ɝɞɟ K1 – ɤɨɧɫɬɚɧɬɚ ɤɪɢɫɬɚɥɥɨɝɪɚɮɢɱɟɫɤɨɣ ɦɚɝɧɢɬɧɨɣ ɚɧɢɡɨɬɪɨɩɢɢ.
Ɉɞɧɚɤɨ, ɩɨɫɤɨɥɶɤɭ ɧɟ ɜɫɟ ɦɚɝɧɢɬɧɵɟ ɦɨɦɟɧɬɵ ɜ ɩɟɪɟɯɨɞɧɨɣ ɨɛɥɚɫɬɢ ɧɚɩɪɚɜɥɟɧɵ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ «ɥɟɝɤɨɣ» ɨɫɢ, ɚ ɭɝɨɥ ij ɩɥɚɜɧɨ ɦɟɧɹɟɬɫɹ ɨɬ ɨɞɧɨɝɨ ɞɨɦɟɧɚ ɤ ɞɪɭɝɨɦɭ, ɫɥɟɞɭɟɬ ɜɜɟɫɬɢ ɧɟɤɨɬɨɪɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ȕ < 1. Ɍɨɝɞɚ ɷɧɟɪɝɢɹ ɦɚɝɧɢɬɧɨɣ ɚɧɢɡɨɬɪɨɩɢɢ ɛɭɞɟɬ ɨɩɪɟɞɟɥɹɬɶɫɹ ɜɵɪɚɠɟɧɢɟɦ
Ja EK1Gɝɪ,
ɬ. ɟ. ɟɟ ɡɧɚɱɟɧɢɟ ɛɭɞɟɬ ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɬɨɥɳɢɧɟ ɩɟɪɟɯɨɞɧɨɣ ɨɛɥɚɫɬɢ.
ɋ ɭɱɟɬɨɦ ɨɛɦɟɧɧɨɣ ɷɧɟɪɝɢɢ ɢ ɷɧɟɪɝɢɢ ɚɧɢɡɨɬɪɨɩɢɢ ɞɥɹ ɟɞɢɧɢɰɵ ɩɨɜɟɪɯɧɨɫɬɢ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ (ɭɞɟɥɶɧɨɣ ɷɧɟɪɝɢɢ ɝɪɚɧɢɰɵ) ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɟ
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+ Ȗ = |
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ɂɡ (3.22) ɦɨɠɧɨ ɧɚɣɬɢ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɬɨɥɳɢɧɵ ɞɨɦɟɧɧɨɣ ɝɪɚ- |
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ɧɢɰɵ (ɢɡ ɭɫɥɨɜɢɹ ɦɢɧɢɦɭɦɚ Ȗɝɪ): |
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ɨɬɤɭɞɚ |
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EK1ɚ |
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ɉɨɞɫɬɚɜɥɹɹ (3.24) ɜ (3.22), ɩɨɥɭɱɢɦ ɫɥɟɞɭɸɳɟɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ |
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ɷɧɟɪɝɢɢ ɝɪɚɧɢɰɵ: |
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EK1Ⱥ |
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Ⱦɥɹ ɨɰɟɧɤɢ ɩɚɪɚɦɟɬɪɨɜ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ ɩɨ ɩɨɪɹɞɤɭ ɜɟɥɢɱɢɧ ɦɨɠɧɨ ɫɱɢɬɚɬɶ, ɱɬɨ ɨɛɦɟɧɧɚɹ ɷɧɟɪɝɢɹ ɪɚɜɧɚ ɬɟɩɥɨɜɨɣ ɷɧɟɪɝɢɢ ɜ ɬɨɱɤɟ Ʉɸɪɢ (Ⱥ = kĬ). ȼ ɷɬɨɦ ɫɥɭɱɚɟ (3.24) ɢ (3.25) ɭɩɪɨɫɬɹɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
į |
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k4 |
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§ k4K1 . |
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Ɍɨɝɞɚ ɞɥɹ ɠɟɥɟɡɚ (Ĭ = 1043 Ʉ, K1 = 5 Â 104 Ⱦɠ/ɦ3, ɚ = 2,5 Â 10–10 ɦ ɢ k = 1,38 Â 10–23 Ⱦɠ/Ʉ) ɩɨɥɭɱɢɦ: įɝɪ § 350 Â 10–10 ɦ, ɱɬɨ ɫɨɫɬɚɜɥɹɟɬ ɩɪɢɛɥɢɡɢɬɟɥɶɧɨ 140 ɚɬɨɦɧɵɯ ɫɥɨɟɜ, ɢ Ȗɝɪ § 2 Â 10–3 Ⱦɠ/ɦ2.
ɂɡ (3.24) ɢ (3.26) ɫɥɟɞɭɟɬ, ɱɬɨ ɱɟɦ ɛɨɥɶɲɟ ɚɧɢɡɨɬɪɨɩɢɹ ɦɚɬɟɪɢɚɥɚ, ɬɟɦ ɦɟɧɶɲɟ ɬɨɥɳɢɧɚ ɩɟɪɟɯɨɞɧɨɣ (ɝɪɚɧɢɱɧɨɣ) ɨɛɥɚɫɬɢ. ɉɪɢɜɟɞɟɧɧɵɟ ɜɵɲɟ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɷɧɟɪɝɢɢ ɢ ɬɨɥɳɢɧɵ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ ɩɪɢɛɥɢɠɟɧɧɵ, ɬɚɤ ɤɚɤ ɭɝɨɥ ij ɦɟɠɞɭ ɦɚɝɧɢɬɧɵɦɢ ɦɨɦɟɧɬɚɦɢ ɜ ɝɪɚɧɢɰɟ ɢɡɦɟɧɹɟɬɫɹ ɧɟɪɚɜɧɨɦɟɪɧɨ, ɚɫɢɦɩɬɨɬɢɱɟɫɤɢ ɩɪɢɛɥɢɠɚɹɫɶ ɤ ɨɪɢɟɧɬɚɰɢɢ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɜɧɭɬɪɢ ɫɨɫɟɞɧɢɯ ɞɨɦɟɧɨɜ. Ɉɬɫɸɞɚ ɭɞɟɥɶɧɚɹ ɷɧɟɪɝɢɹ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɨɞɧɨɝɨ ɚɬɨɦɧɨɝɨ ɫɥɨɹ ɤ ɞɪɭɝɨɦɭ ɜɧɭɬɪɢ ɫɚɦɨɣ ɩɟɪɟɯɨɞɧɨɣ ɨɛɥɚɫɬɢ (ɪɢɫ. 3.8).
