EP / Теория ЭП Драчев
.pdfȼ 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) |
31
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
|
|
CK JS |
G ªMH ɦº |
|||
|
|
|
« |
|
», |
|
|
|
|
||||
|
|
|
L ¬ ɪɚɞ |
¼ |
||
|
ʌ R4 |
|
|
|
|
|
ɝɞɟ J |
|
– ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɜɚɥɚ; |
||||
|
||||||
S |
2 |
|
|
|
|
|
|
|
|
|
|
|
|
G – ɦɨɞɭɥɶ ɭɩɪɭɝɨɫɬɢ ɫɞɜɢɝɚ; |
|
|
|
|
||
L – ɞɥɢɧɚ ɜɚɥɚ. |
|
|
|
|
||
Ⱦɥɹ ɭɩɪɭɝɨɝɨ ɫɬɟɪɠɧɹ ɩɪɢ ɟɝɨ ɪɚɫɬɹɠɟɧɢɢ ɢɥɢ ɫɠɚɬɢɢ ɤɨɷɮɮɢɰɢɟɧɬ ɠɺɫɬɤɨ- |
ɫɬɢ
|
GS E ªɇɆº |
, |
|||
ɋɅ |
|
« |
|
» |
|
L |
|
||||
|
¬ |
ɦ ¼ |
|
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 |
|
|
ǻijɉɊ2 |
|
|
ǻiji2 |
, |
ɋɉɊ |
|
ɋɄ |
|
||||
|
|
2 |
|
2 |
|
ɬɨɝɞɚ ɩɪɢɜɟɞɟɧɧɚɹ ɠɟɫɬɤɨɫɬɶ
|
|
|
|
§ |
ǻij2 |
· |
|
|
|
1 |
|
|
|
C |
|
|
|
¨ |
i |
¸ |
|
|
|
. |
(2.49) |
||
|
ɋ |
|
2 |
ɋ |
|
|
|||||||
|
ɉɊ |
|
Ʉ |
¨ |
¸ |
|
Ʉ |
|
|
2 |
|
||
|
|
|
|
© |
ǻijɉɊ ¹ |
|
|
|
i |
|
|
|
Ⱦɥɹ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɞɥɹ ɩɪɢɜɟɞɟɧɧɨɝɨ ɢ ɪɟɚɥɶɧɨɝɨ ɡɜɟɧɚ
Wɉ |
|
|
ǻijɉɊ2 |
|
|
ǻL2i |
, |
ɋɉɊ |
|
ɋɄ |
|
||||
|
|
2 |
|
2 |
|
32
ɬɨɝɞɚ ɩɪɢɜɟɞɟɧɧɚɹ ɠɟɫɬɤɨɫɬɶ ɨɩɪɟɞɟɥɢɬɫɹ ɤɚɤ
|
|
|
|
§ |
ǻL2 · |
|
|
|
|
|
C |
|
|
|
¨ |
i |
¸ |
|
|
ȡ2 . |
(2.50) |
|
ɋ |
|
|
ɋ |
|
|||||
|
ɉɊ |
|
Ʌ |
¨ |
2 ¸ |
|
Ʌ |
|
||
|
|
|
|
© |
ǻijɉɊ ¹ |
|
|
|
|
2.7.2. ɉɪɢɜɟɞɟɧɢɟ ɦɧɨɝɨɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ ɤ ɞɜɭɯɦɚɫɫɨɜɨɣ
Ɋɚɫɫɦɨɬɪɢɦ ɭɩɪɭɝɭɸ ɫɢɫɬɟɦɭ ɫ ɨɞɧɢɦ ɭɩɪɭɝɢɦ ɷɥɟɦɟɧɬɨɦ – ɫɯɟɦɭ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜɟɧɬɢɥɹɬɨɪɚ (ɪɢɫ. 2.13).
