Free oscillation measurements

Torsion Pendulum Free-oscillation measurements are made with a torsion pendulum (Figure 16.7). The sample is given an initial torsional displacement, and the frequency and amplitude decay of the oscillations are observed on release. G is determined from the sample geometry, moment of inertia of the oscillating mechanism, and the observed period of oscillation. For example, with a cylindrical specimen of length L and radius R,... 

In reality, neither the viscosity p (= G"/(q) nor the storage modulus G correctly defines the relationship between tensions and deformations except in the case of pure sinusoidal oscillations (9). In fact, what is measured in free oscillations is the dynamic modulus not at a real frequency but at a complex frequency. 

The problem appearing in the calculation of G and G from free oscillations under torsion lies in that (7 is measured at a complex frequency and not at a real value co as is usual in forced oscillations (11). Consequently,... 

Thus, the ensemble average of the Bohlinian is the equilibrium internal energy. It is evident that the actual choice of the angular frequency com in the Bohlinian is a convention. It depends on the normalization of Bohlin s constant (Equation (26)). What is the correct angular frequency It seems from the physical aspect that the correct choice is that the angular frequency is ca0. In this case, Bohlin s constant of motion corresponds to the maximum free energy of the linearly damped oscillator measured at time t=0, so it is the exergy of the linearly damped oscillator. 

Two unknowns require two measurements. For a free oscillator these measurements are the resonant frequency and the damping. For a forced oscillator the favored combination is the amplitude ratio and phase angle over a range of applied frequencies. This combination is not available for the evaluation of coatings because of the requirement that one surface be free. The two measurements described in the example below are damping and phase angle. 

Internal friction (IF), e.g. [102]. IF is a mechanical testing procedure which may be understood as a special technique of DMT A. The mechanical damping of the free oscillation is measured depending on the temperature at a constant frequency. The internal friction parameter is proportional to the natural logarithm of the ratio of two subsequent amplitudes of the oscillation and hence is also related to the damping factor tan (5, (see also section 12.1). 

The parameter "A listed in the table Is a measure of the severity of the disturbance It is the ratio of the peak local power obtained in a free oscillation to the minlmuffl local power Amplitude ratios of the magnitudes indicated have never been obtained in any of the Hanford reactors... 

FIG. 6-7. Torsion pendulum for dynamic measurements on soft solids with free oscillations (Plazek, Vrancken, and Berge ), with modiHed moment arms. 

The free oscillation devices cover in general a frequency range of 0.01 to 25 Hz. The precise temperature control needed for all viscoelastic measurements can be achieved by suitable design any mechanical connections with parts of the apparatus outside the thermostat must be made through members of low heat conductivity. 

The tensile strength and stress of the IPMC are measured in the same manner as those of the IP. The bending stiffness of a fully hydrated IPMC sample is estimated using the free oscillation attenuation method. By bending the sample to the appropriate initial displacement, the free vibration response can be recorded. The natural frequency of the cantilever, is obtained from the fast Fourier transform of the free vibration response curve. The stiffness of the IPMC, Egg, is determined using Eq. 4, which is based on the thin cantilever beam theory of material mechanics ... 

One of the more interesting results of these calculations is the contribution to the heat capacity. Figure 10.10 shows the temperature dependence of this contribution to the heat capacity for CH3-CCU as calculated from Pitzer s tabulation with 7r = 5.25 x 10-47 kg m2 and VQ/R — 1493 K. The heat capacity increases initially, reaches a maximum near the value expected for an anharmonic oscillator, but then decreases asymptotically to the value of / expected for a free rotator as kT increases above Vo. The total entropy calculated for this molecule at 286.53 K is 318.86 J K l-mol l, which compares very favorably with the value of 318.94T 0.6 TK-1-mol 1 calculated from Third Law measurements.7... 

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