 6 of this handbook. 

ISO 3597-2 2003 Textile-glass-reinforced plastics - Determination of mechanical properties on rods made of roving-reinforced resin - Part 2 Determination of flexural strength ISO 5893 2002 Rubber and plastics test equipment - Tensile, flexural and compression types (constant rate of traverse) - Specification ISO 6721-3 1995 Plastics - Determination of dynamic mechanical properties - Part 3 Flexural vibration - Resonance-curve 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. 

The experiments discussed in this book are diverse, but they break down into two broad categories (1) resonant infrared methods in which ultrafast IR pulses are tuned to the wavelength of the vibrational transition and (2) Raman methods (in some instances referred to as impulsive stimulated scattering), in which two visible wavelengths have a difference in frequency equal to the vibrational frequency. In some experiments, infrared and Raman techniques are combined in a single measurement. 

Resonance (Vihroscope) Method. The principle underlying the operation of the ibroscope is that of a vibrating string, the natural fundamental frequency / (in Hz) of which is given by... 

Free vibration methods such as the torsion pendulum are covered by ISO 4663 and are limited to cry low strains and frequencies, and are in much less frequent use these days than the forced vibration nonresonant systems on which this chapter will focus. The early Du Pont DMA and German Myrenne used input energy to maintain the resonant oscillation amplitude, but the main limitations were variable frequency according to the sample size (which had to be glassy or plastic) or one frequency only (1 Hz) respectively. 

Vibration Method (DW 53217 T5). A U-shaped tube is clamped at both ends and filled with paint. When the tube is subjected to vibration its resonance frequency depends on the mass in a given tube volume and thus on the density of the paint. The tube is calibrated with two media of known density and the density of the sample is then calculated from the resonance frequency. This method is used for liquid and pasty coating materials [9.9]. 

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. 

Vibrational methods applied to proteins and model complexes include IR, resonance Raman, and NRVS [173, 178-180]. The interpretation of these vibrational data combined with DPT studies on the reaction mechanisms of heme proteins is frequently based on the porphine approximation, i.e. aU porphyrin ring substituents are neglected. Whereas this is intuitively a good approximation for D4h-symmetric macrocycles (e.g., TPP complexes), it is noteworthy that the biologically observed hemes all contain asymmetric substitution patterns on the porphyrin ring [181]. 

A prismatic rod as specimen can be used in different procedures for determining the complex modulus by the flexural vibration-resonance-curve method (ISO 6721-3). Using a frequency synthesizer, the frequency can be varied over a range from approx. 10 Hz to 10 Hz. E and tan S can be calculated. 

Part 3 (1994) Flexural vibration - Resonance curve method (Technical corrigendum - TC 1 1995)... 

ES, resonance electrostatic method FO, forced oscillation dynamic-mechanical analysis FV, free vibration TP, torsion pendulum TSC, thermally stimulated discharge current measurement D, dielectric VR, vibrating reed. 

While vibrational spectroscopy is not capable of the structural resolution of X-ray diffraction, it nevertheless has some important advantageous features. First, it is not generally limited by physical state samples can be in the form of powders, crystals, films, solutions, membranous aggregates, etc. Second, a number of different experimental methods probe the structure-dependent vibrational modes of the system infrared (IR), Raman (both visible and UV-exeited resonance), vibrational circular dichroism, and Raman optical activity, many of these with time-resolution capabilities. Finally, in addition to providing structural information, vibrational spectra are sensitive to intra- and intennolecular interaction forces, and thus they also give information about these properties of the system. 

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