A new method of statistically describing the dislocation component of low-temperature internal friction in nanostructured materials. The latter term is applied to ultrafine polycrystals with high density intragranular and grain boundary dislocations, the lines of which are divided into nanometer-scale fragments (dislocation relaxants) with random geometrical and energy parameters. The resonant interaction of elastic vibrations and thermally activated excitations of such relaxators are examined, and the maxima caused by these relaxators along the internal friction temperature dependence are analyzed. It is shown that at low temperatures, the shape of the peaks and the region of their localization along the temperature axis are largely determined by the dispersion of the relaxator activation energy. An algorithm is written in order to analyze the internal friction recorded in the experiment, allowing us to identify the physical model corresponding to the relaxator, and obtain empirical estimates of its parameters.

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