EP / Теория ЭП Драчев
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ȼ ɞɚɥɶɧɟɣɲɟɦ ɢɡɦɟɧɟɧɢɟ ɫɤɨɪɨɫɬɢ ɛɭɞɟɬ ɩɪɨɢɫɯɨɞɢɬɶ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ, ɹɜɥɹɸɳɟɝɨɫɹ ɨɫɧɨɜɧɵɦ ɭɩɪɚɜɥɹɸɳɢɦ ɜɨɡɞɟɣɫɬɜɢɟɦ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ.
Ɋɢɫ. 2.12. Ɇɟɯɚɧɢɱɟɫɤɢɣ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɩɪɢ ɫɢɧɭɫɨɢɞɚɥɶɧɨɦ ɢɡɦɟɧɟɧɢɢ ɦɨɦɟɧɬɚ Ɇ(t)
ɉɪɢ ɪɟɚɤɬɢɜɧɨɦ ɫɬɚɬɢɱɟɫɤɨɦ ɦɨɦɟɧɬɟ ɞɨ M MC ɞɜɢɝɚɬɟɥɶ ɛɭɞɟɬ ɫɬɨɹɬɶ, ɬɚɤ
ɤɚɤ ɧɟ ɫɩɨɫɨɛɟɧ ɪɚɡɨɝɧɚɬɶ ɞɜɢɝɚɬɟɥɶ ɜ ɨɛɪɚɬɧɭɸ ɫɬɨɪɨɧɭ. ɉɪɨɰɟɫɫ ɩɭɫɤɚ ɧɚɱɧɟɬɫɹ ɫ ɬɨɝɨ ɦɨɦɟɧɬɚ ɜɪɟɦɟɧɢ, ɤɨɝɞɚ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɩɪɟɜɵɫɢɬ ɪɟɚɤɬɢɜɧɵɣ ɫɬɚ-
ɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ Ɇ > MC . Ɂɚɤɨɧ ɢɡɦɟɧɟɧɢɹ ɫɤɨɪɨɫɬɢ ɞɥɹ ɪɟɚɤɬɢɜɧɨɝɨ ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ ɧɭɠɧɨ ɜɵɜɟɫɬɢ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ.
2.7. Ɇɟɯɚɧɢɱɟɫɤɚɹ ɱɚɫɬɶ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ
ɫ ɭɩɪɭɝɨɣ ɫɜɹɡɶɸ
Ⱦɨ ɫɢɯ ɩɨɪ ɪɚɫɫɦɚɬɪɢɜɚɥɢɫɶ ɦɟɯɚɧɢɱɟɫɤɢɟ ɫɢɫɬɟɦɵ ɫ ɢɞɟɚɥɶɧɨ ɠɟɫɬɤɢɦɢ ɫɜɹɡɹɦɢ. ɉɪɚɤɬɢɱɟɫɤɢ ɠɟɫɬɤɨɫɬɢ ɜɚɥɨɜ, ɫɨɟɞɢɧɢɬɟɥɶɧɵɯ ɦɭɮɬ, ɩɟɪɟɞɚɱ (ɤɚɧɚɬɵ, ɪɟɦɧɢ, ɜɚɥɵ ɜ ɩɟɪɟɞɚɱɚɯ ɢ ɬ.ɩ.) ɤɨɧɟɱɧɵ, ɦɟɯɚɧɢɱɟɫɤɚɹ ɫɢɫɬɟɦɚ ɩɨɥɭɱɚɟɬ ɧɟɫɤɨɥɶɤɨ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ, ɢ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɫɨɞɟɪɠɢɬ ɬɟɥɚ, ɩɨɞɜɟɪɝɚɸɳɢɟɫɹ ɤɪɭɱɟɧɢɸ, ɢɡɝɢɛɭ, ɪɚɫɬɹɠɟɧɢɸ ɢ ɫɠɚɬɢɸ.
ɀɟɫɬɤɨɫɬɶɸ ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɤɨɷɮɮɢɰɢɟɧɬ ɫɜɹɡɢ ɋɄ (ɋɅ) ɦɟɠɞɭ ɭɝɥɨɜɨɣ ɞɟɮɨɪɦɚɰɢɟɣ ɜɚɥɚ ǻij (ɢɥɢ ɥɢɧɟɣɧɨɣ ɞɟɮɨɪɦɚɰɢɟɣ ǻL) ɢ ɜɨɡɧɢɤɚɸɳɢɦ ɜ ɭɩɪɭɝɨɦ ɷɥɟɦɟɧɬɟ ɭɩɪɭɝɢɦ ɦɨɦɟɧɬɨɦ Ɇɍ (ɢɥɢ ɭɩɪɭɝɨɣ ɫɢɥɨɣ Fɍ). Ȼɭɞɟɦ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɥɢɧɟɣɧɵɣ ɡɚɤɨɧ ɞɟɮɨɪɦɚɰɢɢ (ɡɚɤɨɧ Ƚɭɤɚ). ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɩɪɢɥɨɠɟɧɢɟ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ ɧɟ ɩɪɢɜɨɞɢɬ ɤ ɨɫɬɚɬɨɱɧɵɦ ɞɟɮɨɪɦɚɰɢɹɦ, ɚ ɩɪɢ ɫɧɹɬɢɢ ɦɨɦɟɧɬɚ ɧɚ ɜɯɨɞɟ ɫɢɫɬɟɦɚ ɜɨɡɜɪɚɳɚɟɬɫɹ ɜ ɢɫɯɨɞɧɨɟ ɩɨɥɨɠɟɧɢɟ.
Ɇɍ |
ɋɄ ǻij, |
(2.47) |
Fɍ |
ɋɅ 'L . |
(2.48) |
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Ʉɨɷɮɮɢɰɢɟɧɬɵ ɠɺɫɬɤɨɫɬɢ ɋɄ ɢ ɋɅ ɨɩɪɟɞɟɥɹɸɬɫɹ ɝɟɨɦɟɬɪɢɱɟɫɤɢɦɢ ɪɚɡɦɟ-
ɪɚɦɢ ɭɩɪɭɝɨɝɨ ɷɥɟɦɟɧɬɚ ɢ ɡɚɜɢɫɹɬ ɨɬ ɦɚɬɟɪɢɚɥɚ, ɢɡ ɤɨɬɨɪɨɝɨ ɨɧ ɢɡɝɨɬɨɜɥɟɧ. Ⱦɥɹ ɜɚɥɚ ɪɚɞɢɭɫɨɦ R ɩɪɢ ɟɝɨ ɤɪɭɱɟɧɢɢ ɤɨɷɮɮɢɰɢɟɧɬ ɠɺɫɬɤɨɫɬɢ
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G – ɦɨɞɭɥɶ ɭɩɪɭɝɨɫɬɢ ɫɞɜɢɝɚ; |
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L – ɞɥɢɧɚ ɜɚɥɚ. |
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Ⱦɥɹ ɭɩɪɭɝɨɝɨ ɫɬɟɪɠɧɹ ɩɪɢ ɟɝɨ ɪɚɫɬɹɠɟɧɢɢ ɢɥɢ ɫɠɚɬɢɢ ɤɨɷɮɮɢɰɢɟɧɬ ɠɺɫɬɤɨ- |
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ɝɞɟ L – ɞɥɢɧɚ ɫɬɟɪɠɧɹ;
GS – ɩɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ;
E – ɦɨɞɭɥɶ ɭɩɪɭɝɨɫɬɢ.