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ɉɪɢ ɧɚɥɢɱɢɢ ɭɩɪɭɝɢɯ ɷɥɟɦɟɧɬɨɜ ɧɟ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ȼ |
ɜɫɟɝɞɚ ɭɞɚɺɬɫɹ ɩɨɥɭɱɢɬɶ ɨɞɧɨɦɚɫɫɨ- |
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ɜɭɸ ɪɚɫɱɺɬɧɭɸ ɫɯɟɦɭ, ɢ ɜ ɡɚɜɢɫɢɦɨɫɬɢ |
|
|
|
|
Ⱦ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ɨɬ ɱɢɫɥɚ ɭɩɪɭɝɢɯ ɷɥɟɦɟɧɬɨɜ ɩɨɥɭɱɚɸɬ- |
|
|
|
|
|
|
|
|
|
|
|
|
|
ɋɄ |
ɫɹ ɦɧɨɝɨɦɚɫɫɨɜɵɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɫɢɫ- |
||||||
|
|
|
|
|
|
|
|
|
|
|
|
||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ɬɟɦɵ – ɞɜɭɯɦɚɫɫɨɜɚɹ, ɬɪɟɯɦɚɫɫɨɜɚɹ ɢ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ɬ. ɞ. |
|
|
Ɋɢɫ. 2.13. Ʉɢɧɟɦɚɬɢɱɟɫɤɚɹ ɫɯɟɦɚ |
ȼ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɯɟɦɟ |
ɜɟɧɬɢɥɹ- |
||||||||||||||||
|
ɬɨɪɚ ɦɨɠɧɨ ɪɚɫɫɦɨɬɪɟɬɶ ɱɟɬɵɪɟ ɦɚɫ- |
||||||||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
ɜɟɧɬɢɥɹɬɨɪɚ |
|
|
||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ɫɵ ɫ ɦɨɦɟɧɬɚɦɢ ɢɧɟɪɰɢɢ: ɪɨɬɨɪɚ ɞɜɢ- |
|
|
|
|
|
|
J1 |
|
|
J2 |
|
|
|
ɝɚɬɟɥɹ į·JȾȼ, ɩɨɥɭɦɭɮɬ J1 ɢ J2, ɪɚɛɨɱɟ- |
|||||||
į JȾȼ |
|
|
|
|
|
|
|
|
ɝɨ ɤɨɥɟɫɚ JɉɊ, ɫɨɟɞɢɧɟɧɧɵɟ |
ɬɪɟɦɹ ɭɩ- |
|||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
JɉɊ |
ɪɭɝɢɦɢ ɷɥɟɦɟɧɬɚɦɢ: ɜɚɥɨɦ ɞɜɢɝɚɬɟɥɹ |
|||||
|
C1 |
|
|
C2 |
|
|
|
C3 |
|||||||||||
|
|
|
|
|
|
|
|
ɞɨ ɩɨɥɭɦɭɮɬɵ ɠɟɫɬɤɨɫɬɶɸ ɋ1, ɭɩɪɭɝɨɣ |
|||||||||||
|
|
|
|
|
|
|
|
|
|
||||||||||
|
|
|
|
|
|
|
|
|
|
||||||||||
Ɋɢɫ. 2.14. ɑɟɬɵɪɟɯɦɚɫɫɨɜɚɹ ɭɩɪɭɝɚɹ |
ɦɭɮɬɨɣ – ɋ2, ɜɚɥɨɦ ɜɟɧɬɢɥɹɬɨɪɚ ɞɨ |
||||||||||||||||||
ɪɚɛɨɱɟɝɨ ɤɨɥɟɫɚ – ɋ3. ɉɨɥɭɱɢɥɢ ɱɟɬɵ- |
|||||||||||||||||||
|
|
|
|
|
ɫɢɫɬɟɦɚ |
ɪɟɯɦɚɫɫɨɜɭɸ ɫɢɫɬɟɦɭ (ɪɢɫ. 2.14), ɜ ɤɨ- |
|||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ɬɨɪɨɣ ɜɪɚɳɚɸɳɢɟɫɹ ɦɚɫɫɵ ɫɨɟɞɢɧɟɧɵ |
|
|
|
|
|
|
|
|
ɋ12 |
|
|
|
|
|
|
|
|
|
ɨɬɪɟɡɤɚɦɢ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɦɢ ɩɨɞɚɬ- |
||
|
įǜJȾȼ |
|
|
|
|
|
|
|
|
JɉɊ |
|
||||||||
|
|
|
|
|
|
|
|
|
|
|
|