Ɋɢɫ. 3.8. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ ɢ ɝɪɚɧɢɱɧɨɣ ɷɧɟɪɝɢɢ ɜ ɩɟɪɟɯɨɞɧɨɣ ɨɛɥɚɫɬɢ
ɉɪɢ ɛɨɥɟɟ ɞɟɬɚɥɶɧɨɦ ɪɚɫɫɦɨɬɪɟɧɢɢ ɩɪɢɪɨɞɵ ɩɟɪɟɯɨɞɧɨɣ ɨɛɥɚɫɬɢ ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ ɹɜɥɟɧɢɟ ɦɚɝɧɢɬɨɫɬɪɢɤɰɢɢ ɢ ɦɚɝɧɢɬɨɭɩɪɭɝɭɸ ɷɧɟɪɝɢɸ. Ʉɪɨɦɟ ɬɨɝɨ, ɞɥɹ ɦɚɬɟɪɢɚɥɨɜ ɫ ɛɨɥɶɲɨɣ ɤɨɧɫɬɚɧɬɨɣ ɚɧɢɡɨɬɪɨɩɢɢ, ɩɪɢɜɨɞɹɳɟɣ ɤ ɛɨɥɶɲɢɦ ɡɧɚɱɟɧɢɹɦ ɝɪɚɧɢɱɧɨɣ ɷɧɟɪɝɢɢ, ɷɧɟɪɝɟɬɢɱɟɫɤɢ ɛɨɥɟɟ ɜɵɝɨɞɧɵɦ ɦɨɠɟɬ ɨɤɚɡɚɬɶɫɹ ɨɛɪɚɡɨɜɚɧɢɟ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɦɚɝɧɢɬɧɵɯ ɩɨɥɸɫɨɜ ɜɡɚɦɟɧ ɡɚɦɵɤɚɸɳɢɯ ɞɨɦɟɧɨɜ.
92
ȼ ɬɨɧɤɢɯ ɦɚɝɧɢɬɧɵɯ ɩɥɟɧɤɚɯ ɫɬɪɭɤɬɭɪɚ 180º-ɣ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ ɦɨɠɟɬ ɨɬɥɢɱɚɬɶɫɹ ɨɬ ɪɚɫɫɦɨɬɪɟɧɧɨɣ ɜɵɲɟ. Ⱦɟɥɨ ɜ ɬɨɦ, ɱɬɨ ɬɨɥɳɢɧɚ ɩɥɟɧɤɢ ɦɨɠɟɬ ɛɵɬɶ ɦɟɧɶɲɟ ɬɪɟɛɭɟɦɨɣ ɬɨɥɳɢɧɵ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɷɧɟɪɝɟɬɢɱɟɫɤɢ ɛɨɥɟɟ ɜɵɝɨɞɧɵɦ ɫɬɚɧɨɜɢɬɫɹ ɩɨɜɨɪɨɬ ɜɟɤɬɨɪɨɜ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɧɟ ɜ ɩɥɨɫɤɨɫɬɢ, ɚ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɩɥɨɫɤɨɫɬɢ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ. Ɍɚɤɚɹ ɝɪɚɧɢɰɚ ɧɚɡɵɜɚɟɬɫɹ ɧɟɟɥɟɜɫɤɨɣ (ɪɢɫ. 3.9).
Ɋɢɫ. 3.9. Ⱦɨɦɟɧɧɵɟ ɝɪɚɧɢɰɵ: ɚ – ɛɥɨɯɨɜɫɤɚɹ; ɛ – ɧɟɟɥɟɜɫɤɚɹ
ɋɬɪɭɤɬɭɪɚ 90º-ɯ ɝɪɚɧɢɰ ɧɟɫɤɨɥɶɤɨ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɫɬɪɭɤɬɭɪɵ ɛɥɨɯɨɜɫɤɨɣ 180º-ɣ ɝɪɚɧɢɰɵ. Ɉɞɧɚɤɨ ɜ ɥɸɛɨɦ ɫɥɭɱɚɟ ɨɪɢɟɧɬɚɰɢɹ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ ɜ ɝɪɚɧɢɰɟ ɩɨɞɱɢɧɹɟɬɫɹ ɬɪɟɛɨɜɚɧɢɸ ɦɢɧɢɦɭɦɚ ɫɭɦɦɚɪɧɨɣ ɷɧɟɪɝɢɢ.
ȼɨɩɪɨɫ ɨ ɪɚɡɦɟɪɚɯ ɫɚɦɢɯ ɞɨɦɟɧɨɜ ɪɚɫɫɦɨɬɪɢɦ ɧɚ ɩɪɢɦɟɪɟ ɨɞɧɨɨɫɧɨɝɨ ɮɟɪɪɨɦɚɝɧɟɬɢɤɚ, ɫɬɪɭɤɬɭɪɚ ɤɨɬɨɪɨɝɨ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 3.10. ɉɭɫɬɶ ɮɟɪɪɨɦɚɝɧɢɬɧɨɟ ɬɟɥɨ ɢɦɟɟɬ ɮɨɪɦɭ ɩɪɹɦɨɭɝɨɥɶɧɨɝɨ ɩɚɪɚɥɥɟɥɟɩɢɩɟɞɚ ɫɨ ɫɬɨɪɨɧɚɦɢ lx, ly, lz = L, ɢ
ɩɭɫɬɶ ɨɫɶ z – ɷɬɨ ɧɚɩɪɚɜɥɟɧɢɟ ɥɟɝɤɨɝɨ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ. ȼɧɭɬɪɢ ɬɟɥɚ ɜɟɤɬɨɪɵ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɆS ɧɚɩɪɚɜ-
ɥɟɧɵ ɜɞɨɥɶ «ɥɟɝɤɨɣ» ɨɫɢ (ɞɨɦɟɧɵ I,
III, V, VII), ɚ ɭ ɩɨɜɟɪɯɧɨɫɬɢ, ɜ ɫɢɥɭ ɭɫɥɨɜɢɹ ɦɢɧɢɦɭɦɚ ɦɚɝɧɢɬɨɫɬɚɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ, – ɩɚɪɚɥɥɟɥɶɧɨ ɩɨɜɟɪɯɧɨɫɬɢ ɜ ɡɚɦɵɤɚɸɳɢɯ ɩɪɢɡɦɚɬɢɱɟɫɤɢɯ ɞɨɦɟɧɚɯ (II, IV, VI). ɍɞɟɥɶɧɚɹ ɷɧɟɪɝɢɹ ɚɧɢɡɨɬɪɨɩɢɢ ɜ ɡɚɦɵ-
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ɤɚɸɳɢɯ ɞɨɦɟɧɚɯ: Ȗɚ = K1. Ɉɛɴɟɦ ɤɚɠɞɨɣ ɩɪɢɡɦɚɬɢɱɟɫɤɨɣ ɨɛɥɚɫɬɢ ɫɨɫɬɚɜɥɹɟɬ Vɩɪ = d 2ly /4 (d – ɲɢɪɢɧɚ ɞɨɦɟɧɚ), ɚ ɢɯ ɱɢɫɥɨ ɩɨ ɨɛɟɢɦ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɦ ɫɬɨɪɨɧɚɦ ɬɟɥɚ n = 2lx/d. ɋɭɦɦɚɪɧɵɣ ɨɛɴɟɦ ɩɪɢɡɦɚɬɢɱɟɫɤɢɯ ɞɨɦɟɧɨɜ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ
V = V |
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ɚ ɫɭɦɦɚɪɧɚɹ ɷɧɟɪɝɢɹ ɚɧɢɡɨɬɪɨɩɢɢ ɜɵɪɚɠɟɧɢɟɦ |
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ɍɞɟɥɶɧɚɹ ɷɧɟɪɝɢɹ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ (3.25), ɩɥɨɳɚɞɶ ɤɚɠɞɨɣ ɝɪɚɧɢɰɵ Sɝɪ = ly L, ɚ ɢɯ ɱɢɫɥɨ ɪɚɜɧɨ lx /d. ɋɭɦɦɚɪ-
ɧɭɸ ɷɧɟɪɝɢɢ ɜɫɟɯ ɞɨɦɟɧɧɵɯ ɝɪɚɧɢɰ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ
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ɉɨɥɧɚɹ ɷɧɟɪɝɢɹ ɫɬɪɭɤɬɭɪɵ ɛɭɞɟɬ ɜɵɝɥɹɞɟɬɶ ɬɚɤ: |
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ȺE ·1 4 |
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ɂɡ (3.31) ɜɢɞɧɨ, ɱɬɨ ɲɢɪɢɧɚ ɞɨɦɟɧɨɜ ɡɚɜɢɫɢɬ ɧɟ ɬɨɥɶɤɨ ɨɬ ɩɚɪɚɦɟɬɪɨɜ ɦɚɬɟɪɢɚɥɚ, ɧɨ ɢ ɨɬ ɪɚɡɦɟɪɨɜ ɮɟɪɪɨɦɚɝɧɢɬɧɨɝɨ ɬɟɥɚ (d ~ ~ L1/2). Ɋɚɫɱɟɬɧɚɹ ɲɢɪɢɧɚ ɞɨɦɟɧɨɜ ɭ ɤɨɛɚɥɶɬɚ ɩɪɢ L = 1 ɫɦ ɫɨɫɬɚɜɥɹɟɬ d = 3 Â 10–3 ɫɦ, ɬ. ɟ. ~105 ɚɬɨɦɧɵɯ ɩɥɨɫɤɨɫɬɟɣ, ɜ ɬɨ ɜɪɟɦɹ ɤɚɤ įɝɪ = 10–6…10–7 ɫɦ, ɢɥɢ 10…100 ɚɬɨɦɧɵɯ ɩɥɨɫɤɨɫɬɟɣ.