ȼɟɥɢɱɢɧɭ 1/ɋ, ɨɛɪɚɬɧɭɸ ɠɟɫɬɤɨɫɬɢ, ɧɚɡɵɜɚɸɬ ɩɨɞɚɬɥɢɜɨɫɬɶɸ. Ɏɢɡɢɱɟɫɤɢ ɩɨɞɚɬɥɢɜɨɫɬɶ ɨɩɪɟɞɟɥɹɟɬ ɞɟɮɨɪɦɚɰɢɸ ɷɥɟɦɟɧɬɚ ɩɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ, ɚ ɤɨɷɮɮɢɰɢɟɧɬ ɠɟɫɬɤɨɫɬɢ – ɜɟɥɢɱɢɧɭ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ ɩɪɢ ɨɩɪɟɞɟɥɟɧɧɨɣ ɞɟɮɨɪɦɚɰɢɢ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɟɦ ɛɨɥɶɲɟ ɤɨɷɮɮɢɰɢɟɧɬ ɠɺɫɬɤɨɫɬɢ ɭɩɪɭɝɨɝɨ ɷɥɟɦɟɧɬɚ, ɬɟɦ ɦɟɧɶɲɚɹ ɞɟɮɨɪɦɚɰɢɹ ɜ ɧɺɦ ɜɨɡɧɢɤɚɟɬ.
2.7.1.ɉɪɢɜɟɞɟɧɢɟ ɭɩɪɭɝɨɫɬɢ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ
ɉɪɢ ɫɨɫɬɚɜɥɟɧɢɢ ɪɚɫɱɺɬɧɵɯ ɫɯɟɦ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɪɢɜɟɞɟɧɢɟ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɠɟɫɬɤɨɫɬɢ ɭɩɪɭɝɨɝɨ ɷɥɟɦɟɧɬɚ. Ʉɪɢɬɟɪɢɟɦ ɩɪɢɜɟɞɟɧɢɹ ɹɜɥɹɟɬɫɹ ɪɚɜɟɧɫɬɜɨ ɡɚɩɚɫɚ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɜ ɪɟɚɥɶɧɨɣ ɢ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɚɯ.
Ⱦɥɹ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɞɥɹ ɩɪɢɜɟɞɟɧɧɨɝɨ ɢ ɪɟɚɥɶɧɨɝɨ ɡɜɟɧɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
Wɉ |
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ɬɨɝɞɚ ɩɪɢɜɟɞɟɧɧɚɹ ɠɟɫɬɤɨɫɬɶ
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(2.49) |
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Ⱦɥɹ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɞɥɹ ɩɪɢɜɟɞɟɧɧɨɝɨ ɢ ɪɟɚɥɶɧɨɝɨ ɡɜɟɧɚ
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ɬɨɝɞɚ ɩɪɢɜɟɞɟɧɧɚɹ ɠɟɫɬɤɨɫɬɶ ɨɩɪɟɞɟɥɢɬɫɹ ɤɚɤ
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2.7.2. ɉɪɢɜɟɞɟɧɢɟ ɦɧɨɝɨɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ ɤ ɞɜɭɯɦɚɫɫɨɜɨɣ
Ɋɚɫɫɦɨɬɪɢɦ ɭɩɪɭɝɭɸ ɫɢɫɬɟɦɭ ɫ ɨɞɧɢɦ ɭɩɪɭɝɢɦ ɷɥɟɦɟɧɬɨɦ – ɫɯɟɦɭ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜɟɧɬɢɥɹɬɨɪɚ (ɪɢɫ. 2.13).
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ɉɪɢ ɧɚɥɢɱɢɢ ɭɩɪɭɝɢɯ ɷɥɟɦɟɧɬɨɜ ɧɟ |
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ɜɫɟɝɞɚ ɭɞɚɺɬɫɹ ɩɨɥɭɱɢɬɶ ɨɞɧɨɦɚɫɫɨ- |
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ɜɭɸ ɪɚɫɱɺɬɧɭɸ ɫɯɟɦɭ, ɢ ɜ ɡɚɜɢɫɢɦɨɫɬɢ |
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ɨɬ ɱɢɫɥɚ ɭɩɪɭɝɢɯ ɷɥɟɦɟɧɬɨɜ ɩɨɥɭɱɚɸɬ- |
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ɋɄ |
ɫɹ ɦɧɨɝɨɦɚɫɫɨɜɵɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɫɢɫ- |
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ɬɟɦɵ – ɞɜɭɯɦɚɫɫɨɜɚɹ, ɬɪɟɯɦɚɫɫɨɜɚɹ ɢ |
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ɬ. ɞ. |
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Ɋɢɫ. 2.13. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ |
ȼ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɯɟɦɟ |
ɜɟɧɬɢɥɹ- |
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ɬɨɪɚ ɦɨɠɧɨ ɪɚɫɫɦɨɬɪɟɬɶ ɱɟɬɵɪɟ ɦɚɫ- |
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ɜɟɧɬɢɥɹɬɨɪɚ |
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ɫɵ ɫ ɦɨɦɟɧɬɚɦɢ ɢɧɟɪɰɢɢ: ɪɨɬɨɪɚ ɞɜɢ- |
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ɝɚɬɟɥɹ į·JȾȼ, ɩɨɥɭɦɭɮɬ J1 ɢ J2, ɪɚɛɨɱɟ- |
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į JȾȼ |
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ɝɨ ɤɨɥɟɫɚ JɉɊ, ɫɨɟɞɢɧɟɧɧɵɟ |
ɬɪɟɦɹ ɭɩ- |
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JɉɊ |
ɪɭɝɢɦɢ ɷɥɟɦɟɧɬɚɦɢ: ɜɚɥɨɦ ɞɜɢɝɚɬɟɥɹ |
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ɞɨ ɩɨɥɭɦɭɮɬɵ ɠɟɫɬɤɨɫɬɶɸ ɋ1, ɭɩɪɭɝɨɣ |
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Ɋɢɫ. 2.14. ɑɟɬɵɪɟɯɦɚɫɫɨɜɚɹ ɭɩɪɭɝɚɹ |
ɦɭɮɬɨɣ – ɋ2, ɜɚɥɨɦ ɜɟɧɬɢɥɹɬɨɪɚ ɞɨ |
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ɪɚɛɨɱɟɝɨ ɤɨɥɟɫɚ – ɋ3. ɉɨɥɭɱɢɥɢ ɱɟɬɵ- |
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ɪɟɯɦɚɫɫɨɜɭɸ ɫɢɫɬɟɦɭ (ɪɢɫ. 2.14), ɜ ɤɨ- |
