ЭКСПЕРИМЕНТАЛЬНОЕ ИССЛЕДОВАНИЕ ФРАКТАЛЬНЫХ

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ȼȿɋɌɇɂɄ ɉɇɂɉɍ
Ɇɟɯɚɧɢɤɚ
2013
ʋ2
ɍȾɄ 539.4
Ɇ.ȼ. Ȼɚɧɧɢɤɨɜ1, Ⱥ.ɘ. Ɏɟɞɨɪɨɜɚ1, Ⱥ.ɂ. Ɍɟɪɟɯɢɧɚ2, Ɉ.Ⱥ. ɉɥɟɯɨɜ1
ɂɧɫɬɢɬɭɬ ɦɟɯɚɧɢɤɢ ɫɩɥɨɲɧɵɯ ɫɪɟɞ ɍɪɈ ɊȺɇ, ɉɟɪɦɶ, Ɋɨɫɫɢɹ
ɉɟɪɦɫɤɢɣ ɧɚɰɢɨɧɚɥɶɧɵɣ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɢɣ ɩɨɥɢɬɟɯɧɢɱɟɫɤɢɣ
ɭɧɢɜɟɪɫɢɬɟɬ, ɉɟɪɦɶ, Ɋɨɫɫɢɹ
1
2
ɗɄɋɉȿɊɂɆȿɇɌȺɅɖɇɈȿ ɂɋɋɅȿȾɈȼȺɇɂȿ ɎɊȺɄɌȺɅɖɇɕɏ
ɁȺɄɈɇɈɆȿɊɇɈɋɌȿɃ ɊɈɋɌȺ ɍɋɌȺɅɈɋɌɇɈɃ ɌɊȿɓɂɇɕ
ɂ ȾɂɋɋɂɉȺɐɂɂ ɗɇȿɊȽɂɂ ȼ ȿȿ ȼȿɊɒɂɇȿ
ɋɬɚɬɶɹ ɩɨɫɜɹɳɟɧɚ ɢɫɫɥɟɞɨɜɚɧɢɸ ɡɚɪɨɠɞɟɧɢɹ ɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɭɫɬɚɥɨɫɬɧɵɯ ɬɪɟɳɢɧ ɜ
ɬɢɬɚɧɨɜɵɯ ɫɩɥɚɜɚɯ ɦɟɬɨɞɨɦ ɢɧɮɪɚɤɪɚɫɧɨɣ ɬɟɪɦɨɝɪɚɮɢɢ ɩɪɢ ɰɢɤɥɢɱɟɫɤɨɣ ɧɚɝɪɭɡɤɟ ɢ ɫ ɩɨɦɨɳɶɸ
ɚɧɚɥɢɡɚ ɩɨɜɟɪɯɧɨɫɬɢ ɪɚɡɪɭɲɟɧɢɹ. ɉɪɨɜɟɞɟɧɵ ɞɜɟ ɫɟɪɢɢ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɧɚ ɩɥɨɫɤɢɯ ɝɥɚɞɤɢɯ ɢ ɧɚ
ɨɛɪɚɡɰɚɯ ɫ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɜɵɪɚɳɟɧɧɨɣ ɭɫɬɚɥɨɫɬɧɨɣ ɬɪɟɳɢɧɨɣ. ɂɫɫɥɟɞɨɜɚɧɚ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɚɹ
ɢ ɜɪɟɦɟɧɧɚɹ ɷɜɨɥɸɰɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɜ ɜɟɪɲɢɧɟ ɬɪɟɳɢɧɵ, ɨɩɪɟɞɟɥɟɧɚ ɮɨɪɦɚ ɩɥɚɫɬɢɱɟɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ ɢ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɬɟɩɥɨɜɵɞɟɥɟɧɢɹ. ɇɚ ɨɫɧɨɜɚɧɢɢ ɪɟɡɭɥɶɬɚɬɨɜ ɫɪɚɜɧɢɬɟɥɶɧɨɝɨ ɚɧɚɥɢɡɚ
ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɢ ɭɪɚɜɧɟɧɢɣ ɥɢɧɟɣɧɨɣ ɦɟɯɚɧɢɤɢ ɪɚɡɪɭɲɟɧɢɹ ɩɨɤɚɡɚɧɨ, ɱɬɨ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɚɹ ɮɨɪɦɚ ɢ ɯɚɪɚɤɬɟɪ ɞɢɫɫɢɩɚɰɢɢ ɬɟɩɥɚ ɜ ɡɨɧɟ ɜɟɪɲɢɧɵ ɬɪɟɳɢɧɵ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ
ɩɪɨɫɬɨɣ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ. ȼ ɪɚɛɨɬɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɩɨɥɭɱɟɧ ɷɮɮɟɤɬ ɨɯɥɚɠɞɟɧɢɹ ɡɚ ɫɱɟɬ
ɭɩɪɭɝɨɣ ɞɟɮɨɪɦɚɰɢɢ ɦɚɬɟɪɢɚɥɚ, ɚ ɬɚɤɠɟ ɢɫɫɥɟɞɨɜɚɧɵ ɨɫɨɛɟɧɧɨɫɬɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɧɚɩɪɹɠɟɧɢɣ
ɜ ɜɟɪɲɢɧɟ ɬɪɟɳɢɧɵ. ȼɵɫɨɤɨɫɤɨɪɨɫɬɧɚɹ ɫɴɟɦɤɚ (ɧɚ ɱɚɫɬɨɬɟ 1 ɤȽɰ) ɩɨɡɜɨɥɢɥɚ ɨɩɪɟɞɟɥɢɬɶ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɢ ɮɨɪɦɭ ɡɨɧɵ ɪɚɫɫɟɢɜɚɟɦɨɣ ɷɧɟɪɝɢɢ ɢɡ-ɡɚ ɩɥɚɫɬɢɱɟɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ ɜ ɜɟɪɲɢɧɟ ɬɪɟɳɢɧɵ, ɚ ɬɚɤɠɟ ɫɪɚɜɧɢɬɶ ɫɤɨɪɨɫɬɶ ɞɢɫɫɢɩɚɰɢɢ ɷɧɟɪɝɢɢ ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɭɪɨɜɧɟɣ ɧɚɩɪɹɠɟɧɢɹ. Ɋɚɡɪɭɲɟɧɧɵɟ ɨɛɪɚɡɰɵ ɢɫɫɥɟɞɨɜɚɥɢɫɶ ɫ ɩɨɦɨɳɶɸ ɷɥɟɤɬɪɨɧɧɨɝɨ ɦɢɤɪɨɫɤɨɩɚ ɢ ɢɧɬɟɪɮɟɪɨɦɟɬɪɚ New
View ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɫɤɟɣɥɢɧɝɨɜɵɯ ɡɚɤɨɧɨɦɟɪɧɨɫɬɟɣ ɨɛɪɚɡɨɜɚɧɢɹ ɢ ɪɨɫɬɚ ɬɪɟɳɢɧɵ. ɉɨɥɭɱɟɧɧɵɟ ɪɟɡɭɥɶɬɚɬɵ ɩɨɡɜɨɥɹɸɬ ɧɚɦ ɩɪɨɜɟɪɢɬɶ ɫɭɳɟɫɬɜɭɸɳɢɟ ɦɨɞɟɥɢ ɧɟɭɩɪɭɝɨɣ ɞɟɮɨɪɦɚɰɢɢ ɜ ɜɟɪɲɢɧɟ ɬɪɟɳɢɧɵ, ɚ ɬɚɤɠɟ ɭɥɭɱɲɢɬɶ ɦɟɬɨɞɵ ɤɨɧɬɪɨɥɹ ɧɚɤɨɩɥɟɧɢɹ ɦɢɤɪɨɩɨɜɪɟɠɞɟɧɢɣ ɜ ɩɪɨɰɟɫɫɟ
ɭɫɬɚɥɨɫɬɧɨɝɨ ɞɟɮɨɪɦɢɪɨɜɚɧɢɹ.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɭɫɬɚɥɨɫɬɶ, ɞɢɫɫɢɩɚɰɢɹ ɷɧɟɪɝɢɢ, ɬɟɪɦɨɭɩɪɭɝɢɣ ɷɮɮɟɤɬ, ɢɧɮɪɚɤɪɚɫɧɚɹ
ɬɟɪɦɨɝɪɚɮɢɹ, ɮɪɚɤɬɨɝɪɚɮɢɹ.
21
Ɇ.ȼ. Ȼɚɧɧɢɤɨɜ, Ⱥ.ɘ. Ɏɟɞɨɪɨɜɚ, Ⱥ.ɂ. Ɍɟɪɟɯɢɧɚ, Ɉ.Ⱥ. ɉɥɟɯɨɜ
M.V. Bannikov1, A.Y. Fedorova1, A.I. Terekhina2, O.A. Plekhov1
1
Institute of Continuous Media Mechanics UrB RAS, Perm, Russian Federation
2
Perm National Research Polytechnic University, Perm, Russian Federation
EXPERIMENTAL STUDY OF FRACTAL PROPERTIES
OF FATIGUE CRACK GROWTH AND ENERGY
DISSIPATION IN CRACK TIP
Paper is devoted to investigation of initiation and propagation of cracks in titanium alloys by infrared thermography study of heat generation under cyclic loading and fractography analyses of fracture
surface. Two series of experiments on flat smooth specimens and flat specimens with preliminary grown
fatigue crack are carried out. Spatial and time temperature evolution into crack tip is investigated, the
shape and dissipative intensity at crack process zone are estimated. Based on a result of comparative
analysis of the experimental data and the linear fracture mechanics equations it is shown that the spatial
distribution and character of heat dissipation zone into the crack tip doesn’t correspond to the conventional models. High-speed shooting (at a frequency of 1 kHz) allowed us to determine the intensity and
shape of zone of energy dissipation caused by plastic deformation at the crack tip, as well as to compare the rate of energy dissipation for different stress levels. Fractured specimens were analyzed by
interferometer microscope and SEM to verify the existing models of inelastic deformation at the crack tip
and to improve methods of monitoring of damage accumulation during fatigue test.