ɇɟɨɛɯɨɞɢɦɨ ɩɨɦɧɢɬɶ, ɱɬɨ ɩɚɪɚɦɟɬɪɵ ɮɟɪɪɨɦɚɝɧɢɬɧɨɝɨ ɦɚɬɟɪɢɚɥɚ ɆS, Ⱥ, K1, ȜS ɡɚɜɢɫɹɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ, ɱɬɨ ɨɛɭɫɥɨɜɥɢɜɚɟɬ ɬɟɦ-
ɩɟɪɚɬɭɪɧɵɟ ɢɡɦɟɧɟɧɢɹ ɜɫɟɣ ɞɨɦɟɧɧɨɣ ɫɬɪɭɤɬɭɪɵ ɜ ɰɟɥɨɦ. Ɉɞɧɨɞɨɦɟɧɧɵɟ ɱɚɫɬɢɰɵ. ȿɫɥɢ ɭɦɟɧɶɲɚɬɶ ɪɚɡɦɟɪɵ ɮɟɪɪɨɦɚɝ-
ɧɢɬɧɨɝɨ ɬɟɥɚ (ɧɚɩɪɢɦɟɪ, ɩɪɢ ɬɪɚɧɫɮɨɪɦɚɰɢɢ ɟɝɨ ɜ ɩɨɪɨɲɨɤ), ɬɨ ɪɚɡɦɟɪɵ ɱɚɫɬɢɰ ɦɨɝɭɬ ɫɬɚɬɶ ɫɨɢɡɦɟɪɢɦɵɦɢ ɫ ɪɚɜɧɨɜɟɫɧɵɦɢ ɪɚɡɦɟɪɚɦɢ
94
ɞɨɦɟɧɨɜ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɚɥɢɱɢɟ ɞɨɦɟɧɧɵɯ ɝɪɚɧɢɰ ɜ ɱɚɫɬɢɰɟ ɫɬɚɧɨɜɢɬɫɹ ɷɧɟɪɝɟɬɢɱɟɫɤɢ ɧɟɜɵɝɨɞɧɵɦ, ɢ ɱɚɫɬɢɰɚ ɦɨɠɟɬ ɩɪɟɜɪɚɬɢɬɶɫɹ ɜ ɨɞɢɧ ɞɨɦɟɧ, ɡɚɧɢɦɚɸɳɢɣ ɜɟɫɶ ɟɟ ɨɛɴɟɦ. ɉɨɧɹɬɧɨ, ɱɬɨ ɨɞɧɨɞɨɦɟɧɧɨɫɬɶ ɱɚɫɬɢɰɵ ɩɪɟɞɩɨɥɚɝɚɟɬ ɧɚɥɢɱɢɟ ɦɚɝɧɢɬɨɫɬɚɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ «ɦɚɝɧɢɬɧɵɯ ɡɚɪɹɞɨɜ», ɤɨɬɨɪɵɟ ɜɨɡɧɢɤɚɸɬ ɧɚ ɟɟ ɩɨɜɟɪɯɧɨɫɬɢ. Ɋɚɡɦɟɪ ɱɚɫɬɢɰɵ, ɩɪɢ ɤɨɬɨɪɨɦ ɨɧɚ ɫɬɚɧɨɜɢɬɫɹ ɨɞɧɨɞɨɦɟɧɧɨɣ, ɧɚɡɵɜɚɟɬɫɹ ɤɪɢɬɢɱɟɫɤɢɦ ɪɚɡɦɟɪɨɦ. Ɉɧ ɡɚɜɢɫɢɬ ɨɬ ɩɚɪɚɦɟɬɪɨɜ ɮɟɪɪɨɦɚɝɧɢɬɧɨɝɨ ɦɚɬɟɪɢɚɥɚ ɢ ɮɨɪɦɵ ɱɚɫɬɢɰɵ. Ⱦɥɹ ɪɚɡɧɵɯ ɦɚɬɟɪɢɚɥɨɜ ɤɪɢɬɢɱɟɫɤɢɣ ɪɚɡɦɟɪ – ɪɚɡɧɵɣ. Ⱦɥɹ ɨɰɟɧɤɢ ɜɥɢɹɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɦɚɬɟɪɢɚɥɚ ɧɚ ɡɧɚɱɟɧɢɟ ɤɪɢɬɢɱɟɫɤɨɝɨ ɪɚɡɦɟɪɚ ɪɚɫɫɦɨɬɪɢɦ ɱɚɫɬɢɰɭ ɫɮɟɪɢɱɟɫɤɨɣ ɮɨɪɦɵ ɞɢɚɦɟɬɪɨɦ D, ɤɨɬɨɪɚɹ ɧɚɯɨɞɢɬɫɹ ɧɚ ɝɪɚɧɢ ɩɟɪɟɯɨɞɚ ɤ ɨɞɧɨɞɨ- ɦɟɧɧɨɦɭɫɨɫɬɨɹɧɢɸɢɫɨɞɟɪɠɢɬɬɨɥɶɤɨɞɜɚ180º-ɣɞɨɦɟɧɚ(ɪɢɫ. 3.11, ɚ).