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ɬɨɪɨɣ ɜɪɚɳɚɸɳɢɟɫɹ ɦɚɫɫɵ ɫɨɟɞɢɧɟɧɵ |
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ɋ12 |
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ɨɬɪɟɡɤɚɦɢ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɦɢ ɩɨɞɚɬ- |
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JɉɊ |
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ɥɢɜɨɫɬɹɦ ɜɚɥɨɜ. |
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Ɉɛɵɱɧɨ ɦɧɨɝɨɦɚɫɫɨɜɭɸ |
ɫɢɫɬɟɦɭ |
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M12 |
ɩɪɢɜɨɞɹɬ ɤ ɧɚɢɛɨɥɟɟ ɩɨɞɚɬɥɢɜɨɦɭ ɡɜɟ- |
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ɧɭ (ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ – ɋ2), ɩɪɢ ɷɬɨɦ |
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ɜɪɚɳɚɸɳɢɟɫɹ ɦɚɫɫɵ ɫ ɦɚɥɵɦɢ ɦɨɦɟɧ- |
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ɬɚɦɢ ɢɧɟɪɰɢɢ ɩɪɢɫɨɟɞɢɧɹɸɬ ɤ ɝɥɚɜɧɵɦ |
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12 |
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ɦɚɫɫɚɦ ɫ ɝɨɪɚɡɞɨ ɛɨɥɶɲɢɦɢ ɦɨɦɟɧɬɚ- |
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ɦɢ ɢɧɟɪɰɢɢ. ȼ ɫɯɟɦɟ ɜɟɧɬɢɥɹɬɨɪɚ ɨɬ- |
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ɧɟɫɟɦ J1 ɤ į·JȾȼ, ɚ J2 – ɤ JɉɊ ɢ ɩɨɥɭɱɢɦ |
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Ɋɢɫ. 2.15. Ɋɚɫɱɟɬɧɚɹ ɫɯɟɦɚ |
ɞɜɭɯɦɚɫɫɨɜɭɸ ɭɩɪɭɝɭɸ ɫɢɫɬɟɦɭ (ɪɢɫ. |
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2.15). ȼ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ɪɚɫɫɦɚɬɪɢɜɚ- |
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ɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ |
ɟɦ ɝɥɚɜɧɵɟ ɦɚɫɫɵ į·JȾȼ ɢ JɉɊ. ɗɤɜɢɜɚ- |
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ɥɟɧɬɧɭɸ ɠɟɫɬɤɨɫɬɶ ɋ12 ɞɜɭɯɦɚɫɫɨɜɨɣ |
ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ ɨɩɪɟɞɟɥɹɸɬ ɱɟɪɟɡ ɫɭɦɦɭ ɩɨɞɚɬɥɢɜɨɫɬɟɣ ɭɩɪɭɝɢɯ ɷɥɟɦɟɧɬɨɜ ɪɟɚɥɶɧɨɣ ɫɯɟɦɵ
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Ƚɥɚɜɧɚɹ ɦɚɫɫɚ į·JȾȼ ɜɪɚɳɚɟɬɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ Ȧ1, ɤ ɧɟɣ ɩɪɢɥɨɠɟɧ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ Ɇ ɢ ɦɨɦɟɧɬ ɫɬɚɬɢɱɟɫɤɢɣ ǻɆɋ. Ƚɥɚɜɧɚɹ ɦɚɫɫɚ JɉɊ ɜɪɚɳɚɟɬɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ
33
Ȧ2, ɤ ɧɟɣ ɩɪɢɥɨɠɟɧ ɦɨɦɟɧɬ Ɇɋ. Ɋɚɡɪɟɠɟɦ ɫɢɫɬɟɦɭ ɩɨ ɭɩɪɭɝɨɦɭ ɷɥɟɦɟɧɬɭ, ɜ ɦɟɫɬɟ ɪɚɡɪɟɡɚ ɩɪɢɥɨɠɢɦ ɩɚɪɭ ɦɨɦɟɧɬɨɜ Ɇ12. Ɇɨɦɟɧɬ Ɇ12 ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɦɨɦɟɧɬ ɭɩɪɭɝɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɝɥɚɜɧɵɦɢ ɦɚɫɫɚɦɢ į·JȾȼ ɢ JɉɊ.
2.7.3.ɍɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ ɢ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ
Ⱦɜɢɠɟɧɢɟ ɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ (Ⱦɍɋ) ɨɩɢɫɵɜɚɟɬɫɹ ɫɢɫɬɟɦɨɣ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ (ɪɢɫ.2.15):
Ɇ 'Ɇ į J |
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dȦ1 |
M , |
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dt |
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Ɇ12 |
ɋ12 ǻij12 |
ɋ12 ij1 ij2 ɋ12 ³Ȧ1dt ³Ȧ2dt . |
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ɉɟɪɟɩɢɲɟɦ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ (2.52) ɜ ɨɩɟɪɚɬɨɪɧɨɣ ɮɨɪɦɟ:
ɆǻɆɋ į JȾȼ p M12,
M12 |
MC JɉɊ p, |
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(2.52)
(2.53)
ɉɨ ɫɢɫɬɟɦɟ ɭɪɚɜɧɟɧɢɣ (2.53) ɫɬɪɨɢɬɫɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɍɋ (ɪɢɫ. 2.16). Ɉɬɥɢɱɢɟ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɵ Ⱦɍɋ ɨɬ ɫɯɟɦɵ ɫɢɫɬɟɦɵ ɫ ɢɞɟɚɥɶɧɨ ɠɟɫɬɤɢɦɢ ɫɜɹɡɹɦɢ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɝɥɚɜɧɵɟ ɦɚɫɫɵ ɪɚɡɞɟɥɟɧɵ, ɦɟɠɞɭ ɧɢɦɢ – ɢɧɬɟɝɪɢɪɭɸɳɟɟ ɡɜɟɧɨ ɋ12/ɪ, ɩɪɟɞɫɬɚɜɥɹɸɳɟɟ ɠɟɫɬɤɨɫɬɶ.