Keywords: fatigue, energy dissipation, thermo elasticity effect, infrared thermography, fractography.
ȼɜɟɞɟɧɢɟ
Ⱦɢɫɫɢɩɚɰɢɹ ɬɟɩɥɚ, ɜɵɡɜɚɧɧɚɹ ɷɜɨɥɸɰɢɟɣ ɫɬɪɭɤɬɭɪɵ ɦɚɬɟɪɢɚɥɚ
ɩɪɢ ɰɢɤɥɢɱɟɫɤɨɦ ɞɟɮɨɪɦɢɪɨɜɚɧɢɢ, ɹɜɥɹɟɬɫɹ ɨɛɴɟɤɬɨɦ ɢɧɬɟɧɫɢɜɧɵɯ
ɢɫɫɥɟɞɨɜɚɧɢɣ ɧɚ ɩɪɨɬɹɠɟɧɢɢ ɩɨɫɥɟɞɧɢɯ ɞɟɫɹɬɢɥɟɬɢɣ. ȼ ɧɚɫɬɨɹɳɟɟ
ɜɪɟɦɹ ɞɨɫɬɨɜɟɪɧɨ ɢɡɜɟɫɬɧɨ, ɱɬɨ ɜ ɭɫɥɨɜɢɹɯ ɰɢɤɥɢɱɟɫɤɨɝɨ ɞɟɮɨɪɦɢɪɨɜɚɧɢɹ ɩɪɨɰɟɫɫɵ ɥɨɤɚɥɢɡɚɰɢɢ ɞɟɮɨɪɦɚɰɢɢ ɫɨɩɪɨɜɨɠɞɚɸɬɫɹ ɢɧɬɟɧɫɢɜɧɵɦ ɜɵɞɟɥɟɧɢɟɦ ɬɟɩɥɚ, ɱɬɨ ɞɟɥɚɟɬ ɜɨɡɦɨɠɧɵɦ ɢɯ ɪɚɧɧɟɟ ɨɛɧɚɪɭɠɟɧɢɟ
ɦɟɬɨɞɚɦɢ ɢɧɮɪɚɤɪɚɫɧɨɣ ɬɟɪɦɨɝɪɚɮɢɢ [1].
Ȼɥɚɝɨɞɚɪɹ ɫɜɨɟɣ ɭɧɢɜɟɪɫɚɥɶɧɨɫɬɢ ɦɟɬɨɞ ɢɧɮɪɚɤɪɚɫɧɨɣ ɬɟɪɦɨɝɪɚɮɢɢ ɜ ɩɨɫɥɟɞɧɟɟ ɜɪɟɦɹ ɚɤɬɢɜɧɨ ɩɪɢɦɟɧɹɟɬɫɹ ɩɪɢ ɩɪɨɜɟɞɟɧɢɢ ɦɟɯɚɧɢɱɟɫɤɢɯ ɢɫɩɵɬɚɧɢɣ ɤɚɤ ɫ ɰɟɥɶɸ ɩɨɥɭɱɟɧɢɹ ɞɟɬɚɥɶɧɨɣ ɢɧɮɨɪɦɚɰɢɢ
ɨ ɩɪɨɰɟɫɫɟ ɡɚɪɨɠɞɟɧɢɹ ɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɭɫɬɚɥɨɫɬɧɵɯ ɬɪɟɳɢɧ [2–3],
ɬɚɤ ɢ ɞɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ ɡɚɤɨɧɨɦɟɪɧɨɫɬɟɣ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɧɚɤɨɩɥɟɧɢɹ
ɷɧɟɪɝɢɢ ɜ ɩɪɨɰɟɫɫɟ ɞɟɮɨɪɦɢɪɨɜɚɧɢɹ [4–9]. ȼɨɡɦɨɠɧɨɫɬɢ ɦɟɬɨɞɚ ɢɧɮɪɚɤɪɚɫɧɨɣ ɬɟɪɦɨɝɪɚɮɢɢ ɩɨɡɜɨɥɹɸɬ ɜ ɪɟɠɢɦɟ ɪɟɚɥɶɧɨɝɨ ɜɪɟɦɟɧɢ ɢɫɫɥɟɞɨɜɚɬɶ ɩɪɨɰɟɫɫɵ ɢɡɦɟɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ, ɜɵɡɜɚɧɧɵɟ ɬɟɪɦɨɭɩɪɭɝɨɫɬɶɸ ɢ ɥɨɤɚɥɢɡɚɰɢɟɣ ɞɟɮɨɪɦɚɰɢɢ ɜ ɜɟɪɲɢɧɟ ɬɪɟɳɢɧɵ, ɚ ɬɚɤɠɟ ɷɮɮɟɤɬɚɦɢ ɬɪɟɧɢɹ ɧɚ ɛɟɪɟɝɚɯ ɬɪɟɳɢɧɵ ɜ ɩɪɨɰɟɫɫɟ ɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ.
22
ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɟ ɢɫɫɥɟɞɨɜɚɧɢɟ ɮɪɚɤɬɚɥɶɧɵɯ ɡɚɤɨɧɨɦɟɪɧɨɫɬɟɣ ɪɨɫɬɚ
Ⱦɚɧɧɚɹ ɪɚɛɨɬɚ ɩɨɫɜɹɳɟɧɚ ɢɫɫɥɟɞɨɜɚɧɢɸ ɬɟɪɦɨɭɩɪɭɝɨɝɨ ɢ ɬɟɪɦɨɩɥɚɫɬɢɱɟɫɤɨɝɨ ɷɮɮɟɤɬɨɜ ɜ ɜɟɪɲɢɧɟ ɬɪɟɳɢɧɵ, ɪɚɫɩɪɨɫɬɪɚɧɹɸɳɟɣɫɹ
ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɪɚɫɬɹɝɢɜɚɸɳɟɝɨ ɰɢɤɥɢɱɟɫɤɨɝɨ ɧɚɩɪɹɠɟɧɢɹ, ɩɪɢɥɨɠɟɧɧɨɝɨ ɩɨ ɧɨɪɦɚɥɢ ɤ ɩɥɨɫɤɨɫɬɢ ɬɪɟɳɢɧɵ. ȼ ɪɚɛɨɬɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ
ɩɨɥɭɱɟɧɵ ɷɮɮɟɤɬɵ ɨɯɥɚɠɞɟɧɢɹ, ɜɵɡɜɚɧɧɵɟ ɭɩɪɭɝɨɣ ɞɟɮɨɪɦɚɰɢɟɣ ɦɚɬɟɪɢɚɥɚ ɜ ɜɟɪɲɢɧɟ ɬɪɟɳɢɧɵ, ɢ ɢɫɫɥɟɞɨɜɚɧɵ ɨɫɨɛɟɧɧɨɫɬɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɧɚɩɪɹɠɟɧɢɣ ɜ ɜɟɪɲɢɧɟ ɬɪɟɳɢɧɵ. ȼɵɫɨɤɨɫɤɨɪɨɫɬɧɚɹ ɫɴɟɦɤɚ ɩɨɡɜɨɥɢɥɚ ɨɩɪɟɞɟɥɢɬɶ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɢ ɮɨɪɦɭ ɡɨɧɵ ɞɢɫɫɢɩɚɰɢɢ ɷɧɟɪɝɢɢ,
ɜɵɡɜɚɧɧɭɸ ɥɨɤɚɥɢɡɚɰɢɟɣ ɩɥɚɫɬɢɱɟɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ ɜ ɜɟɪɲɢɧɟ ɬɪɟɳɢɧɵ, ɚ ɬɚɤɠɟ ɫɨɩɨɫɬɚɜɢɬɶ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɞɢɫɫɢɩɚɰɢɢ ɷɧɟɪɝɢɢ ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɭɪɨɜɧɟɣ ɧɚɩɪɹɠɟɧɢɹ.
1. Ɇɚɬɟɪɢɚɥɵ ɢ ɭɫɥɨɜɢɹ ɷɤɫɩɟɪɢɦɟɧɬɚ
ȼ ɪɚɛɨɬɟ ɢɫɫɥɟɞɨɜɚɧɵ ɨɫɨɛɟɧɧɨɫɬɢ ɩɪɨɰɟɫɫɚ ɬɟɩɥɨɜɵɞɟɥɟɧɢɹ ɩɪɢ
ɰɢɤɥɢɱɟɫɤɨɦ ɧɚɝɪɭɠɟɧɢɢ ɨɛɪɚɡɰɨɜ ɬɢɬɚɧɚ ɈɌ-4 ɫ ɱɚɫɬɨɬɚɦɢ ɨɬ 1 ɞɨ 10 Ƚɰ
[7]. Ʉɜɚɡɢɫɬɚɬɢɱɟɫɤɢɟ ɢɫɩɵɬɚɧɢɹ ɢɫɫɥɟɞɭɟɦɨɝɨ ɦɚɬɟɪɢɚɥɚ ɩɨɡɜɨɥɹɸɬ
ɨɩɪɟɞɟɥɢɬɶ ɟɝɨ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ: ɦɨɞɭɥɶ ɘɧɝɚ 64 Ƚɉɚ,
V0,2=683 Ɇɉɚ, Vɜ=790 Ɇɉɚ.