ɥɢɜɨɫɬɹɦ ɜɚɥɨɜ. |
|
||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Ɉɛɵɱɧɨ ɦɧɨɝɨɦɚɫɫɨɜɭɸ |
ɫɢɫɬɟɦɭ |
|
|
|
|
|
|
|
|
|
M12 |
ɩɪɢɜɨɞɹɬ ɤ ɧɚɢɛɨɥɟɟ ɩɨɞɚɬɥɢɜɨɦɭ ɡɜɟ- |
|||||||||
|
|
|
|
|
|
|
|
|
ɧɭ (ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ – ɋ2), ɩɪɢ ɷɬɨɦ |
||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
įǜJȾȼ |
|
|
|
|
|
|
|
|
JɉɊ |
ɜɪɚɳɚɸɳɢɟɫɹ ɦɚɫɫɵ ɫ ɦɚɥɵɦɢ ɦɨɦɟɧ- |
|||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ɬɚɦɢ ɢɧɟɪɰɢɢ ɩɪɢɫɨɟɞɢɧɹɸɬ ɤ ɝɥɚɜɧɵɦ |
|
|
|
|
|
|
|
ɋ |
12 |
|
|
|
|
|
|
|
|
|
|
ɦɚɫɫɚɦ ɫ ɝɨɪɚɡɞɨ ɛɨɥɶɲɢɦɢ ɦɨɦɟɧɬɚ- |
|
|
Ȧ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
1 |
|
|
|
|
|
|
|
Ȧ2 |
|||||||||||
|
|
|
|
|
|
|
|
||||||||||||
M |
|
ǻMC |
|
|
|
|
|
|
|
|
Mɋ |
ɦɢ ɢɧɟɪɰɢɢ. ȼ ɫɯɟɦɟ ɜɟɧɬɢɥɹɬɨɪɚ ɨɬ- |
|||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ɧɟɫɟɦ J1 ɤ į·JȾȼ, ɚ J2 – ɤ JɉɊ ɢ ɩɨɥɭɱɢɦ |
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Ɋɢɫ. 2.15. Ɋɚɫɱɟɬɧɚɹ ɫɯɟɦɚ |
ɞɜɭɯɦɚɫɫɨɜɭɸ ɭɩɪɭɝɭɸ ɫɢɫɬɟɦɭ (ɪɢɫ. |
|
2.15). ȼ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ɪɚɫɫɦɚɬɪɢɜɚ- |
||
|
||
ɞɜɭɯɦɚɫɫɨɜɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ |
ɟɦ ɝɥɚɜɧɵɟ ɦɚɫɫɵ į·JȾȼ ɢ JɉɊ. ɗɤɜɢɜɚ- |
|
|
||
|
ɥɟɧɬɧɭɸ ɠɟɫɬɤɨɫɬɶ ɋ12 ɞɜɭɯɦɚɫɫɨɜɨɣ |
ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ ɨɩɪɟɞɟɥɹɸɬ ɱɟɪɟɡ ɫɭɦɦɭ ɩɨɞɚɬɥɢɜɨɫɬɟɣ ɭɩɪɭɝɢɯ ɷɥɟɦɟɧɬɨɜ ɪɟɚɥɶɧɨɣ ɫɯɟɦɵ
1 |
|
1 |
|
1 |
|
1 |
. |
(2.51) |
|
|
|
|
|||||
ɋɗɄȼ |
|
ɋ1 |
ɋ2 |
ɋ3 |
|
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 |
|
|
|
dȦ1 |
M , |
|||
|
|
|
|
|||||
|
ɋ |
|
Ⱦȼ |
|
dt |
12 |
||
M |
M |
J |
|
dȦ2 |
, |
|
||
|
|
|||||||
12 |
C |
ɉɊ |
|
|
dt |
|
||
|
|
|
|
|
|
|||
Ɇ12 |
ɋ12 ǻij12 |
ɋ12 ij1 ij2 ɋ12 ³Ȧ1dt ³Ȧ2dt . |
ɉɟɪɟɩɢɲɟɦ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ (2.52) ɜ ɨɩɟɪɚɬɨɪɧɨɣ ɮɨɪɦɟ:
ɆǻɆɋ į JȾȼ p M12,
M12 |
MC JɉɊ p, |
||
|
ɋ |
Ȧ1 Ȧ2 |
. |
Ɇ |
|
||
12 |
12 |
p |
|
|
|
(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.