ɉɨɥɭɱɢɦ ɩɟɪɟɞɚɬɨɱɧɭɸ ɮɭɧɤɰɢɸ Ⱦɍɋ, ɞɥɹ ɱɟɝɨ ɩɪɟɨɛɪɚɡɭɟɦ ɫɬɪɭɤɬɭɪɧɭɸ ɫɯɟɦɭ ɪɢɫ. 2.16. ɇɚ ɪɢɫ. 2.17 ɩɪɢɜɟɞɟɧɚ ɩɪɟɨɛɪɚɡɨɜɚɧɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ, ɜ ɤɨɬɨɪɨɣ ɨɛɪɚɬɧɵɟ ɫɜɹɡɢ ɩɟɪɟɧɟɫɟɧɵ ɧɚ ɜɵɯɨɞ ɫɢɫɬɟɦɵ.
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Ɋɢɫ. 2.16. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɍɋ
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įJȾȼp
Ɋɢɫ. 2.17. ɉɪɟɨɛɪɚɡɨɜɚɧɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɩɪɢ ǻɆɋ = 0, Ɇɋ = 0
34
ɉɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɷɬɨɣ ɫɯɟɦɵ ɢɦɟɟɬ ɜɢɞ
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Ʉɚɤ ɜɢɞɧɨ ɢɡ (2.54), ɩɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɫɨɞɟɪɠɢɬ ɞɜɚ ɡɜɟɧɚ:
–ɢɧɬɟɝɪɢɪɭɸɳɟɟ ɡɜɟɧɨ ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɭɫɢɥɟɧɢɹ 1/J = 1/(į·JȾȼ + JɉɊ) – ɷɬɨ ɡɜɟɧɨ ɩɪɟɞɫɬɚɜɥɹɟɬ ɢɞɟɚɥɶɧɨ ɠɟɫɬɤɭɸ ɫɢɫɬɟɦɭ;
–ɤɨɧɫɟɪɜɚɬɢɜɧɨɟ ɡɜɟɧɨ (ɤɨɥɟɛɚɬɟɥɶɧɨɟ ɡɜɟɧɨ ɛɟɡ ɞɟɦɩɮɢɪɨɜɚɧɢɹ ɤɨɥɟɛɚɧɢɣ) ɫ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ ɌɄ ɢ ɱɚɫɬɨɬɨɣ ɫɪɟɡɚ ȍɄ = ȍ12:
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JɉɊ į JȾȼ C12 |
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JɉɊ į JȾȼ C12 |
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JɉɊ į JȾȼ |
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ɉɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɤɨɧɫɟɪɜɚɬɢɜɧɨɝɨ ɡɜɟɧɚ ɡɚɩɢɫɵɜɚɟɬɫɹ ɜ ɜɢɞɟ
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ɉɪɢ ɋ12 = f ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɌɄ = 0, ɱɚɫɬɨɬɚ ɫɪɟɡɚ ȍ12 = f, ɩɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ ɩɪɟɜɪɚɳɚɟɬɫɹ ɜ ɩɟɪɟɞɚɬɨɱɧɭɸ ɮɭɧɤɰɢɸ ɡɜɟɧɚ ɫ ɢɞɟɚɥɶɧɨ ɠɟɫɬɤɢɦɢ ɫɜɹɡɹɦɢ.
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TK2 j ȍ 2 1 |
1 TK2 ȍ2 . |
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1/Ɍ
Ɋɢɫ. 2.18. ɑɚɫɬɨɬɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ Ⱦɍɋ
ɇɟɬɪɭɞɧɨ ɭɛɟɞɢɬɶɫɹ, ɱɬɨ ɚɦɩɥɢɬɭɞɚ ɤɨɧɫɟɪɜɚɬɢɜɧɨɝɨ ɡɜɟɧɚ ɛɭɞɟɬ ɪɚɜɧɚ ɛɟɫɤɨɧɟɱɧɨ-
ɫɬɢ Ⱥ =f ɩɪɢ ȍ =1/ɌɄ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɢ ɱɚɫɬɨɬɟ ɫɪɟɡɚ ɤɨɧɫɟɪɜɚɬɢɜɧɨɝɨ ɡɜɟɧɚ ȍ12 ɧɚɫɬɭɩɚɟɬ ɹɜɥɟɧɢɟ ɪɟɡɨɧɚɧɫɚ (ɷɬɭ ɱɚɫɬɨɬɭ ȍ12 = ȍɊȿɁ ɧɚɡɵɜɚɸɬ ɪɟɡɨɧɚɧɫɧɨɣ), ɅȺɑɏ ɷɬɨɝɨ ɡɜɟɧɚ ɬɟɪɩɢɬ ɪɚɡɪɵɜ. ɅȺɑɏ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ.
ȍ2.18. ȿɫɥɢ ɜɨɡɦɭɳɟɧɢɹ ɩɪɨɯɨɞɹɬ ɫ ɱɚɫɬɨɬɨɣ ȍ12, ɜ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɟ ɜɨɡɧɢɤɚɸɬ ɪɟɡɨɧɚɧɫɧɵɟ ɤɨɥɟɛɚɧɢɹ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ ɫ ɚɦɩɥɢɬɭɞɨɣ Ⱥ = f.
35
2.7.4. ɉɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɜ ɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɟ
Ɋɚɫɫɦɨɬɪɢɦ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɩɪɢɥɨɠɟɧɢɹ ɫɤɚɱɤɨɦ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ Ɇ (ɪɢɫ. 2.19) ɩɪɢ ǻɆɋ = 0 ɢ Ɇɋ = 0 ɩɨ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɟ Ⱦɍɋ (ɫɦ. ɪɢɫ. 2.16). ɉɨɫɥɟ ɩɪɢɥɨɠɟɧɢɹ ɫɤɚɱɤɚ Ɇ ɞɜɢɝɚɬɟɥɹ, ɟɫɥɢ ɋ12 = f, ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ Ȧ2(t) ɩɨɣɞɟɬ ɩɨ ɥɢɧɟɣɧɨɦɭ ɡɚɤɨɧɭ ɫ ɭɫɤɨɪɟɧɢɟɦ İɋɊ.