ɏɢɦɢɱɟɫɤɢɣ ɫɨɫɬɚɜ ɫɩɥɚɜɚ ɈɌ-4
ɗɥɟɦɟɧɬ
Al
Ti
Mn
ȼɟɫɨɜɨɣ, %
3,68
95,1
1,22
ɂɫɩɵɬɚɧɢɹ ɩɪɨɜɨɞɢɥɢɫɶ ɧɚ ɪɚɫɬɹɠɧɨɣ 100 ɤɇ ɫɟɪɜɨɝɢɞɪɚɜɥɢɱɟɫɤɨɣ ɦɚɲɢɧɟ Bi-00-100. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɜɟɥɢɱɢɧɵ ɥɨɤɚɥɶɧɨɣ ɞɟɮɨɪɦɚɰɢɢ ɜɨ ɜɪɟɦɹ ɷɤɫɩɟɪɢɦɟɧɬɚ ɢɫɩɨɥɶɡɨɜɚɥɫɹ ɨɫɟɜɨɣ ɷɤɫɬɟɧɡɨɦɟɬɪ
Bi-06-304 ɫ ɩɨɝɪɟɲɧɨɫɬɶɸ ±1,5 ɦɤɦ, ɭɫɬɚɧɨɜɥɟɧɧɵɣ ɧɚ ɛɟɪɟɝɚɯ ɬɪɟɳɢɧɵ. ɂɫɫɥɟɞɭɟɦɵɟ ɨɛɪɚɡɰɵ ɢɡɝɨɬɚɜɥɢɜɚɥɢɫɶ ɢɡ ɥɢɫɬɚ ɬɨɥɳɢɧɨɣ 3 ɦɦ,
ɪɚɡɦɟɪɵ ɪɚɛɨɱɟɣ ɡɨɧɵ 200u55 ɦɦ. Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɧɚɱɚɥɶɧɨɣ ɬɪɟɳɢɧɵ
ɨɛɪɚɡɟɰ ɛɵɥ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɨɫɥɚɛɥɟɧ ɬɪɟɦɹ ɩɟɪɟɤɪɵɜɚɸɳɢɦɢɫɹ ɨɬɜɟɪɫɬɢɹɦɢ ɜ ɰɟɧɬɪɟ ɪɚɛɨɱɟɣ ɡɨɧɵ ɞɢɚɦɟɬɪɨɦ 4 ɢ 3 ɦɦ, ɝɟɨɦɟɬɪɢɹ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 1.
ɇɚ ɧɚɱɚɥɶɧɨɦ ɷɬɚɩɟ ɷɤɫɩɟɪɢɦɟɧɬɚ ɫ ɩɨɦɨɳɶɸ ɩɨɜɵɲɟɧɧɨɣ ɧɚɝɪɭɡɤɢ ((215±238) Ɇɉɚ, ɱɚɫɬɨɬɚ ɧɚɝɪɭɠɟɧɢɹ 20 Ƚɰ) ɫɨɡɞɚɜɚɥɚɫɶ ɭɫɬɚɥɨɫɬɧɚɹ ɬɪɟɳɢɧɚ ɞɥɢɧɨɣ 5 ɦɦ. ȼ ɩɪɨɰɟɫɫɟ ɪɟɝɢɫɬɪɚɰɢɢ ɷɜɨɥɸɰɢɢ ɩɨɥɹ
23
Ɇ.ȼ. Ȼɚɧɧɢɤɨɜ, Ⱥ.ɘ. Ɏɟɞɨɪɨɜɚ, Ⱥ.ɂ. Ɍɟɪɟɯɢɧɚ, Ɉ.Ⱥ. ɉɥɟɯɨɜ
ɬɟɦɩɟɪɚɬɭɪɵ ɧɚɝɪɭɡɤɚ ɭɦɟɧɶɲɚɥɚɫɶ ɫ ɰɟɥɶɸ ɡɚɦɟɞɥɟɧɢɹ ɫɤɨɪɨɫɬɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɬɪɟɳɢɧɵ (ɦɟɧɟɟ 1 ɦɦ/ɦɢɧ) ɢ ɞɟɬɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ
ɩɪɨɰɟɫɫɨɜ ɝɟɧɟɪɚɰɢɢ ɬɟɩɥɚ ɜ ɟɟ ɜɟɪɲɢɧɟ.
ɚ
ɛ
Ɋɢɫ. 1. Ƚɟɨɦɟɬɪɢɹ ɢɫɫɥɟɞɭɟɦɵɯ ɨɛɪɚɡɰɨɜ ɞɥɹ ɢɡɭɱɟɧɢɹ: ɷɮɮɟɤɬɚ ɬɟɪɦɨɭɩɪɭɝɨɫɬɢ (ɚ);
ɬɟɩɥɨɜɵɯ ɷɮɮɟɤɬɨɜ ɜ ɜɟɪɲɢɧɟ ɬɪɟɳɢɧɵ (ɛ)
2
3
1
2
Ɋɢɫ. 2. ȼɧɟɲɧɢɣ ɜɢɞ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɭɫɬɚɧɨɜɤɢ: 1 – ɢɧɮɪɚɤɪɚɫɧɚɹ ɤɚɦɟɪɚ
FLIR SC 5000; 2 – ɡɚɯɜɚɬɵ ɫɟɪɜɨɝɢɞɪɚɜɥɢɱɟɫɤɨɣ ɧɚɝɪɭɠɚɸɳɟɣ ɦɚɲɢɧɵ
Bi-00-100; 3 – ɢɫɫɥɟɞɭɟɦɵɣ ɨɛɪɚɡɟɰ
ɂɫɫɥɟɞɨɜɚɧɢɟ ɩɨɥɹ ɬɟɦɩɟɪɚɬɭɪ ɨɫɭɳɟɫɬɜɥɹɥɨɫɶ ɢɧɮɪɚɤɪɚɫɧɨɣ
ɤɚɦɟɪɨɣ FLIR SC 5000 (ɱɚɫɬɨɬɚ ɫɴɟɦɤɢ ɞɨ 20 ɤȽɰ, ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɟ
ɪɚɡɪɟɲɟɧɢɟ ɞɨ 2·10–4 ɦ). ɉɨɜɟɪɯɧɨɫɬɶ ɨɛɪɚɡɰɨɜ ɩɨɥɢɪɨɜɚɥɚɫɶ ɜ ɧɟ24
ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɟ ɢɫɫɥɟɞɨɜɚɧɢɟ ɮɪɚɤɬɚɥɶɧɵɯ ɡɚɤɨɧɨɦɟɪɧɨɫɬɟɣ ɪɨɫɬɚ
ɫɤɨɥɶɤɨ ɷɬɚɩɨɜ ɚɛɪɚɡɢɜɧɨɣ ɛɭɦɚɝɨɣ (ɧɚ ɡɚɜɟɪɲɚɸɳɟɣ ɫɬɚɞɢɢ ɩɨɥɢɪɨɜɤɢ ɪɚɡɦɟɪ ɚɛɪɚɡɢɜɧɵɯ ɱɚɫɬɢɰ ɧɟ ɩɪɟɜɵɲɚɥ 3 ɦɤɦ), ɩɟɪɟɞ ɷɤɫɩɟɪɢɦɟɧɬɨɦ ɩɨɥɢɪɨɜɚɧɧɚɹ ɩɨɜɟɪɯɧɨɫɬɶ ɩɨɤɪɵɜɚɥɚɫɶ ɬɨɧɤɢɦ ɫɥɨɟɦ ɚɦɨɪɮɧɨɝɨ
ɭɝɥɟɪɨɞɚ.
2. Ɍɟɨɪɟɬɢɱɟɫɤɨɟ ɨɩɢɫɚɧɢɟ ɢɡɦɟɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɦɟɬɚɥɥɚ
ɜ ɩɪɨɰɟɫɫɟ ɰɢɤɥɢɱɟɫɤɨɝɨ ɞɟɮɨɪɦɢɪɨɜɚɧɢɹ
ȼ ɜɟɪɲɢɧɟ ɭɫɬɚɥɨɫɬɧɨɣ ɬɪɟɳɢɧɵ ɩɪɨɢɫɯɨɞɢɬ ɢɧɬɟɧɫɢɜɧɚɹ ɞɢɫɫɢɩɚɰɢɹ ɷɧɟɪɝɢɢ, ɜɵɡɜɚɧɧɚɹ ɥɨɤɚɥɢɡɚɰɢɟɣ ɩɥɚɫɬɢɱɟɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ.
ɏɚɪɚɤɬɟɪɧɵɣ ɪɚɡɦɟɪ ɡɨɧɵ ɞɢɫɫɢɩɚɰɢɢ ɷɧɟɪɝɢɢ ɜ ɪɚɦɤɚɯ ɥɢɧɟɣɧɨɣ ɦɟɯɚɧɢɤɢ ɪɚɡɪɭɲɟɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɟɥɢɱɢɧɨɣ ɤɨɷɮɮɢɰɢɟɧɬɚ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɧɚɩɪɹɠɟɧɢɣ. ȼɟɥɢɱɢɧɭ ɤɨɷɮɮɢɰɢɟɧɬɚ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɧɚɩɪɹɠɟɧɢɣ ɫ ɭɱɟɬɨɦ ɝɟɨɦɟɬɪɢɢ ɨɛɪɚɡɰɚ ɦɨɠɧɨ ɨɰɟɧɢɬɶ, ɢɫɩɨɥɶɡɭɹ ɜɵɪɚɠɟɧɢɟ
12
K V Sa Sec §¨ Sa ·¸ ,
©W ¹
(1)
ɝɞɟ W – ɲɢɪɢɧɚ ɨɛɪɚɡɰɚ; a – ɩɨɥɭɞɥɢɧɚ ɬɪɟɳɢɧɵ.