ɚ ɛ Ɋɢɫ. 3.11. ɋɯɟɦɚ ɞɨɦɟɧɧɨɣ ɫɬɪɭɤɬɭɪɵ ɦɚɥɵɯ ɱɚɫɬɢɰ:
ɚ – ɞɜɭɞɨɦɟɧɧɚɹ ɱɚɫɬɢɰɚ; ɛ – ɨɞɧɨɞɨɦɟɧɧɚɹ ɱɚɫɬɢɰɚ
ɗɧɟɪɝɢɹ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ ȿɝɪ ɱɚɫɬɢɰɵ (ɪɢɫ. 3.11, ɚ) ɨɩɪɟɞɟɥɹɟɬɫɹ ɟɟ ɩɥɨɳɚɞɶɸ ɢ ɩɨ ɦɟɪɟ ɭɦɟɧɶɲɟɧɢɹ ɪɚɡɦɟɪɚ ɱɚɫɬɢɰɵ ɭɦɟɧɶɲɚɟɬɫɹ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ D2. Ɇɚɝɧɢɬɨɫɬɚɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɱɚɫɬɢɰɵ (ɪɢɫ. 3.11, ɛ) ɡɚɜɢɫɢɬ ɨɬ ɟɟ ɨɛɴɟɦɚ ɢ ɩɪɢ ɭɦɟɧɶɲɟɧɢɢ ɪɚɡɦɟɪɚ ɭɦɟɧɶɲɚɟɬɫɹ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ D3. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ȿd ɭɦɟɧɶɲɚɟɬɫɹ ɫɢɥɶɧɟɟ, ɱɟɦ ȿɝɪ, ɢ ɩɪɢ ɧɟɤɨɬɨɪɨɦ ɤɪɢɬɢɱɟɫɤɨɦ ɪɚɡɦɟɪɟ Dɤɪ ɷɧɟɪɝɟ-
ɬɢɱɟɫɤɢ ɛɨɥɟɟ ɜɵɝɨɞɧɵɦ ɫɬɚɧɨɜɢɬɫɹ ɨɞɧɨɞɨɦɟɧɧɨɟ ɫɨɫɬɨɹɧɢɟ. Ɇɨɠɧɨ ɩɪɟɞɩɨɥɨɠɢɬɶ, ɱɬɨ ɤɪɢɬɢɱɟɫɤɢɣ ɪɚɡɦɟɪ ɱɚɫɬɢɰɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɜɟɧɫɬɜɨɦ ɷɬɢɯ ɞɜɭɯ ɷɧɟɪɝɢɣ:
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k4K SD2 |
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ȿɝɪ = ȖɝɪS § |
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1 § 1 |
2 |
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1 § 1 1 |
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· 4 SD3 |
P0SM S2D3 |
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2 |
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P0NM S |
¸V |
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P0NM S |
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ɝɞɟ ɤɨɷɮɮɢɰɢɟɧɬ 1/2 ɩɟɪɟɞ ɫɤɨɛɤɨɣ ɝɨɜɨɪɢɬ ɨ ɬɨɦ, ɱɬɨ ɦɚɝɧɢɬɨɫɬɚɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɱɚɫɬɢɰɵ ɧɚ ɪɢɫ. 3.11, ɚ ɜ ɞɜɚ ɪɚɡɚ ɦɟɧɶɲɟ, ɱɟɦ ɱɚɫɬɢɰɵ ɧɚɪɢɫ. 3.11, ɛ; ɪɚɡɦɚɝɧɢɱɢɜɚɸɳɢɣɮɚɤɬɨɪɫɮɟɪɵ(ɲɚɪɚ) N = 1/3.
ɉɪɢɪɚɜɧɹɜ (3.32) ɢ (3.33), ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɤɪɢɬɢɱɟ-
ɫɤɨɝɨ ɪɚɡɦɟɪɚ |
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D |
ɤɪ |
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Ɉɧɨ ɹɜɥɹɟɬɫɹ ɩɪɢɛɥɢɠɟɧɧɵɦ, ɬɚɤ ɤɚɤ ɛɵɥɨ ɩɨɥɭɱɟɧɨ ɞɥɹ ɫɥɭɱɚɹ ɨɞɧɨɨɫɧɨɝɨ ɦɚɬɟɪɢɚɥɚ ɫɮɟɪɢɱɟɫɤɨɣ ɮɨɪɦɵ. Ɉɞɧɚɤɨ ɪɚɫɱɟɬɵ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɞɚɧɧɨɝɨ ɜɵɪɚɠɟɧɢɹ ɞɚɸɬ ɤɨɪɪɟɤɬɧɵɣ ɩɨ ɩɨɪɹɞɤɭ ɜɟɥɢɱɢɧɵ ɪɟɡɭɥɶɬɚɬ: ɞɥɹ ɠɟɥɟɡɚ Dɤɪ § 0,05 ɦɤɦ, ɞɥɹ ɫɨɟɞɢɧɟɧɢɹ
Mn–Bi Dɤɪ § 8 ɦɤɦ, ɞɥɹ ɛɚɪɢɟɜɨɝɨ ɮɟɪɪɢɬɚ Dɤɪ § 1,5 ɦɤɦ. ɇɟɨɛɯɨɞɢ-
ɦɨɫɬɶ ɨɩɪɟɞɟɥɟɧɢɹ ɤɪɢɬɢɱɟɫɤɢɯ ɪɚɡɦɟɪɨɜ ɱɚɫɬɢɰ ɮɟɪɪɨɦɚɝɧɟɬɢɤɨɜ ɫɜɹɡɚɧɚ ɫ ɬɟɯɧɨɥɨɝɢɟɣ ɩɨɥɭɱɟɧɢɹ ɜɵɫɨɤɨɤɨɷɪɰɢɬɢɜɧɵɯ ɦɚɬɟɪɢɚɥɨɜ ɞɥɹ ɩɨɫɬɨɹɧɧɵɯ ɦɚɝɧɢɬɨɜ.
ɍɦɟɧɶɲɟɧɢɟ ɪɚɡɦɟɪɨɜ ɮɟɪɪɨɦɚɝɧɢɬɧɵɯ ɱɚɫɬɢɰ ɞɨ ɡɧɚɱɟɧɢɣ, ɦɧɨɝɨ ɦɟɧɶɲɢɯ ɤɪɢɬɢɱɟɫɤɨɝɨ, ɦɨɠɟɬ ɩɪɢɜɟɫɬɢ ɤ ɩɨɥɧɨɦɭ ɢɫɱɟɡɧɨɜɟɧɢɸ ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨɣ ɭɩɨɪɹɞɨɱɟɧɧɨɫɬɢ ɫɩɢɧɨɜɵɯ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ ɩɪɢ ɜɫɟɯ ɬɟɦɩɟɪɚɬɭɪɚɯ ɢ ɩɟɪɟɯɨɞɭ ɱɚɫɬɢɰɵ ɜ ɫɭɩɟɪɩɚɪɚɦɚɝɧɢɬɧɨɟ ɫɨɫɬɨɹɧɢɟ. ȿɝɨ ɨɬɥɢɱɢɟ ɨɬ ɩɚɪɚɦɚɝɧɢɬɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɭ ɩɚɪɚɦɚɝɧɟɬɢɤɨɜ ɧɚɛɥɸɞɚɟɬɫɹ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɚɹ ɮɥɭɤɬɭɚɰɢɹ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ ɦɨɥɟɤɭɥ, ɚ ɜ ɫɥɭɱɚɟ ɫɜɟɪɯɦɚɥɨɣ ɱɚɫɬɢɰɵ – ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ ɜɫɟɣ ɱɚɫɬɢɰɵ. Ɋɚɫɱɟɬɵ (ɫ ɭɱɟɬɨɦ ɤɜɚɧɬɨɜɨ-ɦɟɯɚɧɢɱɟɫɤɢɯ ɷɮɮɟɤɬɨɜ ɜ ɫɜɟɪɯɦɚɥɵɯ ɱɚɫɬɢɰɚɯ) ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɩɟɪɟɯɨɞ ɜ ɫɭɩɟɪɩɚɪɚɦɚɝɧɢɬɧɨɟ ɫɨɫɬɨɹɧɢɟ ɩɪɨɢɫɯɨɞɢɬ ɩɪɢ ɪɚɡɦɟɪɟ ɱɚɫɬɢɰɵ ɩɨɪɹɞɤɚ 1 ɧɦ.