|
Ɇ12 |
|
|
|
|
|
|
|
|
|
|
Ɇɋ |
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||
Ɇ |
|
|
1 |
|
Ȧ1 |
|
|
|
C |
|
|
|
|
1 |
|
Ȧ2 |
|||
|
|
|
|
||||||||||||||||
|
|
|
|
|
|
|
|
|
12 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
JȾȼ p |
|
|
|
|
p |
Ɇ12 |
|
|
|
|
JɊɈ p |
|
|||
|
|
|
Ȧ2 |
|
|||||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
ǻɆɋ |
|
|
|
|
|
|
|
|
|
Ɋɢɫ. 2.16. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɍɋ
Ɇ |
|
1 |
|
Ȧ1 |
|
ɋ12 |
M12 |
|
1 |
|
|
Ȧ2 |
|||||
|
|
|
|
|
į JȾȼ ɪ |
|
|
|
ɪ |
|
|
|
JɉɊ ɪ |
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||
|
M12 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
JɉɊ ɪ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
įJȾȼp
Ɋɢɫ. 2.17. ɉɪɟɨɛɪɚɡɨɜɚɧɧɚɹ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɩɪɢ ǻɆɋ = 0, Ɇɋ = 0
34
ɉɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɷɬɨɣ ɫɯɟɦɵ ɢɦɟɟɬ ɜɢɞ
|
ǻȦ2 p |
|
|
|
|
|
C12 |
|
|
|
|
|
||||
W p |
|
|
|
p2 į JȾȼ JɉɊ |
|
|
|
|
||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
'M p 1 |
|
|
|
C12 |
|
JɉɊ į JȾȼ ɪ |
||||||||||
|
|
|
|
|
||||||||||||
|
|
|
|
|
|
|
|
|||||||||
|
|
|
|
p2 į JȾȼ JɉɊ |
|
(2.54) |
||||||||||
|
1 |
|
|
|
|
|
|
|
1 |
|
|
|
. |
|
||
|
|
|
|
|
|
|
|
|
|
|||||||
|
JɉɊ į JȾȼ ɪ |
1 |
|
į JȾȼ JɉɊ |
ɪ |
2 |
|
|||||||||
|
|
|
|
|
|
JɉɊ G JȾȼ C12 |
|
|
|
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:
|
JɉɊ į JȾȼ |
|
:K |
JɉɊ į JȾȼ C12 |
|
ɌɄ |
JɉɊ į JȾȼ C12 |
; |
JɉɊ į JȾȼ |
. |
ɉɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɤɨɧɫɟɪɜɚɬɢɜɧɨɝɨ ɡɜɟɧɚ ɡɚɩɢɫɵɜɚɟɬɫɹ ɜ ɜɢɞɟ
W p |
1 |
ɌɄ2 ɪ2 1 . |
ɉɪɢ ɋ12 = f ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɌɄ = 0, ɱɚɫɬɨɬɚ ɫɪɟɡɚ ȍ12 = f, ɩɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɵ ɩɪɟɜɪɚɳɚɟɬɫɹ ɜ ɩɟɪɟɞɚɬɨɱɧɭɸ ɮɭɧɤɰɢɸ ɡɜɟɧɚ ɫ ɢɞɟɚɥɶɧɨ ɠɟɫɬɤɢɦɢ ɫɜɹɡɹɦɢ.
