Damping curve

Note 2 The term damping curve is sometimes used to describe a loss curve. 

Note 3 A damping curve is usually obtained using a torsion pendulum, involving the measurement of decrease in the axial, torsional displacement of a specimen of uniform cross-section of known shape, with the torsional displacement initiated using a torsion bar of known moment of inertia. 

Note 4 Damping curves are conventionally analysed in terms of the Voigt-Kelvin solid giving a decaying amplitude and a single frequency. 

Note 5 Given the properties of a Voigt-Kelvin solid, a damping curve is described by the equation... 

Exponential coefficient of the time-dependent decay of a damping curve, assuming Voigt-Kelvin behaviour. 

See damping curve and the equation therein (Definition 6.2, note 5). 

Frequency of a damping curve assuming Voigt-Kelvin behaviour. 

Natural logarithm of the ratio of the displacement of a damping curve separated by one period of the displacement. 

Note 2 The logarithmic decrement can be used to evaluate the decay constant, p. From the equation for the damping curve of a Voigt-Kelvin solid. 

In the glassy region, the polymer is below its glass transition temperature, Tg, and typically has a modulus of 1010 dynes/cm2. The transition region includes the Tg, which is taken as the point of inflection of the modulus or the maximum in the damping curve. The modulus drops by a factor of 1000 in this region. The... 

Figure 12 shows typical modulus and damping curves for an uncross-linked, amorphous polymer (a copolymer of styrene and butadiene) 25),... 

Dynamic-Mechanical Measurement. This is a very sensitive tool and has been used intensively by Nielsen (17) and by Takayanagi (18). When the damping curves from a torsion pendulum test are obtained for the parent components and for the polyblend and die results are compared, a compatible polyblend will show a damping maximum between those of the parent polymers whereas the incompatible polyblend gives two damping maxima at temperatures corresponding to those of the parent components. Dynamic mechanical measurement can also give information on the moduli of the parent polymer and the polyblend. It can be shear modulus or tensile modulus. If the modulus-temperature curve of a polyblend locates between those of the two parent polymers, the polyblend is compatible. If the modulus-temperature curve shows multiple transitions, the polyblend is incompatible. 

Figure 7.14. Damping curve fora rubber vulcanisate.

The damping curve B in Figure 7.15 then shows both improvements in comparison with A. 

The torsional measurements show only one maximum on the damping curve. This means that there is a good segmental miscibility between the networks in the UPR-BPA/DC system. 

Fig. 7. Electromagnetic waves and sound waves. When the frequency of the waves (light or sound) equals the natural frequency of the chemical group or polymer, an absorption peak is found. The energy is converted into molecular motion, i.e., heat. Illustrated for the damping curve are the / -transition, the glass transition, and the liquid-liquid transition.

Theories of Effective Damping. If one assumes that a range of temperatures and/or frequencies will be encountered, then the area under the damping curve (E or tan 6) determines the effectiveness of the polymer better than the hight of the transition alone, see Figure 11. For E, the effective area is called the loss area, LA. This is determined after subtracting the background, as in any spectroscopic experiment. There are two theories to determine the quantity LA. 

Fig. 19. The basic shape of the damping curve must fit the intended application. Table II. Mechanical Instrumentation for Measuring the Glass Transition and Damping...

The reader should note that PEMA homopolymer yields the highest values for E" vs temperature. Figure 4, but the lowest values for tan vs temperature. Figure 5. This peculiar feature of damping curves will be discussed further below. 

DMA tests were eondueted with the specimens soaked in various environments for 0, 24, 72, 168, and 320 h. Pads exposed to slurry showed the lowest storage modulus G (especially at the temperatures below 0 °C) and the highest chain mobility reflected by the highest peak of the damping curve. The effect of time for which pads were soaked in pH 4 buffer solution on the reduction of the pad s dynamic storage modulus (i.e., pad softening) is shown in Fig. 2.14. The pad softening due to the increase in the chain mobility can be... 

One can consider the ultimate degree of grain refinement from the following point of view. It is well known that grain refinement by any method follows a damping curve. Obviously, the ultimate refinement is achieved when decreasing intensity of a parameter, which controls the process, results in no more refinement (see Figure 17). 

Rheovlbron data also show that the system potentially has a higher upper use temperature than the Epon 828 - Versamld 140 system, since the elastic modulus, E, drops more slowly. The area under the tan 6 curve for this system is greater than that of a corresponding epoxy system. The areas under the damping curves are listed in Table I. The data imply Improved energy absorption capability for the new system. 

The area under the damping curve for the epoxy-eplsulflde resin system... 

Figure 6. Scheme of relative wave heights (hr) versus the uv dose for A serum albumin R RNase. K catalytic presodium wave (peptide wave), M damping curve for O2 maximum, Pj+2-both Brdicka protein waves, Pj first Brdicka protein wave. 

---