ɉɪɢ ɋ12 < f, ɩɨɫɥɟ ɩɪɢɥɨɠɟɧɢɹ ɫɤɚɱɤɚ Ɇ ɞɜɢɝɚɬɟɥɹ ɭɩɪɭɝɢɣ ɦɨɦɟɧɬ Ɇ12 = 0, ɞɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ (M – M12)>0 ɢ ɩɨɫɥɟ ɩɟɪɜɨɝɨ ɢɧɬɟɝɪɚɥɶɧɨɝɨ ɡɜɟɧɚ ɧɚ ɭɱɚɫɬɤɟ t0…t1 ɫɤɨɪɨɫɬɶ Ȧ1 ɧɚɱɧɟɬ ɧɚɪɚɫɬɚɬɶ ɩɨ ɥɢɧɟɣɧɨɦɭ ɡɚɤɨɧɭ. ɉɨɫɥɟ ɜɬɨɪɨɝɨ ɢɧɬɟɝɪɚɥɶɧɨɝɨ ɡɜɟɧɚ ɧɚɱɧɟɬ ɧɚɪɚɫɬɚɬɶ Ɇ12. Ⱦɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ (M – M12) ɧɚɱɧɟɬ ɫɧɢɠɚɬɶɫɹ, ɬɟɦɩ ɧɚɪɚɫɬɚɧɢɹ Ȧ1 ɫɧɢɠɚɟɬɫɹ. ɋ ɪɨɫɬɨɦ Ɇ12 ɩɨɫɥɟ ɬɪɟɬɶɟɝɨ ɢɧɬɟɝɪɚɥɶɧɨɝɨ ɡɜɟɧɚ ɩɨɹɜɥɹɟɬɫɹ ɫɤɨɪɨɫɬɶ Ȧ2, ɧɚ ɜɯɨɞɟ ɜɬɨɪɨɝɨ ɢɧɬɟɝɪɚɥɶɧɨɝɨ ɡɜɟɧɚ ɩɨɹɜɥɹɟɬɫɹ ɪɚɡɧɨɫɬɶ (Ȧ1 – Ȧ2) > 0. Ɇ12 ɩɪɨɞɨɥɠɚɟɬ ɧɚɪɚɫɬɚɬɶ ɜ ɫɜɹɡɢ ɫ ɩɪɨɞɨɥɠɚɸɳɢɦɫɹ ɪɨɫɬɨɦ Ȧ1. ȼ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t1 ɞɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ (M – M12) = 0, Ȧ1 ɩɪɟɤɪɚɳɚɟɬ ɧɚɪɚɫɬɚɧɢɟ, ɞɨɫɬɢɝɚɹ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɧɚ ɷɬɨɦ ɭɱɚɫɬɤɟ.
Ɋɚɫɫɦɚɬɪɢɜɚɹ ɩɨɞɨɛɧɵɦ ɫɩɨɫɨɛɨɦ ɩɨɫɥɟɞɭɸɳɢɟ ɭɱɚɫɬɤɢ, ɦɨɠɧɨ ɩɪɨɚɧɚɥɢ-
M
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Ɇ12(t) |
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Ɇ |
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t3 |
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Ɋɢɫ.2.19. ȼɪɟɦɟɧɧɵɟ ɞɢɚɝɪɚɦɦɵ ɦɨɦɟɧɬɚ Ɇ12, ɫɤɨɪɨɫɬɟɣ Ȧ1 ɢ Ȧ2 ɞɥɹ Ⱦɍɋ ɩɪɢ ɫɤɚɱɤɟ ɦɨɦɟɧɬɚ Ɇ
ɡɢɪɨɜɚɬɶ ɞɚɥɶɧɟɣɲɟɟ ɩɨɜɟɞɟɧɢɟ ɫɤɨɪɨɫɬɟɣ Ȧ1, Ȧ2 ɢ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ Ɇ12 ɩɪɢ ɫɤɚɱɤɟ ɦɨɦɟɧɬɚ Ɇ. ȼ ɩɨɦɨɳɶ ɢɡɭɱɟɧɢɸ ɞɚɥɶɧɟɣɲɟɝɨ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɩɪɟɞɥɚɝɚɟɬɫɹ ɬɚɛɥ. 2.2.
ɉɪɢɜɟɞɟɧɧɵɣ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɜ ɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɟ ɩɨɞɬɜɟɪɠɞɚɟɬ, ɱɬɨ ɨɧ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɧɟɡɚɬɭɯɚɸɳɢɦɢ ɤɨɥɟɛɚɧɢɹɦɢ ɫ ɱɚɫɬɨɬɨɣ
ȍɊȿɁ.
ɉɪɢ ɧɭɥɟɜɵɯ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɭɩɪɭɝɢɣ ɦɨɦɟɧɬ ɢɡɦɟɧɹɟɬɫɹ ɩɨ ɡɚɤɨɧɭ
Ɇ12 t JɉɊ İ 1 cos:t MC , |
(2.55) |
36
ɬɨɝɞɚ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ ɨɩɪɟɞɟɥɢɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
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M12CP |
JɉɊ İɋɊ Ɇɋ , |
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ɝɞɟ |
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dȦ |
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Ɍɚɛɥɢɰɚ 2.2 |
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ɉɨɜɟɞɟɧɢɟ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ Ɇ12 ɢ ɫɤɨɪɨɫɬɟɣ Ȧ1 ɢ Ȧ2 |
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ɩɪɢ ɫɤɚɱɤɟ ɦɨɦɟɧɬɚ Ɇ ɩɨ ɭɱɚɫɬɤɚɦ |
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Ɋɚɡɧɨɫɬɶ |
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M12 |
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M – M12 |
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ɛɨɥɶɲɟ ɧɭɥɹ |
Ĺ |
ɛɨɥɶɲɟ ɧɭɥɹ |
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max1 |
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t1 |
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ɦɟɧɶɲɟ ɧɭɥɹ |
Ļ |
ɛɨɥɶɲɟ ɧɭɥɹ |
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Ĺ |
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t2 |
ɦɟɧɶɲɟ ɧɭɥɹ |
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t2 |
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ɦɟɧɶɲɟ ɧɭɥɹ |
Ļ |
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Ļ |
Ĺ |
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t3 |
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min1 |
ɦɟɧɶɲɟ ɧɭɥɹ |
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Ĺ |
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t3 |
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ɛɨɥɶɲɟ ɧɭɥɹ |
Ĺ |
ɦɟɧɶɲɟ ɧɭɥɹ |
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Ļ |
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t4 |
ɛɨɥɶɲɟ ɧɭɥɹ |
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t4 |
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ɛɨɥɶɲɟ ɧɭɥɹ |
Ĺ |
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max2 |
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Ɇɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ Ɇ12ɆȺɄɋ ɜ ɩɟɪɟɞɚɱɟ ɩɪɟɜɵɲɚɟɬ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ Ɇ ɢ ɦɨɠɟɬ ɜɵɡɜɚɬɶ ɨɫɬɚɬɨɱɧɵɟ ɞɟɮɨɪɦɚɰɢɢ, ɟɫɥɢ ɩɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɧɟ ɩɪɟɞɭɫɦɨɬɪɟɬɶ ɦɟɪɵ ɩɨ ɟɝɨ ɫɧɢɠɟɧɢɸ.