Ɍɨɧɤɢɟ ɦɚɝɧɢɬɧɵɟ ɩɥɟɧɤɢ
Ɍɨɧɤɢɟ ɦɚɝɧɢɬɧɵɟ ɩɥɟɧɤɢ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɢɯ ɫɨɫɬɚɜɚ ɢ ɝɟɨɦɟɬɪɢɢ ɨɫɚɠɞɚɸɬɫɹ ɜɚɤɭɭɦɧɵɦɢ ɢɥɢ ɯɢɦɢɱɟɫɤɢɦɢ ɦɟɬɨɞɚɦɢ ɧɚ ɩɨɞɥɨɠɤɢ ɢɡ ɪɚɡɥɢɱɧɵɯ ɦɚɬɟɪɢɚɥɨɜ ɢ ɢɦɟɸɬ ɬɨɥɳɢɧɭ ɨɬ ɦɨɧɨɚɬɨɦɧɨɝɨ ɫɥɨɹ ɞɨ ɧɟɫɤɨɥɶɤɢɯ ɦɢɤɪɨɦɟɬɪɨɜ. ɉɨɫɤɨɥɶɤɭ ɝɟɨɦɟɬɪɢɱɟɫɤɢɟ ɪɚɡɦɟɪɵ ɩɥɟɧɤɢ ɜ ɟɟ ɩɥɨɫɤɨɫɬɢ, ɤɚɤ ɩɪɚɜɢɥɨ, ɧɚɦɧɨɝɨ ɩɪɟɜɵɲɚɸɬ ɬɨɥɳɢ-
96
ɧɭ, ɬɨ ɩɥɟɧɤɭ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɞɜɭɦɟɪɧɭɸ ɫɢɫɬɟɦɭ. ȼ ɫɜɹɡɢ ɫ ɷɬɢɦ ɨɫɧɨɜɧɵɟ ɦɚɝɧɢɬɧɵɟ ɩɚɪɚɦɟɬɪɵ ɩɥɟɧɤɢ (ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶ, ɬɟɦɩɟɪɚɬɭɪɚ Ʉɸɪɢ, ɚɧɢɡɨɬɪɨɩɢɹ ɢ ɦɚɝɧɢɬɨɫɬɪɢɤɰɢɹ) ɦɨɝɭɬ ɫɢɥɶɧɨ ɨɬɥɢɱɚɬɶɫɹ ɨɬ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɩɚɪɚɦɟɬɪɨɜ ɨɛɴɟɦɧɨɝɨ ɦɚɬɟɪɢɚɥɚ. Ɂɧɚɱɢɬɟɥɶɧɭɸ ɪɨɥɶ ɢɝɪɚɸɬ ɩɨɜɟɪɯɧɨɫɬɧɵɟ ɚɬɨɦɧɵɟ ɫɥɨɢ ɩɥɟɧɤɢ, ɚɬɨɦɵ ɤɨɬɨɪɵɯ ɜɛɥɢɡɢ ɫɜɨɛɨɞɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɢ ɩɨɜɟɪɯɧɨɫɬɢ, ɩɪɢɦɵɤɚɸɳɟɣ ɤ ɩɨɞɥɨɠɤɟ, ɧɚɯɨɞɹɬɫɹ ɜ ɨɤɪɭɠɟɧɢɢ, ɨɬɥɢɱɧɨɦ ɨɬ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɨɤɪɭɠɟɧɢɹ ɜ ɨɛɴɟɦɟ. ɗɬɨ ɩɪɢɜɨɞɢɬ ɤ ɬɨɦɭ, ɱɬɨ ɜ ɩɨɜɟɪɯɧɨɫɬɧɵɯ ɫɥɨɹɯ ɢɡ-ɡɚ ɭɦɟɧɶɲɟɧɢɹ ɦɚɝɧɢɬɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɚɬɨɦɨɜ ɫɭɦɦɚɪɧɵɟ ɦɚɝɧɢɬɧɵɟ ɦɨɦɟɧɬɵ, ɚ ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶ ɭɦɟɧɶɲɚɸɬɫɹ. ȼ ɩɥɟɧɤɚɯ ɬɨɥɳɢɧɨɣ ɞɟɫɹɬɤɢ ɧɚɧɨɦɟɬɪɨɜ ɜɥɢɹɧɢɟ ɫɜɨɣɫɬɜ ɩɨɜɟɪɯɧɨɫɬɧɵɯ ɚɬɨɦɧɵɯ ɫɥɨɟɜ ɧɚ ɦɚɝɧɢɬɧɵɟ ɫɜɨɣɫɬɜɚ ɜɫɟɣ ɩɥɟɧɤɢ ɦɨɠɟɬ ɛɵɬɶ ɨɩɪɟɞɟɥɹɸɳɢɦ. ɉɨ ɦɟɪɟ ɭɜɟɥɢɱɟɧɢɹ ɬɨɥɳɢɧɵ ɩɥɟɧɤɢ ɟɟ ɫɜɨɣɫɬɜɚ ɩɪɢɛɥɢɠɚɸɬɫɹ ɤ ɫɜɨɣɫɬɜɚɦ ɨɛɴɟɦɧɨɝɨ ɦɚɬɟɪɢɚɥɚ.