ɉɪɢ p = j·ȍ ɩɨɥɭɱɢɦ W j : |
|
1 |
TK |
2 j : 2 1 . |
Ⱥɦɩɥɢɬɭɞɭ ɤɨɧɫɟɪɜɚɬɢɜɧɨɝɨ ɡɜɟɧɚ ɞɚɟɬ ɦɨɞɭɥɶ ɷɬɨɝɨ ɤɨɦɩɥɟɤɫɧɨɝɨ ɱɢɫɥɚ
|
1 |
1 |
A |
TK2 j ȍ 2 1 |
1 TK2 ȍ2 . |
ɤ
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
|
|
|
Ɇ12(t) |
|
|
|
Ɇ |
|
|
|
|
t0 |
t1 |
t2 |
t3 |
t4 |
t |
t5 |
|||||
Ȧ |
|
|
|
|
|
|
|
|
|
|
İɋɊ |
|
Ȧ1(t) |
|
|
|
|
|
|
|
Ȧ2(t) |
|
|
|
|
|
|
|
t |
t0 |
t1 |
t2 |
t3 |
t4 |
t5 |
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
|
M12CP |
JɉɊ İɋɊ Ɇɋ , |
|
(2.56) |
|||
ɝɞɟ |
|
|
|
|
|
|
|
|
|
dȦ |
|
M MC |
|
. |
(2.57) |
İ |
ɋɊ |
dt |
|
į JȾȼ JɉɊ |
|||
|
|
|
|
|
|
|
|
|
|
|
|
Ɍɚɛɥɢɰɚ 2.2 |
|
|
ɉɨɜɟɞɟɧɢɟ ɭɩɪɭɝɨɝɨ ɦɨɦɟɧɬɚ Ɇ12 ɢ ɫɤɨɪɨɫɬɟɣ Ȧ1 ɢ Ȧ2 |
|
||||
|
|
ɩɪɢ ɫɤɚɱɤɟ ɦɨɦɟɧɬɚ Ɇ ɩɨ ɭɱɚɫɬɤɚɦ |
|
|
|||
|
|
|
|
|
|
|
|
|
|
Ɋɚɡɧɨɫɬɶ |
Ȧ1 |
Ɋɚɡɧɨɫɬɶ Ȧ1 – |
|
M12 |
Ȧ2 |
|
|
M – M12 |
|
Ȧ2 |
|
|
|
|
t0 |
0 |
0 |
0 |
|
0 |
0 |
|
|
|
|
|
|
|
|
t0 – t1 |
ɛɨɥɶɲɟ ɧɭɥɹ |
Ĺ |
ɛɨɥɶɲɟ ɧɭɥɹ |
|
Ĺ |
Ĺ |
|
|
|
|
|
|
|
|
|
|
t1 |
0 |
max1 |
ɛɨɥɶɲɟ ɧɭɥɹ |
|
ĹĹ |
Ĺ |
|
|
|
|
|
|
|
|
t1 |
– t2 |
ɦɟɧɶɲɟ ɧɭɥɹ |
Ļ |
ɛɨɥɶɲɟ ɧɭɥɹ |
|
Ĺ |
Ĺ |
|
|
|
|
|
|
|
|
|
t2 |
ɦɟɧɶɲɟ ɧɭɥɹ |
ĻĻ |
0 |
|
max1 |
ĹĹ |
|
|
|
|
|
|
|
|
t2 |
– t3 |
ɦɟɧɶɲɟ ɧɭɥɹ |
Ļ |
ɦɟɧɶɲɟ ɧɭɥɹ |
|
Ļ |
Ĺ |
|
|
|
|
|
|
|
|
|
t3 |
0 |
min1 |
ɦɟɧɶɲɟ ɧɭɥɹ |
|
ĻĻ |
Ĺ |
|
|
|
|
|
|
|
|
t3 |
– t4 |
ɛɨɥɶɲɟ ɧɭɥɹ |
Ĺ |
ɦɟɧɶɲɟ ɧɭɥɹ |
|
Ļ |
Ĺ |
|
t4 |
ɛɨɥɶɲɟ ɧɭɥɹ |
ĹĹ |
0 |
|
min1 |
max1 |
|
|
|
|
|
|
|
|
t4 |
– t5 |
ɛɨɥɶɲɟ ɧɭɥɹ |
Ĺ |
ɛɨɥɶɲɟ ɧɭɥɹ |
|
Ĺ |
Ĺ |
|
|
|
|
|
|
|
|
|
t5 |
0 |
max2 |
ɛɨɥɶɲɟ ɧɭɥɹ |
|
ĹĹ |
Ĺ |
|
|
|
|
|
|
|
|
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
|
Ɇ12ɆȺɄɋ |
|
2 JɉɊ İɋɊ Ɇɋ |
. |
(2.58) |
|||
ɄȾɂɇ |
|
|
||||||
|
Ɇ |
|
J |
İ |
|
Ɇ |
|
|
|
12ɋɊ |
|
ɉɊ |
|
ɋɊ |
ɋ |
|
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 |
ɋ |
M12 |
|
C12 |
|
12 |
|
|
- |
|
|
|
|
|
ɪ |
|
|
|
|
Ȧ2 |
|
|
|