ɗɜɨɥɸɰɢɹ ɬɟɦɩɟɪɚɬɭɪɵ Ɍ ɩɪɢ ɰɢɤɥɢɱɟɫɤɨɦ ɞɟɮɨɪɦɢɪɨɜɚɧɢɢ
V V A 'V sin Zt ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ ɨɞɧɨɪɨɞɧɨɫɬɢ ɟɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ,
ɜ ɨɬɫɭɬɫɬɜɢɟ ɫɬɪɭɤɬɭɪɧɵɯ ɩɟɪɟɯɨɞɨɜ ɢ ɩɥɚɫɬɢɱɟɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ, ɦɨɠɟɬ ɛɵɬɶ ɨɩɢɫɚɧɚ ɭɪɚɜɧɟɧɢɟɦ Ʉɟɥɶɜɢɧɚ
LogTt E 1 2Q Z
'V cos Zt ,
Uc
(2)
ɝɞɟ E – ɤɨɷɮɮɢɰɢɟɧɬ ɬɟɦɩɟɪɚɬɭɪɧɨɝɨ ɪɚɫɲɢɪɟɧɢɹ; U – ɩɥɨɬɧɨɫɬɶ; ɫ –
ɭɞɟɥɶɧɚɹ ɬɟɩɥɨɟɦɤɨɫɬɶ; Q – ɤɨɷɮɮɢɰɢɟɧɬ ɉɭɚɫɫɨɧɚ; Z – ɭɝɥɨɜɚɹ ɱɚɫɬɨɬɚ ɧɚɝɪɭɠɟɧɢɹ; (.)t – ɩɪɨɢɡɜɨɞɧɚɹ ɩɨ ɜɪɟɦɟɧɢ.
Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ (2) ɢɦɟɟɬ ɜɢɞ
ª E1 2Q
º
T T0 exp «
'Vsin Zt » ,
Uc
¬
¼
(3)
ɪɚɡɥɨɠɟɧɢɟ ɜ ɪɹɞ ɫɨɨɬɧɨɲɟɧɢɹ (3) ɫ ɭɱɟɬɨɦ ɦɚɥɨɫɬɢ ɫɨɨɬɧɨɲɟɧɢɹ,
ɫɬɨɹɳɟɝɨ ɜ ɩɨɤɚɡɚɬɟɥɟ ɷɤɫɩɨɧɟɧɬɵ, ɞɚɟɬ ɫɥɟɞɭɸɳɢɟ ɫɨɨɬɧɨɲɟɧɢɹ ɞɥɹ
ɚɦɩɥɢɬɭɞɵ ɩɟɪɜɨɣ ɢ ɜɬɨɪɨɣ ɝɚɪɦɨɧɢɤɢ:
25
Ɇ.ȼ. Ȼɚɧɧɢɤɨɜ, Ⱥ.ɘ. Ɏɟɞɨɪɨɜɚ, Ⱥ.ɂ. Ɍɟɪɟɯɢɧɚ, Ɉ.Ⱥ. ɉɥɟɯɨɜ
E 1 2Q
T § E1 2Q ·
2
A1 T0
'V, A2 0 ¨
¸ 'V .
Uc
4 © Uc ¹
2
(4)
Ⱥɧɚɥɢɡ ɫɨɨɬɧɨɲɟɧɢɣ (3), (4) ɩɨɡɜɨɥɹɟɬ ɫɞɟɥɚɬɶ ɜɵɜɨɞ ɨ ɬɨɦ, ɱɬɨ
ɜ ɤɥɚɫɫɢɱɟɫɤɨɦ ɫɥɭɱɚɟ (ɫɨɨɬɧɨɲɟɧɢɹ (3)) ɚɦɩɥɢɬɭɞɚ ɜɬɨɪɨɣ ɝɚɪɦɨɧɢɤɢ
ɢɦɟɟɬ ɩɨɪɹɞɨɤ 10–6 ɢ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɦɨɠɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ, ɚɦɩɥɢɬɭɞɵ ɩɟɪɜɨɣ ɢ ɜɬɨɪɨɣ ɝɚɪɦɨɧɢɤ ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɱɚɫɬɨɬɵ
ɢ ɹɜɥɹɸɬɫɹ ɥɢɧɟɣɧɵɦɢ ɮɭɧɤɰɢɹɦɢ ɚɦɩɥɢɬɭɞɵ ɧɚɩɪɹɠɟɧɢɹ ɢ ɤɜɚɞɪɚɬɚ
ɚɦɩɥɢɬɭɞɵ ɧɚɩɪɹɠɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ.
ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɜɵɫɤɚɡɵɜɚɸɬɫɹ ɩɪɟɞɩɨɥɨɠɟɧɢɹ ɨ ɬɨɦ, ɱɬɨ
ɷɮɮɟɤɬ ɬɟɪɦɨɭɩɪɭɝɨɫɬɢ ɹɜɥɹɟɬɫɹ ɫɭɳɟɫɬɜɟɧɧɨ ɧɟɥɢɧɟɣɧɵɦ [1]. Ɂɚɦɟɬɧɵɣ ɜɤɥɚɞ ɜ ɡɚɜɢɫɢɦɨɫɬɶ ɬɟɦɩɟɪɚɬɭɪɵ ɨɬ ɜɪɟɦɟɧɢ ɜɧɨɫɢɬ ɩɪɨɰɟɫɫ ɢɡɦɟɧɟɧɢɹ ɭɩɪɭɝɢɯ ɫɜɨɣɫɬɜ ɦɚɬɟɪɢɚɥɚ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ. ȼ ɩɪɟɞɩɨɥɨɠɟɧɢɢ
ɡɚɜɢɫɢɦɨɫɬɢ ɭɩɪɭɝɢɯ ɦɨɞɭɥɟɣ ɦɚɬɟɪɢɚɥɚ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ( OT , PT ) ɢɡɦɟɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ
§ E 1 2Q V0
V0 (1,5O2 2OP P2 ) ·
OT
P
Log Tt ¨ 2
¸u
T
(3O 2P )2 U c
Uc
P2 (3O 2P )2 U c ¹
©
§
OT
(1,5O2 2OP P2 ) · 2
u'VZcos Zt ¨
P
¸ 'V Zsin 2Zt.
T
2
P2 (3O 2P )2 U c ¹
© 2(3O 2P ) U c
(5)
Ⱥɧɚɥɢɡ ɩɨɜɟɞɟɧɢɹ ɚɦɩɥɢɬɭɞ ɩɟɪɜɨɣ ɢ ɜɬɨɪɨɣ ɝɚɪɦɨɧɢɤ ɩɪɨɜɨɞɢɥɫɹ ɱɢɫɥɟɧɧɨ ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ ɥɢɧɟɣɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɭɩɪɭɝɢɯ
ɫɜɨɣɫɬɜ ɦɚɬɟɪɢɚɥɚ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ. ȼɟɥɢɱɢɧɵ ɞɢɮɮɟɪɟɧɰɢɚɥɨɜ ɭɩɪɭɝɢɯ ɫɜɨɣɫɬɜ OT , PT ɩɨɞɛɢɪɚɥɢɫɶ ɢɡ ɭɫɥɨɜɢɹ ɫɨɜɩɚɞɟɧɢɹ ɫɩɟɤɬɪɨɜ ɡɚɜɢɫɢɦɨɫɬɢ ɬɟɦɩɟɪɚɬɭɪɵ ɨɬ ɜɪɟɦɟɧɢ ɞɥɹ ɨɞɧɨɝɨ ɢɡ ɷɤɫɩɟɪɢɦɟɧɬɨɜ (ɩɪɢ
ɚɦɩɥɢɬɭɞɟ ɧɚɩɪɹɠɟɧɢɣ 160 Ɇɉɚ ɢ ɱɚɫɬɨɬɟ 1 Ƚɰ) ɢ ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɞɥɹ
ɨɫɬɚɥɶɧɵɯ ɭɫɥɨɜɢɣ ɷɤɫɩɟɪɢɦɟɧɬɨɜ. ɉɪɢ ɪɚɫɱɟɬɚɯ ɩɪɢɧɢɦɚɥɢɫɶ ɫɥɟɞɭɸɳɢɟ ɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɤɨɧɫɬɚɧɬ: E 1u105 – ɤɨɷɮɮɢɰɢɟɧɬ ɬɟɦɩɟɪɚɬɭɪɧɨɝɨ ɪɚɫɲɢɪɟɧɢɹ; U 4300 ɤɝ/ɦ3 ; c 500 Ⱦɠ/(ɤɝ˜ Ʉ) ; Q 0,34 ,
ɤɨɷɮɮɢɰɢɟɧɬɵ ɡɚɜɢɫɢɦɨɫɬɢ ɭɩɪɭɝɢɯ ɫɜɨɣɫɬɜ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨɥɭɱɢɥɢɫɶ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ: OT 9,4 u107 ɉɚ/Ʉ, PT 4,6 u107 ɉɚ/Ʉ .
Ɋɚɞɢɭɫ ɡɨɧɵ ɩɥɚɫɬɢɱɟɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɩɥɚɫɬɢɧɵ
2
rp k K2 ,
Vy
26
(6)
ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɟ ɢɫɫɥɟɞɨɜɚɧɢɟ ɮɪɚɤɬɚɥɶɧɵɯ ɡɚɤɨɧɨɦɟɪɧɨɫɬɟɣ ɪɨɫɬɚ
ɝɞɟ k – ɤɨɷɮɮɢɰɢɟɧɬ, ɡɚɜɢɫɹɳɢɣ ɨɬ ɜɢɞɚ ɧɚɩɪɹɠɟɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ
ɢ ɩɪɢɧɢɦɚɟɦɨɣ ɦɨɞɟɥɢ ɩɥɚɫɬɢɱɟɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ; V y – ɧɚɩɪɹɠɟɧɢɟ
ɬɟɱɟɧɢɹ.