Ɉɛɪɚɡɨɜɚɧɢɟ ɫɩɟɰɢɮɢɱɟɫɤɢɯ ɞɨɦɟɧɧɵɯ ɫɬɪɭɤɬɭɪ ɩɪɨɢɫɯɨɞɢɬ, ɜ ɨɫɧɨɜɧɨɦ, ɜ ɩɥɟɧɤɚɯ ɧɚɧɨɦɟɬɪɨɜɨɣ ɬɨɥɳɢɧɵ. ɏɚɪɚɤɬɟɪ ɞɨɦɟɧɨɜ ɢ ɩɟɪɟɯɨɞɧɵɯ ɨɛɥɚɫɬɟɣ ɦɟɠɞɭ ɧɢɦɢ ɡɚɜɢɫɢɬ ɨɬ ɬɨɥɳɢɧɵ ɩɥɟɧɤɢ, ɟɟ ɯɢɦɢɱɟɫɤɨɝɨ ɫɨɫɬɚɜɚ, ɨɩɪɟɞɟɥɹɸɳɟɝɨ ɦɚɝɧɢɬɧɵɟ ɩɚɪɚɦɟɬɪɵ, ɢ ɬɟɯɧɨɥɨɝɢɢ ɢɡɝɨɬɨɜɥɟɧɢɹ. ɗɬɨ ɨɛɴɹɫɧɹɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɹɦɢ ɦɟɠɞɭ ɨɬɞɟɥɶɧɵɦɢ ɜɢɞɚɦɢ ɷɧɟɪɝɢɢ ɜ ɬɨɧɤɨɣ ɦɚɝɧɢɬɧɨɣ ɩɥɟɧɤɟ ɢ ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ – ɦɟɠɞɭ ɦɚɝɧɢɬɨɫɬɚɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɟɣ ȿd ɢ ɷɧɟɪɝɢɟɣ ɦɚɝ-
ɧɢɬɧɨɣ ɚɧɢɡɨɬɪɨɩɢɢ ȿɚ. ȼ ɨɱɟɧɶ ɬɨɧɤɢɯ ɩɥɟɧɤɚɯ ɤɨɷɮɮɢɰɢɟɧɬɵ ɪɚɡ-
ɦɚɝɧɢɱɢɜɚɧɢɹ ɜ ɩɥɨɫɤɨɫɬɢ ɩɥɟɧɤɢ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɟ, ɱɟɦ ɜ ɧɚɩɪɚɜɥɟɧɢɢ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɦ ɟɟ ɩɨɜɟɪɯɧɨɫɬɢ. Ɇɢɧɢɦɭɦɭ ɦɚɝɧɢɬɨɫɬɚɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɪɚɫɩɨɥɨɠɟɧɢɟ ɜɟɤɬɨɪɚ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɜ ɩɥɨɫɤɨɫɬɢ ɩɥɟɧɤɢ. Ⱦɥɹ ɩɥɟɧɨɤ ɬɨɥɳɢɧɨɣ ɦɟɧɟɟ 100 ɧɦ ɪɚɡɦɚɝɧɢɱɢɜɚɸɳɟɟ ɩɨɥɟ ɜ ɩɥɨɫɤɨɫɬɢ ɩɥɟɧɤɢ ɩɪɚɤɬɢɱɟɫɤɢ ɪɚɜɧɨ ɧɭɥɸ, ɢ ɩɨɬɨɦɭ ɬɚɤɢɦ ɩɥɟɧɤɚɦ ɩɪɢɫɭɳɚ ɨɞɧɨɞɨɦɟɧɧɚɹ ɫɬɪɭɤɬɭɪɚ (ɪɢɫ. 3.12, ɚ).
ɚ ɛ ɜ Ɋɢɫ. 3.12. Ⱦɨɦɟɧɧɵɟ ɫɬɪɭɤɬɭɪɵ ɜ ɬɨɧɤɢɯ ɦɚɝɧɢɬɧɵɯ ɩɥɟɧɤɚɯ: ɚ, ɛ – ɨɞɧɨɞɨɦɟɧɧɵɟ ɩɥɟɧɤɢ; ɜ – ɦɧɨɝɨɞɨɦɟɧɧɚɹ ɩɥɟɧɤɚ
97
Ɇɚɝɧɢɬɧɚɹ ɚɧɢɡɨɬɪɨɩɢɹ ɜ ɩɥɟɧɤɚɯ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɪɢɫɬɚɥɥɨɝɪɚɮɢɱɟɫɤɨɣ ɦɚɝɧɢɬɧɨɣ ɚɧɢɡɨɬɪɨɩɢɟɣ ɢ ɧɚɜɟɞɟɧɧɨɣ (ɢɧɞɭɰɢɪɨɜɚɧɧɨɣ) ɚɧɢɡɨɬɪɨɩɢɟɣ, ɤɨɬɨɪɚɹ ɫɨɡɞɚɟɬɫɹ ɢɫɤɭɫɫɬɜɟɧɧɨ ɜ ɩɪɨɰɟɫɫɟ ɟɟ ɢɡɝɨɬɨɜɥɟɧɢɹ (ɧɚɩɪɢɦɟɪ, ɩɪɢɥɨɠɟɧɢɟɦ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ), ɱɬɨ ɭɫɢɥɢɜɚɟɬ ɬɟɧɞɟɧɰɢɸ ɤ ɨɪɢɟɧɬɚɰɢɢ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɜ ɩɥɨɫɤɨɫɬɢ ɩɥɟɧɤɢ. ȼ ɪɹɞɟ ɫɥɭɱɚɟɜ ɜɨɡɧɢɤɚɟɬ ɦɧɨɝɨɞɨɦɟɧɧɚɹ ɫɬɪɭɤɬɭɪɚ (ɬɚɤ ɧɚɡɵɜɚɟɦɵɟ ɩɨɥɨɫɨɜɵɟ ɞɨɦɟɧɵ). ɉɪɢ ɷɬɨɦ, ɟɫɥɢ ɬɨɥɳɢɧɚ ɩɥɟɧɤɢ ɫɨɢɡɦɟɪɢɦɚ ɫ ɬɨɥɳɢɧɨɣ ɛɥɨɯɨɜɫɤɨɣ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ ɦɚɫɫɢɜɧɨɝɨ ɨɛɪɚɡɰɚ (3.24), ɬɨ ɦɟɠɞɭ ɞɨɦɟɧɚɦɢ ɜɨɡɧɢɤɚɟɬ ɧɟɟɥɟɜɫɤɚɹ ɞɨɦɟɧɧɚɹ ɝɪɚɧɢɰɚ (ɫɦ. ɪɢɫ. 3.9, ɛ).
ɉɪɢ ɧɚɥɢɱɢɢ ɜ ɩɥɟɧɤɟ ɡɧɚɱɢɬɟɥɶɧɵɯ ɦɟɯɚɧɢɱɟɫɤɢɯ ɧɚɩɪɹɠɟɧɢɣ, ɫɜɹɡɚɧɧɵɯ, ɧɚɩɪɢɦɟɪ, ɫ ɪɚɡɥɢɱɢɟɦ ɤɪɢɫɬɚɥɥɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɩɥɟɧɤɢ ɢ ɩɨɞɥɨɠɤɢ, ɜ ɩɥɟɧɤɟ ɦɨɠɟɬ ɜɨɡɧɢɤɧɭɬɶ ɨɞɧɨɨɫɧɚɹ ɚɧɢɡɨɬɪɨɩɢɹ, ɧɚɩɪɚɜɥɟɧɧɚɹ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɩɥɨɫɤɨɫɬɢ ɩɥɟɧɤɢ. ȼ ɦɚɬɟɪɢɚɥɚɯ ɫ ɛɨɥɶɲɨɣ ɤɪɢɫɬɚɥɥɨɝɪɚɮɢɱɟɫɤɨɣ ɦɚɝɧɢɬɧɨɣ ɚɧɢɡɨɬɪɨɩɢɟɣ ɨɞɧɨɨɫɧɚɹ ɚɧɢɡɨɬɪɨɩɢɹ ɫɩɨɫɨɛɧɚ ɢɡɦɟɧɢɬɶ ɧɚɩɪɚɜɥɟɧɢɟ ɜɟɤɬɨɪɚ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɫ ɩɚɪɚɥɥɟɥɶɧɨɝɨ ɩɥɨɫɤɨɫɬɢ ɩɥɟɧɤɢ ɧɚ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɟ (ɪɢɫ. 3.12, ɛ).