Ɉɰɟɧɢɜɚɸɬ ɜɥɢɹɧɢɟ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ ɫ ɩɨɦɨɳɶɸ ɤɨɷɮɮɢɰɢɟɧɬɚ ɞɢɧɚɦɢɱɧɨɫɬɢ ɄȾɂɇ, ɩɨɞ ɤɨɬɨɪɵɦ ɩɨɧɢɦɚɸɬ ɨɬɧɨɲɟɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ ɤ ɟɝɨ ɫɪɟɞɧɟɦɭ ɡɧɚɱɟɧɢɸ
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Ɇ12ɆȺɄɋ |
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2 JɉɊ İɋɊ Ɇɋ |
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(2.58) |
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ɉɊ |
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ɋ |
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ȼ ɪɟɚɥɶɧɵɯ ɷɥɟɦɟɧɬɚɯ ɤɢɧɟɦɚɬɢɱɟɫɤɢɯ ɫɯɟɦ ɜɫɟɝɞɚ ɫɭɳɟɫɬɜɭɸɬ ɫɢɥɵ ɜɧɭɬɪɟɧɧɟɝɨ ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ, ɨɤɚɡɵɜɚɸɳɢɟ ɫɭɳɟɫɬɜɟɧɧɨɟ ɜɥɢɹɧɢɟ ɧɚ ɞɢɧɚɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ ɜ ɦɟɯɚɧɢɱɟɫɤɢɯ ɫɢɫɬɟɦɚɯ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɟ ɫɤɨɪɨɫɬɢ ɞɟɮɨɪɦɚɰɢɢ ɜɚɥɨɜ, ɤɚɧɚɬɨɜ, ɦɭɮɬ ɢ ɞɪɭɝɢɯ ɷɥɟɦɟɧɬɨɜ.
Ɇɨɦɟɧɬ ɜɧɭɬɪɟɧɧɟɝɨ ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ ɨɰɟɧɢɜɚɸɬ ɩɨ ɮɨɪɦɭɥɟ
37
ɆȼɌ E12 Ȧ1 Ȧ2 ,
ɝɞɟ Ȧ1, Ȧ2 – ɫɤɨɪɨɫɬɢ ɧɚ ɜɯɨɞɟ ɢ ɜɵɯɨɞɟ ɞɟɮɨɪɦɢɪɭɟɦɨɝɨ ɷɥɟɦɟɧɬɚ; ȕ12 – ɤɨɷɮɮɢɰɢɟɧɬ ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ.
ɉɪɢ ɜɨɡɞɟɣɫɬɜɢɢ ɭɩɪɭɝɢɯ ɤɨɥɟɛɚɧɢɣ ɜ ɞɟɮɨɪɦɢɪɭɟɦɨɦ ɷɥɟɦɟɧɬɟ ɩɪɨɢɫɯɨɞɢɬ ɩɨɝɥɨɳɟɧɢɟ ɷɧɟɪɝɢɢ ɤɨɥɟɛɚɧɢɣ, ɬɚɤ ɤɚɤ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɫɤɨɪɨɫɬɢ ɢɡɦɟɧɹɟɬɫɹ ɢ ɡɧɚɤ ɦɨɦɟɧɬɚ, ɦɨɳɧɨɫɬɶ ɩɨɬɟɪɶ ɜ ɷɥɟɦɟɧɬɟ ɨɫɬɚɟɬɫɹ ɩɨɥɨɠɢɬɟɥɶɧɨɣ.
Ⱦɥɹ ɭɱɟɬɚ ɦɨɦɟɧɬɚ ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ ɜ ɪɚɫɱɟɬɧɭɸ ɢ ɫɬɪɭɤɬɭɪɧɭɸ ɫɯɟɦɵ Ⱦɍɋ ɜɧɨɫɹɬ ȕ12 (ɪɢɫ. 2.20).
ȕ12
ȕ12
į·Jɞɜ |
JɉɊ |
Ȧ1 |
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M12 |
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C12 |
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Ɋɢɫ. 2.20. Ⱦɍɋ ɫ ɭɱɟɬɨɦ ɷɥɟɦɟɧɬɚ ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ |
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ɍɱɟɬ ɜɧɭɬɪɟɧɧɟɝɨ ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ ɩɨɡɜɨɥɹɟɬ ɩɪɢ ɧɚɢɛɨɥɶɲɢɯ ȕ12 ɫɧɢɡɢɬɶ ɦɚɤɫɢɦɭɦ ɞɢɧɚɦɢɱɟɫɤɨɣ ɧɚɝɪɭɡɤɢ ɡɚ ɫɱɟɬ ɟɫɬɟɫɬɜɟɧɧɨɝɨ ɡɚɬɭɯɚɧɢɹ ɩɪɢɦɟɪɧɨ ɧɚ 15%, ɱɬɨ ɫɨɢɡɦɟɪɢɦɨ ɫ ɬɨɱɧɨɫɬɶɸ ɨɩɪɟɞɟɥɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɫɢɫɬɟɦɵ. ɉɨɷɬɨɦɭ ɩɪɢ ɚɧɚɥɢɡɟ ɦɚɤɫɢɦɚɥɶɧɵɯ ɞɢɧɚɦɢɱɟɫɤɢɯ ɧɚɝɪɭɡɨɤ ɜ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɚɯ ɩɭɫɤɚ ɢ ɬɨɪɦɨɠɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɟɫɬɟɫɬɜɟɧɧɵɦ ɞɟɦɩɮɢɪɨɜɚɧɢɟɦ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɝɚɬɶ.