Ɋɢɫ. 2.20. Ⱦɍɋ ɫ ɭɱɟɬɨɦ ɷɥɟɦɟɧɬɚ ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ |
|
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.
|
|
|
|
|
|
|
|
|
Ɇ12 |
|
|
|
|
|
ǻijɡ |
|
|
||||||
į·JȾȼ |
|
|
|
|
|
|
|
JɉɊ |
|
|
|
|
|
|
|
|
|
|
|
|
|||
|
|
C12 |
|
|
|
|
|
||||
|
|
|
|
|
|
|
|||||
|
|
|
|
|
|
|
|
|
|
||
|
Ȧ1 |
|
|
|
|
|
|
Ȧ2 |
ǻijɡ/2 |
ǻijɡ/2 |
ǻij |
|
|
|
|
|
|
|
|
|
|||
ǻMC |
|
|
|
|
MC |
|
|||||
|
|
|
|
|
|
|
|||||
|
Ɇ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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.
|
1 |
Ȧ1 |
|
Ɇ12 |
Ɇɋ |
|
Ɇ |
1 |
ǻij |
1 |
Ȧ2 |
||
|
GJȾȼ p |
|
p |
C12 |
JɉɊ p |
|
ǻɆɋ |
|
|
Ȧ2 |
|
|
|
Ɋɢɫ. 2.22. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɍɋ ɫ ɡɚɡɨɪɨɦ
M |
|
Ɇ12(t) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Ɇ(t) |
|
t0 t1 |
t2 |
t3 |
t4 |
|
t |
|
t5 |
Ȧ
Ȧ1(t)
Ȧ2(t)
t
t0 |
t1 |
t2 |
t3 |
t4 |
t5 |
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.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Ɇ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ɆɋɌ |
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ɋɌ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||
ǻɆɋ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ǻij |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Ɂ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
|
|
|
|
|
|
|
|
|
|
|
1 |
|
|
|
|
|
Ɇ1 |
|
|
|
|
1 |
|
|
|
|
Ȧ2 |
|||||||
|
|
|
|
|
|
|
|
Ȧ1 |
|
|
|
|
ȕ12p+ɋ1 |
|
|
|
|
|
|
|
|
||||||||||||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
JɉɊp |
|
|
|||||||||||||||||
Ɇ |
|
|
|
|
|
|
|
|
|
|
|
|
ɪ |
|
|
|
|
|
|
|
|
|
|
|
|||||||||||||||||||
|
|
|
|
|
|
|
|
G JȾȼ ɪ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Ȧ2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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