Ⱦɥɹ ɨɰɟɧɤɢ ɫɨɨɬɧɨɲɟɧɢɹ ɦɟɠɞɭ ɷɧɟɪɝɢɹɦɢ ȿd ɢ ȿɚ ɜɜɨɞɹɬ ɩɚɪɚɦɟɬɪ, ɤɨɬɨɪɵɣ ɧɚɡɵɜɚɟɬɫɹ ɮɚɤɬɨɪɨɦ ɤɚɱɟɫɬɜɚ q:
q 2Kɢ P0M S2 , |
(3.35) |
ɝɞɟ Kɢ – ɤɨɧɫɬɚɧɬɚ ɨɞɧɨɨɫɧɨɣ ɚɧɢɡɨɬɪɨɩɢɢ.
ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɡɧɚɱɟɧɢɹ q ɞɥɹ ɩɥɟɧɨɤ, ɢɦɟɸɳɢɯ ɪɚɡɧɭɸ ɬɨɥɳɢɧɭ, ɜɨɡɦɨɠɧɨ ɨɛɪɚɡɨɜɚɧɢɟ ɪɚɡɧɨɨɛɪɚɡɧɵɯ ɞɨɦɟɧɧɵɯ ɫɬɪɭɤɬɭɪ: ɧɚɩɪɢɦɟɪ, ɞɥɹ ɩɥɟɧɨɤ ɫ q > 1 ɜɨɡɦɨɠɧɨ ɨɛɪɚɡɨɜɚɧɢɟ ɫɬɪɭɤɬɭɪɵ, ɩɨɤɚɡɚɧɧɨɣ ɧɚ ɪɢɫ. 3.12, ɜ.
3.7. ɐɢɥɢɧɞɪɢɱɟɫɤɢɟ ɦɚɝɧɢɬɧɵɟ ɞɨɦɟɧɵ
ɐɢɥɢɧɞɪɢɱɟɫɤɢɟ ɦɚɝɧɢɬɧɵɟ ɞɨɦɟɧɵ (ɐɆȾ) ɜɨɡɧɢɤɚɸɬ ɜ ɬɨɧɤɢɯ ɩɥɟɧɤɚɯ ɢɥɢ ɩɥɚɫɬɢɧɚɯ ɧɟɤɨɬɨɪɵɯ ɦɚɝɧɢɬɧɵɯ ɦɚɬɟɪɢɚɥɨɜ ɜ ɬɨɦ ɫɥɭɱɚɟ, ɟɫɥɢ ɦɚɬɟɪɢɚɥ ɨɛɥɚɞɚɟɬ ɞɨɫɬɚɬɨɱɧɨ ɫɢɥɶɧɨɣ ɨɞɧɨɨɫɧɨɣ ɚɧɢɡɨɬɪɨɩɢɟɣ ɜ ɧɚɩɪɚɜɥɟɧɢɢ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɦ ɩɥɨɫɤɨɫɬɢ ɩɥɟɧɤɢ ɩɪɢ ɩɪɢɥɨɠɟɧɢɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɝɨ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ȼ ɨɬɫɭɬɫɬɜɢɟ ɜɧɟɲɧɟɝɨ ɩɨɥɹ ɜ ɬɚɤɢɯ ɦɚɬɟɪɢɚɥɚɯ ɫɭɳɟɫɬɜɭɟɬ ɥɚɛɢɪɢɧɬ-
98
ɧɚɹ ɞɨɦɟɧɧɚɹ ɫɬɪɭɤɬɭɪɚ, ɜ ɤɨɬɨɪɨɣ ɞɨɦɟɧɧɵɟ ɝɪɚɧɢɰɵ ɧɟ ɩɥɨɫɤɢɟ, ɚ ɹɜɥɹɸɬɫɹ ɫɥɨɠɧɵɦɢ ɰɢɥɢɧɞɪɢɱɟɫɤɢɦɢ ɩɨɜɟɪɯɧɨɫɬɹɦɢ ɫ ɨɛɪɚɡɭɸɳɟɣ, ɩɚɪɚɥɥɟɥɶɧɨɣ «ɥɟɝɤɨɣ» ɨɫɢ. ɇɚ ɪɢɫ. 3.13, ɚ ɩɨɤɚɡɚɧɚ ɥɚɛɢɪɢɧɬɧɚɹ ɞɨɦɟɧɧɚɹ ɫɬɪɭɤɬɭɪɚ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɦɨɧɨɤɪɢɫɬɚɥɥɢɱɟɫɤɨɣ ɩɥɟɧɤɢ (6 ɦɤɦ) ɮɟɪɪɨɝɪɚɧɚɬɚ.
ɚ |
ɛ |
ɜ |
ɝ |
Ɋɢɫ. 3.13. ɂɡɦɟɧɟɧɢɟ ɜɢɞɚ ɞɨɦɟɧɧɨɣ ɫɬɪɭɤɬɭɪɵ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ: ɚ – ɇ = 0; ɛ – ɇ1 > 0; ɜ – ɇ2 > ɇ1; ɝ – ɰɢɥɢɧɞɪɢɱɟɫɤɢɟ ɞɨɦɟɧɵ
ɋɜɟɬɥɵɟ ɢ ɬɟɦɧɵɟ ɨɛɥɚɫɬɢ – ɞɨɦɟɧɵ ɫ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɦɢ ɧɚɩɪɚɜɥɟɧɢɹɦɢ ɜɟɤɬɨɪɚ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ. Ɉɛɴɟɦɵ ɬɚɤɢɯ ɞɨɦɟɧɨɜ ɨɞɢɧɚɤɨɜɵ. ȼɧɟɲɧɟɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ (ɩɨɥɟ ɫɦɟɳɟɧɢɹ), ɧɚɩɪɚɜɥɟɧɧɨɟ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɩɥɨɫɤɨɫɬɢ ɩɥɟɧɤɢ, ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɨɛɴɟɦɚ ɞɨɦɟɧɨɜ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ, ɫɨɜɩɚɞɚɸɳɢɦ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɜɧɟɲɧɟɝɨ ɩɨɥɹ (ɬɟɦɧɵɟ ɨɛɥɚɫɬɢ ɧɚ ɪɢɫ. 3.13, ɛ). ɍɜɟɥɢɱɟɧɢɟ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɩɨɥɹ ɫɩɨɫɨɛɫɬɜɭɟɬ ɞɚɥɶɧɟɣɲɟɦɭ ɪɨɫɬɭ ɞɨɦɟɧɨɜ ɢ ɪɚɡɪɵɜɭ ɧɟɤɨɬɨɪɵɯ ɢɡ ɧɢɯ (ɪɢɫ. 3.13, ɜ). ɉɪɢ ɨɩɪɟɞɟɥɟɧɧɨɦ ɡɧɚɱɟɧɢɢ ɩɨɥɹ ɜɨɡɧɢɤɚɸɬ ɐɆȾ, ɩɪɟɞɫɬɚɜɥɹɸɳɢɟ ɫɨɛɨɣ ɰɢɥɢɧɞɪɵ, ɩɪɨɧɢɡɵɜɚɸɳɢɟ ɩɥɟɧɤɭ ɩɨ ɟɟ ɬɨɥɳɢɧɟ (ɪɢɫ. 3.13, ɝ). ɉɪɢ ɭɜɟɥɢɱɟɧɢɢ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɩɨɥɹ ɜɵɲɟ ɧɟɤɨɬɨɪɨɝɨ ɤɪɢɬɢɱɟɫɤɨɝɨ ɡɧɚɱɟɧɢɹ ɜɫɹ ɩɥɟɧɤɚ ɫɬɚɧɨɜɢɬɫɹ ɨɞɧɨɪɨɞɧɨ ɧɚɦɚɝɧɢɱɟɧɧɨɣ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɜɧɟɲɧɟɝɨ ɩɨɥɹ (ɧɚ ɪɢɫɭɧɤɟ ɛɭɞɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɫɩɥɨɲɧɨɟ ɬɟɦɧɨɟ ɩɨɥɟ).
