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where t0 is the frequency factor, Q the activation energy, R the gas constants, and s the absolute temperature.
When w is employed in the measurement, the internal friction peak will be maximum at
where w2*3.1415*.@(f is the ordinary frequency /secj
tPP^wP exp(Q/RT1j/w 0
is obtained. By taking natural logarithm of the equation is given
lnw1 -Q/RT1+ lnw0Making another specimen of the same material with different frequency (by changing a dimension or the method of the measurement on the same specimen), one will be able to observe a similar resonance peak at another temperature, s2 with a different frequency, w2 , and a similar equation.
@lnw2 -Q/RT2+ lnw0will be made.
In the last two equations, wi(-2*3.1415*f) and Ti can be determined experimentally, and by plottin the two sets of [w, T] in the diagram of lw vs 1/RT, as shown in the figure on the right, the inclination of the straight line connecting the two points will give us the activation energy Q.
The data pile up on the relation between the internal friction and activation energy is most advanced and plenty in the study of iron, steel and other metals and greatly helps the research and development of various advanced materials.
The aparratures to measure the high temperature elastics moduli, EG-HT and JE-HT, are not only measuring the dynamical elastic constants but also able to measure in parallel internal friction, from which the activation energy and the frequency factor are easily obtained to study physical properties of materials. Especially, in the case of EG-HT, the parallel measurements of Young's modulus and modulus of rigidity have been realized for the first time, and, in addition, damping in lateral and twisting vibrations can be measured simultanuously. The precise study of internal friction in different vibrational modes and directions is now possible by our equipments, which woud enhance largely the study of properties of materials.
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