Modulus in-phase

An Extended (Sufficiency) Criterion for the Vanishing of the Tensorial Field Observability of Molecular States in a Hamiltonian Formalism An Interpretation Lagrangeans in Phase-Modulus Formalism A. Background to the Nonrelativistic and Relativistic Cases Nonreladvistic Electron... 

In Figure 9.2, the in-phase modulus G = b/a and this is the modulus G assumed to be measured in a static test. The out-of-phase modulus G" = c/a. The magnitude of the complex modulus is ... 

This is in fact the in-phase modulus G. The factor 12 appears to be an error carried over from the previous edition when the factor k (called C in the ISO) was three times the factor defined in the British Standard, but in this latest version is actually the same. 

Then defining an in-phase modulus, G, and out-of-phase modulus, G" (Equations 13-79) ... 

The effect of the state of cure on in-phase modulus E is shown in Figure 6.7 for different frequencies while the displacement amplitude was kept constant (4 pm). 

FIGURE 6.7 In-phase modulus in dynamic compression as a function of the state of cure, SOC, of the samples, for different values of the frequency. 

The correlation factor is about 1, indicating a good correlation for this linear function between the state of cure and in phase modulus. 

A few results are thus given in terms of the static compression modulus which is expressed as a function of the pressure for different percentage of plasticizer with 2% sulfur in Figure 8.1 and with 5% sulfur in Figure 8.2. Moreover, the dynamic in-phase modulus E is measured as a function of the forcing frequency for different scrap rubber vulcanized with sulfur in Figure 8.3, whereas the corresponding values... 

P loss factor, in Figure 8.4 DOP plasticizer, for dioctyl phthalate db for decibel, in Figure 8.5 E static compression modulus, in Figure 8.1 E dynamic in phase modulus, in Figure 8.3... 

Based on the measurement of the stress, a, resulting on the application of periodic strain, e, with equipment as shown in Fig. 4.155, one can develop a simple formalism of viscoelasticity that permits the extraction of the in-phase modulus, G, the storage modulus, and the out-of-phase modulus, G", the loss modulus. This description is analogous to the treatment of the heat capacity measured by temperature-modulated calorimetry as discussed with Fig. 4.161 of Sect. 4.5. The ratio G7G is the loss tangent, tan 6. The equations for the stress o are easily derived using addition theorems for trigonometric functions. A complex form of the shear modulus, G, can be used, as indicated in Fig. 4.160. 

Equation 6.73 can be rewritten by introducing an in-phase modulus G (real) and a 90° out-of-phase modulus G" (imaginary) ... 

Most of the rubbers are deformed dynamically and specified dynamic properties are required. Therefore the effect of strain amplitude on the dynamic modulus was observed very intensively. The modulus of filled mbbers decreases with increasing applied dynamic strain up to intermediate amplitudes. A detailed smdy of the low frequency dynamic properties of filled natural rubber was carried out by Fletcher and Gent [71] and was later extended by Payne [72, 73]. In cyclic strain tests the shear modulus can be simply expressed as a complex modulus, G = G + iG" where G is the in-phase modulus and G" the out-of-phase modulus. The phase angle 8 is given by, tan 5 = G"/G. ... 

Scherspeichermodul shear storage modulus, in-phase modulus, elastic modulus... 

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