ɇɚ ɪɢɫ. 3.14 ɫɯɟɦɚɬɢɱɟɫɤɢ ɩɨɤɚɡɚɧɨ ɫɬɪɨɟɧɢɟ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɞɨɦɟɧɚ ɜ ɩɥɟɧɤɟ ɬɨɥɳɢɧɨɣ h.
ɉɥɸɫɵ ɢ ɦɢɧɭɫɵ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɩɥɟɧɤɢ ɨɡɧɚɱɚɸɬ ɦɚɝɧɢɬɧɵɟ ɡɚɪɹɞɵ (ɩɨɥɸɫɚ). Ɋɚɫɫɦɨɬɪɢɦ ɭɫɥɨɜɢɹ ɫɬɚɛɢɥɶɧɨɫɬɢ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɞɨɦɟɧɚ ɪɚɞɢɭɫɚ r ɜ ɛɟɫɤɨɧɟɱɧɨɣ ɩɥɟɧɤɟ ɬɨɥɳɢɧɨɣ h ɜɨ ɜɧɟɲɧɟɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ, ɧɚɩɪɚɜɥɟɧɧɨɦ ɚɧɬɢɩɚɪɚɥɥɟɥɶɧɨ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɞɨɦɟɧɚ. ɍɫɬɨɣɱɢɜɨɟ ɫɨɫɬɨɹɧɢɟ ɞɨɦɟɧɚ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɦɢɧɢɦɚɥɶɧɨɦɭ ɡɧɚɱɟɧɢɸ ɟɝɨ ɩɨɥɧɨɣ ɷɧɟɪɝɢɢ:
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Ɍɨɥɶɤɨ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɋɉɛȽɗɌɍ "ɅɗɌɂ" ɢɦ. ȼ.ɂ. ɍɥɶɹɧɨɜɚ (Ʌɟɧɢɧɚ)
ȿ = ȿɦ + ȿɝɪ + ȿd, |
(3.36) |
ɝɞɟ ȿɦ – ɦɚɝɧɢɬɧɚɹ ɷɧɟɪɝɢɹ (ɷɧɟɪɝɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɫ ɜɧɟɲɧɢɦ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ); ȿɝɪ – ɷɧɟɪɝɢɹ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ; ȿd – ɦɚɝɧɢɬɨɫɬɚɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ (ɷɧɟɪɝɢɹ ɪɚɡɦɚɝɧɢɱɢɜɚɧɢɹ).
Ɋɢɫ. 3.14. ɋɬɪɨɟɧɢɟ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɞɨɦɟɧɚ
Ɇɚɝɧɢɬɧɚɹ ɷɧɟɪɝɢɹ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɨɛɴɟɦɭ ɞɨɦɟɧɚ ɢ ɞɥɹ ɫɜɨɟɣ ɦɢɧɢɦɢɡɚɰɢɢ ɫɬɪɟɦɢɬɫɹ ɫɠɚɬɶ ɞɨɦɟɧ (ɭɦɟɧɶɲɢɬɶ ɟɝɨ ɪɚɞɢɭɫ):
ȿ |
= 2ȝ ɇ |
Ɇ |
ʌr2h. |
(3.37) |
ɦ |
0 ɜɧ |
S |
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ɗɧɟɪɝɢɹ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɟɟ ɩɥɨɳɚɞɢ ɢ, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɫɬɪɟɦɢɬɫɹ ɭɦɟɧɶɲɢɬɶ ɪɚɞɢɭɫ ɞɨɦɟɧɚ:
ȿɝɪ = 2ʌrhȖɝɪ. |
(3.38) |
Ɇɚɝɧɢɬɨɫɬɚɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɫɬɪɟɦɢɬɫɹ ɪɚɫɬɹɧɭɬɶ ɞɨɦɟɧ ɢ, ɜ ɤɨɧɟɱɧɨɦ ɫɱɟɬɟ, ɩɟɪɟɜɟɫɬɢ ɩɥɟɧɤɭ ɜ ɫɨɫɬɨɹɧɢɟ ɫ ɥɚɛɢɪɢɧɬɧɨɣ ɫɬɪɭɤɬɭɪɨɣ, ɩɪɢ ɤɨɬɨɪɨɣ ɷɧɟɪɝɢɹ ɪɚɡɦɚɝɧɢɱɢɜɚɧɢɹ ɦɢɧɢɦɚɥɶɧɚ. Ɉɧɚ ɫɥɨɠɧɵɦ ɨɛɪɚɡɨɦ ɡɚɜɢɫɢɬ ɨɬ ɆS, ɪɚɞɢɭɫɚ ɞɨɦɟɧɚ, ɬɨɥɳɢɧɵ
ɩɥɟɧɤɢ, ɩɨɫɤɨɥɶɤɭ ɢɦɟɧɧɨ ɨɧɢ ɨɩɪɟɞɟɥɹɸɬ ɤɨɷɮɮɢɰɢɟɧɬɵ ɪɚɡɦɚɝɧɢɱɢɜɚɧɢɹ, ɚ ɡɧɚɱɢɬ, ɢ ɷɧɟɪɝɢɸ.
Ɇɢɧɢɦɭɦ ɫɭɦɦɚɪɧɨɣ ɷɧɟɪɝɢɢ ɐɆȾ (3.36), ɢɥɢ ɫɭɦɦɚɪɧɚɹ «ɫɢɥɚ», ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɞɨɦɟɧ, ɫ ɭɱɟɬɨɦ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɝɨ ɯɚɪɚɤɬɟɪɚ ɜɨɡɞɟɣɫɬɜɢɹ ɫɨɫɬɚɜɥɹɸɳɢɯ ɷɧɟɪɝɢɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ
wȿ |
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wȿ |
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wȿɝɪ |
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wȿ |
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wȿ |
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= |
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ɦ |
+ |
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– |
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d |
= 4ȝ ɇ Ɇ ʌrh + 2ʌhȖ |
– |
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d |
. (3.39) |
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wr |
0 ɜɧ S |
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ɝɪ |
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wr |
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ɉɪɢɪɚɜɧɹɟɦ ɜɵɪɚɠɟɧɢɟ (3.39) ɤ ɧɭɥɸ ɢ ɩɪɟɞɫɬɚɜɢɦ ɟɝɨ ɜ ɜɢɞɟ, |
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ɭɞɨɛɧɨɦ ɞɥɹ ɞɚɥɶɧɟɣɲɟɝɨ ɚɧɚɥɢɡɚ: |
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ɇ |
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Jɝɪ |
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wȿd |
= ɇ |
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+ ɇ |
– ɇ . |
(3.40) |
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2P0ɆS r |
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4SP0rhM S |
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ɜɧ |
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