Ɏɨɪɦɭ ɡɨɧɵ ɩɥɚɫɬɢɱɟɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ ɜ ɜɟɪɲɢɧɟ ɬɪɟɳɢɧɵ ɩɪɢ
ɤɜɚɡɢɫɬɚɬɢɱɟɫɤɨɦ ɪɚɫɬɹɠɟɧɢɢ ɦɨɠɧɨ ɨɩɢɫɚɬɶ ɫɨɨɬɧɨɲɟɧɢɹɦɢ:
ɫ ɭɱɟɬɨɦ ɤɪɢɬɟɪɢɹ Ɇɢɡɟɫɚ
rp T
1 K 2 1 cos T 3sin2 T ,
4S V2y
(7)
ɫ ɭɱɟɬɨɦ ɤɪɢɬɟɪɢɹ Ɍɪɟɫɤɚ–ɋɟɧ-ȼɟɧɚɧɚ
rp T
2
1 K 2 cos2 § T · §1 sin § T · · .
¨ ¸¨
¨ ¸¸
2S V2y
© 2 ¹©
© 2 ¹¹
(8)
3. Ɋɟɡɭɥɶɬɚɬɵ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ
ɢɡɦɟɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɨɬ ɧɚɩɪɹɠɟɧɢɹ
ɇɚ ɪɢɫ. 3 ɩɨɤɚɡɚɧɨ ɢɡɦɟɧɟɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ɜ ɜɟɪɲɢɧɟ ɬɪɟɳɢɧɵ, ɧɚɩɪɹɠɟɧɢɹ ɢ ɪɚɫɤɪɵɬɢɹ ɬɪɟɳɢɧɵ ɜ ɩɪɨɰɟɫɫɟ ɧɚɝɪɭɠɟɧɢɹ ɩɪɢ ɚɦɩɥɢɬɭɞɟ ɧɚɩɪɹɠɟɧɢɹ 212 Ɇɉɚ, ɫɪɟɞɧɟɦ ɧɚɩɪɹɠɟɧɢɢ
212 Mɉa ɢ ɱɚɫɬɨɬɟ 5 Ƚɰ. Ⱦɚɧɧɵɟ ɞɚɬɱɢɤɚ ɩɟɪɟɦɟɳɟɧɢɹ, ɡɚɤɪɟɩɥɟɧɧɨɝɨ
ɧɚ ɛɟɪɟɝɚɯ ɬɪɟɳɢɧɵ, ɩɨɡɜɨɥɹɸɬ ɭɬɜɟɪɠɞɚɬɶ, ɱɬɨ ɪɚɫɤɪɵɬɢɟ ɛɟɪɟɝɨɜ
ɬɪɟɳɢɧɵ ɢɡɦɟɧɹɟɬɫɹ ɫɢɧɮɚɡɧɨ ɫ ɩɪɢɥɨɠɟɧɧɵɦ ɧɚɩɪɹɠɟɧɢɟɦ.
Ⱥɧɚɥɢɡ ɬɟɦɩɟɪɚɬɭɪɧɵɯ ɞɚɧɧɵɯ ɩɨɡɜɨɥɹɟɬ ɭɬɜɟɪɠɞɚɬɶ, ɱɬɨ ɦɚɤɫɢɦɭɦ ɩɪɢɥɨɠɟɧɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɢ ɦɚɤɫɢɦɭɦ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɬɟɩɥɨɜɵɞɟɥɟɧɢɹ ɜ ɜɟɪɲɢɧɟ ɭɫɬɚɥɨɫɬɧɨɣ ɬɪɟɳɢɧɵ ɧɟ ɫɨɜɩɚɞɚɸɬ ɜɨ ɜɪɟɦɟɧɢ.
ȼ ɧɚɱɚɥɟ ɷɤɫɩɟɪɢɦɟɧɬɚ ɨɛɪɚɡɟɰ ɧɚɝɪɭɠɟɧ ɫɪɟɞɧɢɦ ɧɚɩɪɹɠɟɧɢɟɦ ɢ ɧɚɯɨɞɢɬɫɹ ɜ ɫɨɫɬɨɹɧɢɢ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ. ɇɚ ɤɚɠɞɨɦ ɰɢɤɥɟ ɧɚɝɪɭɠɟɧɢɹ ɧɚɛɥɸɞɚɟɬɫɹ ɭɱɚɫɬɨɤ ɩɚɞɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ, ɜɵɡɜɚɧɧɵɣ
ɬɟɪɦɨɭɩɪɭɝɢɦ ɷɮɮɟɤɬɨɦ, ɩɟɪɟɯɨɞɹɳɢɣ ɜ ɭɱɚɫɬɨɤ ɪɨɫɬɚ ɬɟɦɩɟɪɚɬɭɪɵ,
ɜɵɡɜɚɧɧɵɣ ɥɨɤɚɥɶɧɵɦ ɩɟɪɟɯɨɞɨɦ ɱɟɪɟɡ ɩɪɟɞɟɥ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ
ɢ ɨɛɪɚɡɨɜɚɧɢɟɦ ɡɨɧɵ ɩɥɚɫɬɢɱɟɫɤɨɝɨ ɞɟɮɨɪɦɢɪɨɜɚɧɢɹ. ɉɪɢ ɩɚɞɟɧɢɢ
ɧɚɩɪɹɠɟɧɢɹ ɬɟɩɥɨɜɵɞɟɥɟɧɢɟ ɜ ɜɟɪɲɢɧɟ ɬɪɟɳɢɧɵ ɩɪɨɞɨɥɠɚɟɬɫɹ. Ƚɟɨɦɟɬɪɢɹ ɡɨɧɵ ɩɥɚɫɬɢɱɟɫɤɨɝɨ ɞɟɮɨɪɦɢɪɨɜɚɧɢɹ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 4.
ɉɪɢ ɭɦɟɧɶɲɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɜ ɜɟɪɲɢɧɟ ɬɪɟɳɢɧɵ ɬɟɩɥɨɜɵɞɟɥɟɧɢɟ
ɜɨɡɪɚɫɬɚɟɬ, ɢ ɬɟɦɩɟɪɚɬɭɪɚ ɞɨɫɬɢɝɚɟɬ ɦɚɤɫɢɦɭɦɚ ɩɪɚɤɬɢɱɟɫɤɢ ɩɪɢ ɧɭɥɟɜɨɦ ɧɚɩɪɹɠɟɧɢɢ. Ɂɚɬɟɦ ɜ ɧɚɱɚɥɟ ɫɥɟɞɭɸɳɟɝɨ ɰɢɤɥɚ ɬɟɦɩɟɪɚɬɭɪɚ ɩɚɞɚɟɬ ɡɚ ɫɱɟɬ ɬɟɪɦɨɭɩɪɭɝɨɝɨ ɷɮɮɟɤɬɚ, ɢ ɩɪɨɰɟɫɫ ɩɪɨɞɨɥɠɚɟɬɫɹ.
27
Ɇ.ȼ. Ȼɚɧɧɢɤɨɜ, Ⱥ.ɘ. Ɏɟɞɨɪɨɜɚ, Ⱥ.ɂ. Ɍɟɪɟɯɢɧɚ, Ɉ.Ⱥ. ɉɥɟɯɨɜ
Ɋɢɫ. 3. ɂɡɦɟɧɟɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ɜ ɜɟɪɲɢɧɟ ɬɪɟɳɢɧɵ (1), ɧɚɩɪɹɠɟɧɢɹ
(2) ɢ ɪɚɫɤɪɵɬɢɹ ɬɪɟɳɢɧɵ (3) ɜ ɩɪɨɰɟɫɫɟ ɧɚɝɪɭɠɟɧɢɹ ɩɪɢ ɚɦɩɥɢɬɭɞɟ ɧɚɩɪɹɠɟɧɢɹ
212 Mɉa, ɫɪɟɞɧɟɦ ɧɚɩɪɹɠɟɧɢɢ 212 Mɉa ɢ ɱɚɫɬɨɬɟ 5 Ƚɰ
Ɋɢɫ. 4. Ɏɨɪɦɚ ɡɨɧɵ ɢɧɬɟɧɫɢɜɧɨɣ ɞɢɫɫɢɩɚɰɢɢ ɷɧɟɪɝɢɢ ɜ ɜɟɪɲɢɧɟ ɭɫɬɚɥɨɫɬɧɨɣ
ɬɪɟɳɢɧɵ ɧɚ ɩɟɪɜɨɦ ɰɢɤɥɟ ɞɟɮɨɪɦɢɪɨɜɚɧɢɹ ɢ ɡɨɧɵ ɩɥɚɫɬɢɱɟɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ,
ɩɨɫɬɪɨɟɧɧɵɯ ɩɨ ɤɪɢɬɟɪɢɹɦ Ɇɢɡɟɫɚ ɢ Ɍɪɟɫɤɚ–ɋɟɧ-ȼɟɧɚɧɚ
Ɇɟɬɨɞ ɢɧɮɪɚɤɪɚɫɧɨɣ ɬɟɪɦɨɝɪɚɮɢɢ ɩɨɡɜɨɥɹɟɬ ɫ ɜɵɫɨɤɨɣ ɬɨɱɧɨɫɬɶɸ ɜɢɡɭɚɥɢɡɢɪɨɜɚɬɶ ɡɨɧɭ ɢɧɬɟɧɫɢɜɧɨɣ ɞɢɫɫɢɩɚɰɢɢ ɷɧɟɪɝɢɢ ɜ ɜɟɪɲɢɧɟ ɭɫɬɚɥɨɫɬɧɨɣ ɬɪɟɳɢɧɵ (ɫɦ. ɪɢɫ. 4). Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ
ɜ ɜɟɪɲɢɧɟ ɬɪɟɳɢɧɵ ɜ ɩɪɨɰɟɫɫɟ ɞɟɮɨɪɦɢɪɨɜɚɧɢɹ ɦɨɠɟɬ ɨɬɥɢɱɚɬɶɫɹ ɨɬ
ɮɨɪɦɵ ɡɨɧɵ ɩɥɚɫɬɢɱɟɫɤɢɯ ɞɟɮɨɪɦɚɰɢɣ ɢɡ-ɡɚ ɩɪɨɰɟɫɫɨɜ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ, ɩɨɷɬɨɦɭ ɞɥɹ ɚɧɚɥɢɡɚ ɝɟɨɦɟɬɪɢɢ ɨɛɥɚɫɬɢ ɢɧɬɟɧɫɢɜɧɨɝɨ ɬɟɩɥɨɜɵɞɟɥɟɧɢɹ, ɜɵɡɜɚɧɧɨɝɨ ɩɥɚɫɬɢɱɟɫɤɨɣ ɞɟɮɨɪɦɚɰɢɟɣ, ɥɨɝɢɱɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɨɥɶɤɨ ɩɟɪɜɵɣ ɰɢɤɥ ɞɟɮɨɪɦɢɪɨɜɚɧɢɹ. ɇɚ ɪɢɫ. 4 ɩɨɤɚɡɚɧɨ ɫɪɚɜɧɟ28
ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɟ ɢɫɫɥɟɞɨɜɚɧɢɟ ɮɪɚɤɬɚɥɶɧɵɯ ɡɚɤɨɧɨɦɟɪɧɨɫɬɟɣ ɪɨɫɬɚ
ɧɢɟ ɧɚɛɥɸɞɚɟɦɨɣ ɮɨɪɦɵ ɡɨɧɵ ɢɧɬɟɧɫɢɜɧɨɣ ɞɢɫɫɢɩɚɰɢɢ ɷɧɟɪɝɢɢ ɧɚ
ɩɟɪɜɨɦ ɰɢɤɥɟ ɞɟɮɨɪɦɢɪɨɜɚɧɢɹ ɢ ɤɥɚɫɫɢɱɟɫɤɢɯ ɪɟɲɟɧɢɣ (3), (4) ɞɥɹ
ɮɨɪɦɵ ɡɨɧɵ ɩɥɚɫɬɢɱɟɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ ɜ ɜɟɪɲɢɧɟ ɬɪɟɳɢɧɵ (ɜ ɪɚɫɱɟɬɚɯ
ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɫɥɟɞɭɸɳɢɟ ɞɚɧɧɵɟ: ɩɨɥɨɜɢɧɚ ɞɥɢɧɵ ɬɪɟɳɢɧɵ 4 ɦɦ,
ɩɪɢɥɨɠɟɧɧɨɟ ɧɚɩɪɹɠɟɧɢɟ 300 Mɉa). Ⱥɧɚɥɢɡ ɪɟɡɭɥɶɬɚɬɨɜ ɩɨɡɜɨɥɹɟɬ
ɫɞɟɥɚɬɶ ɜɵɜɨɞ ɬɨɥɶɤɨ ɨ ɤɚɱɟɫɬɜɟɧɧɨɦ ɫɨɨɬɜɟɬɫɬɜɢɢ ɮɨɪɦɵ ɡɨɧɵ ɩɥɚɫɬɢɱɟɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ ɜ ɜɟɪɲɢɧɟ ɭɫɬɚɥɨɫɬɧɨɣ ɬɪɟɳɢɧɵ ɦɨɞɟɥɹɦ Ɇɢɡɟɫɚ ɢ Ɍɪɟɫɤɚ–ɋɟɧ-ȼɟɧɚɧɚ.
4. Ɏɪɚɤɬɚɥɶɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɪɨɫɬɚ ɭɫɬɚɥɨɫɬɧɨɣ ɬɪɟɳɢɧɵ
Ɋɨɫɬ ɭɫɬɚɥɨɫɬɧɨɣ ɬɪɟɳɢɧɵ ɨɩɢɫɵɜɚɟɬɫɹ ɡɚɤɨɧɨɦ ɉɷɪɢɫɚ:
da C ('K )m ,
dN
(9)
ɝɞɟ da/dN – ɫɤɨɪɨɫɬɶ ɪɨɫɬɚ ɬɪɟɳɢɧɵ; ǻK – ɪɚɡɦɚɯ ɤɨɷɮɮɢɰɢɟɧɬɚ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɧɚɩɪɹɠɟɧɢɣ; C ɢ m ɤɨɧɫɬɚɧɬɵ, ɡɚɜɢɫɹɳɢɟ ɨɬ ɫɜɨɣɫɬɜ ɦɚɬɟɪɢɚɥɚ.
ȼ ɪɚɦɤɚɯ ɷɬɨɝɨ ɫɨɨɬɧɨɲɟɧɢɹ, ɩɨɫɬɪɨɟɧɵ ɤɢɧɟɬɢɱɟɫɤɢɟ ɤɪɢɜɵɟ
ɪɨɫɬɚ ɬɪɟɳɢɧɵ, ɤɨɬɨɪɵɟ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɥɨɝɚɪɢɮɦɢɱɟɫɤɢɯ ɤɨɨɪɞɢɧɚɬɚɯ ɧɚ ɪɢɫ. 5.
Ɋɢɫ. 5. Ʉɢɧɟɬɢɱɟɫɤɢɟ ɤɪɢɜɵɟ ɪɨɫɬɚ ɭɫɬɚɥɨɫɬɧɵɯ ɬɪɟɳɢɧ
ɜ ɬɢɬɚɧɨɜɨɦ ɫɩɥɚɜɟ ɈɌ-4
ȼ ɬɨ ɜɪɟɦɹ, ɤɚɤ ɤɨɷɮɮɢɰɢɟɧɬ ɋ ɡɚɜɢɫɢɬ ɨɬ ɦɟɯɚɧɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ
ɦɚɬɟɪɢɚɥɚ ɢ ɭɫɥɨɜɢɣ ɧɚɝɪɭɠɟɧɢɹ, ɨ ɤɨɷɮɮɢɰɢɟɧɬɟ m ɪɹɞ ɭɱɟɧɵɯ ɢɦɟɟɬ
ɫɜɨɟ ɦɧɟɧɢɟ. Ɍɚɤ, ɜ ɪɚɛɨɬɚɯ [10–13] ɟɝɨ ɫɜɹɡɵɜɚɸɬ ɫ ɮɪɚɤɬɚɥɶɧɵɦ ɪɨɫ29
Ɇ.ȼ. Ȼɚɧɧɢɤɨɜ, Ⱥ.ɘ. Ɏɟɞɨɪɨɜɚ, Ⱥ.ɂ. Ɍɟɪɟɯɢɧɚ, Ɉ.Ⱥ. ɉɥɟɯɨɜ
ɬɨɦ ɬɪɟɳɢɧɵ. ȼ ɪɚɛɨɬɟ [13] ɤɨɷɮɮɢɰɢɟɧɬ m ɩɪɟɞɫɬɚɜɥɟɧ ɫɥɟɞɭɸɳɢɦ
ɨɛɪɚɡɨɦ:
m
2 D , 1 D 2,
2 D
(10)
ɝɞɟ D – ɮɪɚɤɬɚɥɶɧɚɹ ɪɚɡɦɟɪɧɨɫɬɶ. ȼ ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɟ ɩɪɨɜɟɪɟɧɨ ɞɚɧɧɨɟ ɫɨɨɬɧɨɲɟɧɢɟ, ɢ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɮɪɚɤɬɚɥɶɧɨɣ ɪɚɡɦɟɪɧɨɫɬɢ ɬɪɟɳɢɧɵ D ɢɫɩɨɥɶɡɨɜɚɥɚɫɶ ɬɟɯɧɨɥɨɝɢɹ RS-ɚɧɚɥɢɡɚ. ɗɬɚ ɦɟɬɨɞɢɤɚ ɩɨɡɜɨɥɹɟɬ
ɨɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɏɟɪɫɬɚ, ɤɨɬɨɪɵɣ ɫɜɹɡɚɧ ɫ ɮɪɚɤɬɚɥɶɧɨɣ ɪɚɡɦɟɪɧɨɫɬɶɸ ɩɨ ɫɥɟɞɭɸɳɟɣ ɮɨɪɦɭɥɟ:
D = 2 – H.
(11)
Ɍɟɯɧɨɥɨɝɢɹ RS-ɚɧɚɥɢɡɚ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɫɥɟɞɭɸɳɟɦ [14]:
– ɢɫɫɥɟɞɭɟɦɵɣ ɪɹɞ ɞɥɢɧɨɣ N (X_k:k = 1,…,n) ɞɟɥɢɬɫɹ ɧɚ K ɧɟɩɟɪɟɫɟɤɚɸɳɢɯɫɹ ɛɥɨɤɨɜ,
– ɞɚɥɟɟ ɜɵɱɢɫɥɹɸɬɫɹ ɨɬɧɨɲɟɧɢɹ R(t_i,d)/S(t_i,d) ɞɥɹ ɤɚɠɞɨɝɨ ɛɥɨɤɚ, ɝɞɟ R – ɪɚɡɦɚɯ ɧɚɤɨɩɥɟɧɧɵɯ ɫɭɦɦ ɞɥɹ ɤɚɠɞɨɝɨ ɛɥɨɤɚ; S – ɤɨɪɟɧɶ ɢɡ
ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɝɨ ɨɬɤɥɨɧɟɧɢɹ ɞɥɹ ɤɚɠɞɨɝɨ ɛɥɨɤɚ.
ti ª N º i 1 1.
¬« K ¼»
(12)
Ɂɞɟɫɶ ti – ɩɟɪɜɵɟ ɬɨɱɤɢ ɛɥɨɤɨɜ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɧɟɪɚɜɟɧɫɬɜɭ (ti – 1) +
+ d ” N, ɝɞɟ d – ɤɨɥɢɱɟɫɬɜɨ ɷɥɟɦɟɧɬɨɜ ɜ ɛɥɨɤɟ.
R ti , d max^0,W ti ,1 ,...,W ti , d ` min^0,W ti ,1 ,...,W ti ,d`,
(13)
(14)
ɝɞɟ
W ti , k ¦
k
j 1
d
Xti j1 k 1 ¦ j 1 Xti j1 , k 1,d.
d
Ɂɚɬɟɦ ɧɚɯɨɞɢɬɫɹ ɡɧɚɱɟɧɢɟ ɞɢɫɩɟɪɫɢɢ S 2 ti ,d ɞɥɹ ɤɚɠɞɨɝɨ ɛɥɨɤɚ, ɬ.ɟ.
