Frequency-independent damping models

The other most popular model is the frequency independent damping model. The concept of frequency independent damping arose when in 1927 Kimball and Lovell claimed that hysteretic damping is universal in nature. Since then there has been several studies which further strengthened their claim. One of the most popular models in this category is the linear Coulomb friction force model given as (Reid 1956, Muravski 2004)... 

Let us consider again the spectral density J( ), assumed to vary proportionally to co5 at small angular frequencies. The value 8 = 1 is especially important since it corresponds to frequency-independent damping. The corresponding dissipation model, as defined by the relations... 

For the dynamical distribution it will in general be necessary to consider both the auto and cross time correlation functions of the 0-1 and the 1-2 frequencies (117). For example, if the fluctuations, <5A(t), in the anhar-monicity are statistically independent of the fluctuations in the fundamental frequency, the oscillating term (1 — elAt3) in Equation (18) would be damped. In a Bloch model the fluctuations in anharmonicity translate into different dephasing rates for the 0-1 and 1-2 transitions that were discussed previously for two pulse echoes of harmonic oscillators. Thus we see that even if A vanishes, the third-order response can be finite (94). 

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