2.7.5.ɉɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɜ ɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɟ
ɫɡɚɡɨɪɨɦ
ȼɞɟɣɫɬɜɭɸɳɟɦ ɦɟɯɚɧɢɱɟɫɤɨɦ ɨɛɨɪɭɞɨɜɚɧɢɢ ɜɦɟɫɬɟ ɫ ɭɩɪɭɝɨɫɬɶɸ ɞɨɜɨɥɶɧɨ ɱɚɫɬɨ ɜɫɬɪɟɱɚɸɬɫɹ ɡɚɡɨɪɵ ɜ ɦɟɯɚɧɢɱɟɫɤɢɯ ɩɟɪɟɞɚɱɚɯ ɢ ɫɨɱɥɟɧɟɧɢɹɯ. ȼ ɪɚɫɱɟɬ-
ɧɨɣ ɫɯɟɦɟ (ɪɢɫ. 2.21) ɡɚɡɨɪ ɪɚɡɪɵɜɚɟɬ ɦɟɯɚɧɢɱɟɫɤɭɸ ɰɟɩɶ. Ɂɚɜɢɫɢɦɨɫɬɶ Ɇ12 = f(ij1–ij2) ɫɬɚɧɨɜɢɬɫɹ ɧɟɥɢɧɟɣɧɨɣ. Ʉɨɝɞɚ ɜ ɩɪɨɰɟɫɫɟ ɜɨɡɞɟɣɫɬɜɢɹ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ ɞɟɮɨɪɦɚɰɢɹ ɷɥɟɦɟɧɬɚ ǻij ɫɬɚɧɨɜɢɬɫɹ ɦɟɧɶɲɟ ɡɚɡɨɪɚ ǻijɡ ɜ ɦɟɯɚɧɢɱɟɫɤɨɣ ɩɟɪɟɞɚɱɟ, ɭɩɪɭɝɢɣ ɦɨɦɟɧɬ Ɇ12 ɫɬɚɧɨɜɢɬɫɹ ɪɚɜɧɵɦ ɧɭɥɸ, ɤɢɧɟɦɚɬɢɱɟɫɤɚɹ ɰɟɩɶ ɪɚɡɪɵɜɚɟɬɫɹ. ɋɢɫɬɟɦɚ ɩɪɨɞɨɥɠɚɟɬ ɞɜɢɠɟɧɢɟ, ɧɚɪɚɫɬɚɟɬ ɪɚɡɧɨɫɬɶ ɫɤɨɪɨɫɬɟɣ ɢ ɩɨɫɥɟ ɩɪɨɯɨɠɞɟɧɢɹ ɡɚɡɨɪɚ ɦɟɯɚɧɢɱɟɫɤɚɹ ɰɟɩɶ ɡɚɦɵɤɚɟɬɫɹ. ɇɚɪɚɫɬɚɸɳɢɣ ɭɩɪɭɝɢɣ ɦɨɦɟɧɬ ɫɨɡɞɚɟɬ ɭɞɚɪ ɜ ɦɟɯɚɧɢɱɟɫɤɨɣ ɰɟɩɢ.
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Ɋɢɫ. 2.21. Ɋɚɫɱɟɬɧɚɹ ɫɯɟɦɚ Ⱦɍɋ ɫ ɡɚɡɨɪɨɦ ɢ ɡɚɜɢɫɢɦɨɫɬɶ Ɇ12 =f(ǻij)
38
ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɍɋ ɫ ɡɚɡɨɪɨɦ ɢ ɩɟɪɟɯɨɞɧɵɣ ɩɪɨɰɟɫɫ ɩɪɢɥɨɠɟɧɢɹ ɦɨɦɟɧɬɚ Ɇ ɞɜɢɝɚɬɟɥɹ ɫɤɚɱɤɨɦ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 2.22, 2.23. ɉɪɟɞɥɚɝɚɟɬɫɹ ɫɚɦɨ-
ɫɬɨɹɬɟɥɶɧɨ ɩɪɨɚɧɚɥɢɡɢɪɨɜɚɬɶ ɜɪɟɦɟɧɧɵɟ ɞɢɚɝɪɚɦɦɵ ɤɨɨɪɞɢɧɚɬ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ ɫ ɡɚɡɨɪɨɦ.
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Ɋɢɫ. 2.22. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɍɋ ɫ ɡɚɡɨɪɨɦ
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Ɋɢɫ. 2.23. ȼɪɟɦɟɧɧɵɟ ɞɢɚɝɪɚɦɦɵ ɦɨɦɟɧɬɚ Ɇ12, ɫɤɨɪɨɫɬɟɣ Ȧ1 ɢ Ȧ2 ɞɥɹ Ⱦɍɋ ɫ ɡɚɡɨɪɨɦ
Ⱦɢɧɚɦɢɱɟɫɤɢɟ ɤɨɥɟɛɚɬɟɥɶɧɵɟ ɩɪɨɰɟɫɫɵ ɜ ɫɪɟɞɧɟɦ ɧɟ ɜɥɢɹɸɬ ɧɚ ɞɥɢɬɟɥɶɧɨɫɬɶ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ, ɧɨ ɨɬɪɢɰɚɬɟɥɶɧɨ ɫɤɚɡɵɜɚɸɬɫɹ ɧɚ ɭɫɥɨɜɢɹ ɜɵɩɨɥɧɟɧɢɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɨɩɟɪɚɰɢɣ, ɜ ɱɚɫɬɧɨɫɬɢ, ɜ ɬɨɱɧɨɫɬɢ ɪɚɛɨɬɵ ɭɫɬɚɧɨɜɤɢ.
ɉɪɚɤɬɢɱɟɫɤɢ ɜɫɟɝɞɚ ɜɨɡɧɢɤɧɨɜɟɧɢɟ ɭɩɪɭɝɢɯ ɤɨɥɟɛɚɧɢɣ ɭɜɟɥɢɱɢɜɚɸɬ ɞɢɧɚɦɢɱɟɫɤɢɟ ɧɚɝɪɭɡɤɢ ɦɟɯɚɧɢɱɟɫɤɨɝɨ ɨɛɨɪɭɞɨɜɚɧɢɹ ɢ ɟɝɨ ɢɡɧɨɫ.
ɇɚɲɚ ɡɚɞɚɱɚ: ɬɚɤ ɩɪɨɟɤɬɢɪɨɜɚɬɶ ɷɥɟɤɬɪɨɩɪɢɜɨɞ, ɱɬɨɛɵ ɫɧɢɠɚɬɶ ɜɵɛɪɨɫɵ ɭɩɪɭɝɢɯ ɦɨɦɟɧɬɨɜ (ɭɦɟɧɶɲɚɬɶ ɞɢɧɚɦɢɱɟɫɤɢɣ ɤɨɷɮɮɢɰɢɟɧɬ), ɧɭɠɧɨ ɨɩɪɟɞɟɥɟɧɧɵɦ ɨɛɪɚɡɨɦ ɜɵɛɢɪɚɬɶ ɫɬɪɭɤɬɭɪɭ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ, ɟɝɨ ɩɚɪɚɦɟɬɪɵ (ɨɝɪɚɧɢɱɢɜɚɬɶ ɭɫɤɨɪɟɧɢɟ, ɩɪɢɦɟɧɹɬɶ ɫɢɫɬɟɦɭ ɜɵɛɨɪɤɢ ɡɚɡɨɪɨɜ ɢ ɬ.ɩ.).
2.8. Ɉɛɨɛɳɟɧɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ
ȼ ɰɟɥɨɦ ɦɟɯɚɧɢɱɟɫɤɚɹ ɱɚɫɬɶ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ – ɫɥɨɠɧɟɣɲɢɣ ɨɛɴɟɤɬ ɭɩɪɚɜɥɟɧɢɹ (ɪɢɫ. 2.24) ɫ ɫɭɳɟɫɬɜɟɧɧɵɦɢ ɧɟɥɢɧɟɣɧɨɫɬɹɦɢ (ɡɚɡɨɪ ǻijɁ, ɫɭɯɨɟ
39
ɆɋɌ ɢ ɜɹɡɤɨɟ ɬɪɟɧɢɟ ɆȼɌ), ɨɝɪɚɧɢɱɟɧɧɵɣ ɜɟɥɢɱɢɧɚɦɢ ɠɟɫɬɤɨɫɬɢ ɜɚɥɨɜ ɢ ɬ.ɩ. ɇɟɨɛɯɨɞɢɦɨɫɬɶ ɭɱɟɬɚ ɬɟɯ ɢɥɢ ɢɧɵɯ ɩɚɪɚɦɟɬɪɨɜ (ɡɚɡɨɪɵ, ɭɩɪɭɝɨɫɬɢ ɢ ɬ.ɩ.) ɪɟɲɚɸɬɫɹ ɜ ɤɚɠɞɨɦ ɤɨɧɤɪɟɬɧɨɦ ɦɟɯɚɧɢɡɦɟ ɢɧɞɢɜɢɞɭɚɥɶɧɨ. Ɉɛɵɱɧɨ ɫɧɚɱɚɥɚ ɪɟɲɚɸɬɫɹ ɡɚɞɚɱɢ ɫ ɢɞɟɚɥɶɧɨ ɠɟɫɬɤɢɦɢ ɫɜɹɡɹɦɢ, ɢ ɥɢɲɶ ɡɚɬɟɦ ɤɨɪɪɟɤɬɢɪɭɸɬɫɹ ɫ ɭɱɟɬɨɦ ɭɩɪɭɝɨɫɬɢ ɢ ɡɚɡɨɪɨɜ.
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ɆȼɌ
1+b·sign(M12) 
Ɋɢɫ. 2.24. Ɉɛɨɛɳɟɧɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ
ɉɪɢɜɟɞɟɧɢɟ ɜ ɞɜɢɠɟɧɢɟ ɢɫɩɨɥɧɢɬɟɥɶɧɵɯ ɦɟɯɚɧɢɡɦɨɜ ɢ ɭɩɪɚɜɥɟɧɢɟ ɢɯ ɞɜɢɠɟɧɢɟɦ ɞɥɹ ɜɵɩɨɥɧɟɧɢɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɨɩɟɪɚɰɢɣ ɹɜɥɹɟɬɫɹ ɨɫɧɨɜɧɨɣ ɡɚɞɚɱɟɣ Ⱥɗɉ. ɉɨɷɬɨɦɭ ɫɩɟɰɢɚɥɢɫɬ ɩɨ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɦɭ ɷɥɟɤɬɪɨɩɪɢɜɨɞɭ ɞɨɥɠɟɧ ɡɧɚɬɶ ɨɛɳɢɟ ɨɫɨɛɟɧɧɨɫɬɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɫɢɫɬɟɦ, ɜɚɠɧɟɣɲɢɟ ɢɯ ɷɥɟɦɟɧɬɵ, ɫɜɹɡɢ ɢ ɩɚɪɚɦɟɬɪɵ, ɚ ɬɚɤɠɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ ɢɯ ɨɩɢɫɚɧɢɹ ɢ ɚɧɚɥɢɡɚ. Ɉɧ ɞɨɥɠɟɧ ɭɦɟɬɶ ɧɚ ɨɫɧɨɜɟ ɢɡɜɟɫɬɧɨɣ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɯɟɦɵ ɦɟɯɚɧɢɡɦɚ, ɟɝɨ ɬɟɯɧɢɱɟɫɤɢɯ ɞɚɧɧɵɯ ɢ ɫɜɟɞɟɧɢɣ ɨ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɦ ɩɪɨɰɟɫɫɟ ɫɨɫɬɚɜɥɹɬɶ ɪɚɫɱɟɬɧɵɟ ɫɯɟɦɵ ɢ ɪɚɫɫɱɢɬɵɜɚɬɶ ɩɚɪɚɦɟɬɪɵ ɦɟɯɚɧɢɱɟɫɤɨɣ ɱɚɫɬɢ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ, ɨɩɢɫɵɜɚɬɶ ɞɜɢɠɟɧɢɟ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦɢ ɭɪɚɜɧɟɧɢɹɦɢ, ɪɚɫɫɱɢɬɵɜɚɬɶ ɱɚɫɬɨɬɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɢ ɦɟɯɚɧɢɱɟɫɤɢɟ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ. Ⱦɨɥɠɟɧ ɩɨ ɢɡɜɟɫɬɧɨɦɭ ɯɚɪɚɤɬɟɪɭ ɢɡɦɟɧɟɧɢɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɹ ɨɰɟɧɢɜɚɬɶ ɯɚɪɚɤɬɟɪ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ.
2.9.ɍɩɪɚɠɧɟɧɢɹ ɞɥɹ ɫɚɦɨɩɪɨɜɟɪɤɢ
2.9.1.Ɉɩɪɟɞɟɥɢɬɟ ɩɪɢɜɟɞɟɧɧɵɟ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ Ɇɋ ɢ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ JɉɊ ɝɪɭɡɚ, ɟɫɥɢ ɝɪɭɡ ɦɚɫɫɨɣ m=10 ɬ ɩɨɞɧɢɦɚɟɬɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ v=1 ɦ/ɫ, ɚ ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɩɪɢ ɩɨɞɴɟɦɟ Ȧ =100 ɪɚɞ/ɫ.
2.9.2.ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɢɡɦɟɧɢɬɫɹ ɩɪɢɜɟɞɟɧɧɵɟ ɤ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ ɫɬɚɬɢɱɟɫɤɢɣ
ɦɨɦɟɧɬ Ɇɋ ɢ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ JɉɊ ɝɪɭɡɚ, ɟɫɥɢ:
– ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɞɜɢɝɚɬɟɥɹ ɫɧɢɡɢɬɶ ɜɞɜɨɟ?
– ɫɤɨɪɨɫɬɶ ɩɨɞɴɟɦɚ ɫɧɢɡɢɬɶ ɜɞɜɨɟ ɩɪɢ ɬɨɣ ɠɟ ɫɤɨɪɨɫɬɢ ɞɜɢɝɚɬɟɥɹ Ȧ = 100 ɪɚɞ/ɫ?
40