ɞɥɹ X ti ,..., X tid 1 . Ɉɬɫɸɞɚ ɞɥɹ ɤɚɠɞɨɝɨ ɛɥɨɤɚ ɜɵɱɢɫɥɹɸɬɫɹ ɡɧɚɱɟɧɢɹ R/S;
– ɩɨɫɥɟ ɷɬɨɝɨ ɢɡɦɟɧɹɟɦ ɤɨɥɢɱɟɫɬɜɨ ɷɥɟɦɟɧɬɨɜ d ɜ ɛɥɨɤɟ, ɬ.ɟ.
di+1=m·di, ɝɞɟ m>1; ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɞɨɫɬɨɜɟɪɧɨɝɨ ɪɟɡɭɥɶɬɚɬɚ ɧɚɱɚɥɶɧɨɟ
ɤɨɥɢɱɟɫɬɜɨ ɷɥɟɦɟɧɬɨɜ ɜ ɛɥɨɤɟ d0 ɛɟɪɟɬɫɹ ɪɚɜɧɵɦ 10, ɭɜɟɥɢɱɟɧɢɟ d ɜɟɞɟɬɫɹ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɤɨɥɢɱɟɫɬɜɨ ɛɥɨɤɨɜ ɛɭɞɟɬ ɧɟ ɦɟɧɟɟ 6. Ⱦɥɹ ɤɚɠɞɨɝɨ d ɩɨɜɬɨɪɹɟɬɫɹ ɩɪɨɰɟɞɭɪɚ ɧɚɯɨɠɞɟɧɢɹ ɨɬɧɨɲɟɧɢɹ R(ti ,d) / S (ti ,d) ;
30
ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɟ ɢɫɫɥɟɞɨɜɚɧɢɟ ɮɪɚɤɬɚɥɶɧɵɯ ɡɚɤɨɧɨɦɟɪɧɨɫɬɟɣ ɪɨɫɬɚ
– ɢɫɩɨɥɶɡɭɹ ɩɨɥɭɱɟɧɧɵɟ ɪɟɡɭɥɶɬɚɬɵ, ɦɨɠɧɨ ɫɬɪɨɢɬɶ ɝɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ log(R(ti,d)/S(ti,d)) ɨɬɧɨɫɢɬɟɥɶɧɨ log d (ɪɢɫ. 6);
– ɩɪɢɦɟɧɹɟɬɫɹ ɦɟɬɨɞ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɨɜ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɭɝɥɨɜɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɩɪɹɦɨɣ, ɩɪɨɯɨɞɹɳɟɣ ɦɚɤɫɢɦɚɥɶɧɨ ɛɥɢɡɤɨ ɤ ɩɨɥɭɱɟɧɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ, ɭɝɥɨɜɨɣ ɤɨɷɮɮɢɰɢɟɧɬ ɞɥɹ ɞɚɧɧɨɣ ɩɪɹɦɨɣ ɛɭɞɟɬ
ɨɩɪɟɞɟɥɹɬɶ ɩɨɤɚɡɚɬɟɥɶ ɏɟɪɫɬɚ.
ɂɫɫɥɟɞɭɟɦɵɟ ɩɪɨɮɢɥɢ ɛɵɥɢ ɩɨɥɭɱɟɧɵ ɫ ɩɨɦɨɳɶɸ ɰɢɮɪɨɜɨɝɨ
ɢɧɬɟɪɮɟɪɨɦɟɬɪɚ-ɩɪɨɮɢɥɨɦɟɬɪɚ New View, ɤɨɬɨɪɵɣ ɩɨɡɜɨɥɹɟɬ ɩɨɥɭɱɚɬɶ 3-ɦɟɪɧɵɟ ɤɚɪɬɢɧɵ ɩɪɨɮɢɥɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɫ ɬɨɱɧɨɫɬɶɸ ɩɨ ɝɨɪɢɡɨɧɬɚɥɢ 0,5 ɦɤɦ ɢ ɩɨ ɜɟɪɬɢɤɚɥɢ 1 ɧɦ. ɂɡ ɞɚɧɧɵɯ 3-ɦɟɪɧɵɯ ɩɪɨɮɢɥɟɣ
ɜɵɪɟɡɚɥɢɫɶ 1-ɦɟɪɧɵɟ, ɤɨɬɨɪɵɟ ɜɩɨɫɥɟɞɫɬɜɢɢ ɚɧɚɥɢɡɢɪɨɜɚɥɢɫɶ R/S-ɦɟɬɨɞɨɦ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɜɵɱɢɫɥɟɧɢɣ ɩɨɥɭɱɟɧɨ ɫɥɟɞɭɸɳɟɟ ɡɧɚɱɟɧɢɟ ɮɪɚɤɬɚɥɶɧɨɣ ɪɚɡɦɟɪɧɨɫɬɢ: D = 1,01 ± 0,01, ɤɨɬɨɪɨɟ ɩɪɢ ɩɨɞɫɬɚɧɨɜɤɟ ɜ ɮɨɪɦɭɥɭ (10) ɞɚɟɬ ɛɥɢɡɤɢɣ ɤ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɦɭ ɩɨɤɚɡɚɬɟɥɶ m.
Ɋɢɫ. 6. Ɂɚɜɢɫɢɦɨɫɬɶ R/S ɨɬ ɤɨɥɢɱɟɫɬɜɚ ɷɥɟɦɟɧɬɨɜ
ɜ ɛɥɨɤɟ d ɜ ɥɨɝɚɪɢɮɦɢɱɟɫɤɢɯ ɤɨɨɪɞɢɧɚɬɚɯ
Ɂɚɤɥɸɱɟɧɢɟ
ɉɨɥɭɱɟɧɵ ɫɨɨɬɧɨɲɟɧɢɹ, ɨɩɢɫɵɜɚɸɳɢɟ ɢɡɦɟɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ
ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɨɛɪɚɡɰɚ ɜ ɩɪɨɰɟɫɫɟ ɨɞɧɨɨɫɧɨɝɨ ɰɢɤɥɢɱɟɫɤɨɝɨ ɞɟɮɨɪɦɢɪɨɜɚɧɢɹ ɫ ɭɱɟɬɨɦ ɥɢɧɟɣɧɨɝɨ ɢ ɧɟɥɢɧɟɣɧɨɝɨ ɬɟɪɦɨɭɩɪɭɝɨɝɨ ɷɮɮɟɤɬɚ.
ɂɫɫɥɟɞɨɜɚɧɢɟ ɩɪɨɰɟɫɫɨɜ ɢɡɦɟɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɩɪɢ ɰɢɤɥɢɱɟɫɤɨɦ ɞɟɮɨɪɦɢɪɨɜɚɧɢɢ ɜ ɬɢɬɚɧɨɜɨɦ ɫɩɥɚɜɟ ɈɌ-4 ɧɚ ɝɥɚɞɤɢɯ ɨɛɪɚɡɰɚɯ ɩɨɤɚɡɚɥɨ,
ɱɬɨ ɨɛɪɚɬɢɦɨɟ ɢɡɦɟɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɩɪɢ ɭɩɪɭɝɨɦ ɞɟɮɨɪɦɢɪɨɜɚɧɢɢ
ɦɨɠɟɬ ɞɨɫɬɢɝɚɬɶ ɨɞɧɨɝɨ ɝɪɚɞɭɫɚ
31
Ɇ.ȼ. Ȼɚɧɧɢɤɨɜ, Ⱥ.ɘ. Ɏɟɞɨɪɨɜɚ, Ⱥ.ɂ. Ɍɟɪɟɯɢɧɚ, Ɉ.Ⱥ. ɉɥɟɯɨɜ
ɉɨɤɚɡɚɧɨ, ɱɬɨ ɩɪɨɰɟɫɫ ɬɟɩɥɨɜɵɞɟɥɟɧɢɹ ɧɨɫɢɬ ɫɭɳɟɫɬɜɟɧɧɨ ɧɟɥɢɧɟɣɧɵɣ ɯɚɪɚɤɬɟɪ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɦɟɬɨɞɚ ɢɧɮɪɚɤɪɚɫɧɨɣ ɬɟɪɦɨɝɪɚɮɢɢ
ɩɨɡɜɨɥɹɟɬ ɷɮɮɟɤɬɢɜɧɨ ɢɫɫɥɟɞɨɜɚɬɶ ɩɪɨɰɟɫɫɵ, ɫɜɹɡɚɧɧɵɟ ɤɚɤ ɫ ɥɨɤɚɥɢɡɚɰɢɟɣ ɩɥɚɫɬɢɱɟɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ ɜ ɜɟɪɲɢɧɟ ɬɪɟɳɢɧɵ, ɬɚɤ ɢ ɫ ɬɪɟɧɢɟɦ
ɧɚ ɟɟ ɛɟɪɟɝɚɯ.
ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɩɨɤɚɡɚɧɨ, ɱɬɨ ɡɨɧɚ ɩɥɚɫɬɢɱɟɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ ɧɟ ɫɨɜɩɚɞɚɟɬ ɫ ɩɪɟɞɫɤɚɡɚɧɢɹɦɢ ɥɢɧɟɣɧɨɣ ɦɟɯɚɧɢɤɢ ɪɚɡɪɭɲɟɧɢɹ,
ɚ ɦɚɤɫɢɦɭɦ ɬɟɩɥɨɜɵɞɟɥɟɧɢɹ ɞɨɫɬɢɝɚɟɬɫɹ ɧɚ ɧɢɫɯɨɞɹɳɟɣ ɜɟɬɜɢ ɧɚɝɪɭɠɟɧɢɹ.
Ɋɚɫɫɱɢɬɚɧɚ ɮɪɚɤɬɚɥɶɧɚɹ ɪɚɡɦɟɪɧɨɫɬɶ ɩɪɨɮɢɥɹ ɬɪɟɳɢɧɵ, ɤɨɬɨɪɚɹ
ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɚ ɜ ɤɢɧɟɬɢɱɟɫɤɨɦ ɭɪɚɜɧɟɧɢɢ ɞɥɹ ɪɨɫɬɚ ɭɫɬɚɥɨɫɬɧɨɣ ɬɪɟɳɢɧɵ ɢ ɫɨɝɥɚɫɭɟɬɫɹ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ ɞɥɹ
ɫɩɥɚɜɚ ɬɢɬɚɧɚ ɈɌ-4
Ɋɚɛɨɬɚ ɜɵɩɨɥɧɟɧɚ ɩɪɢ ɮɢɧɚɧɫɨɜɨɣ ɩɨɞɞɟɪɠɤɟ ɊɎɎɂ (ɝɪɚɧɬ
ʋ 12-01-31145 ɦɨɥ_ɚ).
Ȼɢɛɥɢɨɝɪɚɮɢɱɟɫɤɢɣ ɫɩɢɫɨɤ
1. ȼɚɜɢɥɨɜ ȼ.ɉ. Ⱦɢɧɚɦɢɱɟɫɤɚɹ ɬɟɩɥɨɜɚɹ ɬɨɦɨɝɪɚɮɢɹ (ɨɛɡɨɪ) // Ɂɚɜɨɞɫɤɚɹ ɥɚɛɨɪɚɬɨɪɢɹ. Ⱦɢɚɝɧɨɫɬɢɤɚ ɦɚɬɟɪɢɚɥɨɜ. – 2006. – Ɍ. 72, ʋ 3. –
C. 26–36.
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3. Theoretical analysis, infrared and structural investigation of energy
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4. ɉɥɟɯɨɜ Ɉ.Ⱥ. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɟ ɢɫɫɥɟɞɨɜɚɧɢɟ ɬɟɪɦɨɞɢɧɚɦɢɤɢ
ɩɥɚɫɬɢɱɟɫɤɨɝɨ ɞɟɮɨɪɦɢɪɨɜɚɧɢɹ ɦɟɬɨɞɨɦ ɢɧɮɪɚɤɪɚɫɧɨɣ ɬɟɪɦɨɝɪɚɮɢɢ //
ɀɌɎ. – 2011. – Ɍ. 81, ɜɵɩ. 2. – ɋ. 144–146.
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32
ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɟ ɢɫɫɥɟɞɨɜɚɧɢɟ ɮɪɚɤɬɚɥɶɧɵɯ ɡɚɤɨɧɨɦɟɪɧɨɫɬɟɣ ɪɨɫɬɚ
6. ɉɥɟɯɨɜ Ɉ.Ⱥ., Santier N., ɇɚɣɦɚɪɤ Ɉ.Ȼ. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɟ ɢɫɫɥɟɞɨɜɚɧɢɟ ɧɚɤɨɩɥɟɧɢɹ ɢ ɞɢɫɫɢɩɚɰɢɢ ɷɧɟɪɝɢɢ ɩɪɢ ɭɩɪɭɝɨ ɩɥɚɫɬɢɱɟɫɤɨɦ ɩɟɪɟɯɨɞɟ // ɀɌɎ. – 2007. – Ɍ. 77. – ȼɵɩ. 9 – C. 1236–1238.
7. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɟ ɢɫɫɥɟɞɨɜɚɧɢɟ ɝɟɧɟɪɚɰɢɢ ɬɟɩɥɚ ɜ ɜɟɪɲɢɧɟ
ɭɫɬɚɥɨɫɬɧɨɣ ɬɪɟɳɢɧɵ / Ⱥ.ɂ. Ɍɟɪɟɯɢɧɚ, Ɇ.ȼ. Ȼɚɧɧɢɤɨɜ, Ɉ.Ⱥ. ɉɥɟɯɨɜ,
ɗ.ȼ. ɉɥɟɯɨɜɚ // ɉɢɫɶɦɚ ɜ ɀɌɎ. – 2012. – Ɍ. 38. – ȼɵɩ. 16.
8. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɟ ɢɫɫɥɟɞɨɜɚɧɢɟ ɚɧɨɦɚɥɢɣ ɞɢɫɫɢɩɚɰɢɢ ɷɧɟɪɝɢɢ ɜ ɧɚɧɨɤɪɨɤɪɢɫɬɚɥɥɢɱɟɫɤɨɦ ɬɢɬɚɧɟ ɩɪɢ ɰɢɤɥɢɱɟɫɤɨɦ ɧɚɝɪɭɠɟɧɢɢ /
Ɉ. ɉɥɟɯɨɜ, Ɉ. ɇɚɣɦɚɪɤ, ɂ. ɋɟɦɟɧɨɜɚ, Ɋ. ȼɚɥɢɟɜ [ɢ ɞɪ.] // ɉɀɌɎ. –
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ɜ ɧɚɧɨɤɪɢɫɬɚɥɥɢɱɟɫɤɨɦ ɬɢɬɚɧɟ ɩɪɢ ɤɜɚɡɢɫɬɚɬɢɱɟɫɤɨɦ ɢ ɞɢɧɚɦɢɱɟɫɤɨɦ
ɧɚɝɪɭɠɟɧɢɢ / Ɉ.Ⱥ. ɉɥɟɯɨɜ, ȼ.ȼ. ɑɭɞɢɧɨɜ, ȼ.Ⱥ.Ʌɟɨɧɬɶɟɜ, Ɉ.Ȼ. ɇɚɣɦɚɪɤ //
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Ɉɛ ɚɜɬɨɪɚɯ
Ȼɚɧɧɢɤɨɜ Ɇɢɯɚɢɥ ȼɥɚɞɢɦɢɪɨɜɢɱ (ɉɟɪɦɶ, Ɋɨɫɫɢɹ) – ɚɫɩɢɪɚɧɬ
ɥɚɛɨɪɚɬɨɪɢɢ ɮɢɡɢɱɟɫɤɢɯ ɨɫɧɨɜ ɩɪɨɱɧɨɫɬɢ ɂɧɫɬɢɬɭɬɚ ɦɟɯɚɧɢɤɢ ɫɩɥɨɲɧɵɯ ɫɪɟɞ ɍɪɈ ɊȺɇ (614013, ɝ. ɉɟɪɦɶ, ɭɥ. Ⱥɤɚɞɟɦɢɤɚ Ʉɨɪɨɥɟɜɚ, 1, e-mail:
[email protected]).
Ɏɟɞɨɪɨɜɚ Ⱥɧɚɫɬɚɫɢɹ ɘɪɶɟɜɧɚ (ɉɟɪɦɶ, Ɋɨɫɫɢɹ) – ɚɫɩɢɪɚɧɬ ɥɚɛɨɪɚɬɨɪɢɢ ɮɢɡɢɱɟɫɤɢɯ ɨɫɧɨɜ ɩɪɨɱɧɨɫɬɢ ɂɧɫɬɢɬɭɬɚ ɦɟɯɚɧɢɤɢ ɫɩɥɨɲɧɵɯ ɫɪɟɞ ɍɪɈ ɊȺɇ (614013, ɝ. ɉɟɪɦɶ, ɭɥ. Ⱥɤɚɞɟɦɢɤɚ Ʉɨɪɨɥɟɜɚ, 1,
e-mail: [email protected]).
Ɍɟɪɟɯɢɧɚ Ⱥɥɟɧɚ ɂɝɨɪɟɜɧɚ (ɉɟɪɦɶ, Ɋɨɫɫɢɹ) – ɫɬɭɞɟɧɬɤɚ ɉɟɪɦɫɤɨɝɨ ɧɚɰɢɨɧɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɨɝɨ ɩɨɥɢɬɟɯɧɢɱɟɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ (614990, ɝ. ɉɟɪɦɶ, Ʉɨɦɫɨɦɨɥɶɫɤɢɣ ɩɪ., 29, e-mail:
[email protected]).
ɉɥɟɯɨɜ Ɉɥɟɝ Ⱥɧɚɬɨɥɶɟɜɢɱ (ɉɟɪɦɶ, Ɋɨɫɫɢɹ) – ɞɨɤɬɨɪ ɮɢɡɢɤɨɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɧɚɭɤ ɂɧɫɬɢɬɭɬɚ ɦɟɯɚɧɢɤɢ ɫɩɥɨɲɧɵɯ ɫɪɟɞ ɍɪɈ ɊȺɇ
(614013, ɝ. ɉɟɪɦɶ, ɭɥ. Ⱥɤɚɞɟɦɢɤɚ Ʉɨɪɨɥɟɜɚ, 1, e-mail: [email protected]).
About the authors
Bannikov Mikhail Vladimirovich (Perm, Russian Federation) –
postgraduate student in laboratory of physical foundations of strength, Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of
Sciences (1, Akademik Korolev st., 614013, Perm, Russian Federation,
e-mail: [email protected]).
35
Ɇ.ȼ. Ȼɚɧɧɢɤɨɜ, Ⱥ.ɘ. Ɏɟɞɨɪɨɜɚ, Ⱥ.ɂ. Ɍɟɪɟɯɢɧɚ, Ɉ.Ⱥ. ɉɥɟɯɨɜ
Fedorova Anastasia Yurievna (Perm, Russian Federation) – postgraduate student in laboratory of physical foundations of strength, Institute
of Continuous Media Mechanics, Ural Branch of the Russian Academy of
Sciences (1, Akademik Korolev st., 614013, Perm, Russian Federation,
e-mail: [email protected]).
Terekhina Alyona Igorevna (Perm, Russian Federation) – student,
Perm National Research Polytechnic University (29, Komsomolsky av.,
614990, Perm, Russian Federation, e-mail: [email protected]).
Plekhov Oleg Anatol’evich (Perm, Russian Federation) – Doctor of
Physical and Mathematical Sciences, Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences (1, Akademik
Korolev st., 614013, Perm, Russian Federation, e-mail: [email protected]).
ɉɨɥɭɱɟɧɨ 28.02.13
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