Механика.Методика решения задач
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ȽɅȺȼȺ 8. ɋɜɨɛɨɞɧɵɟ ɢ ɜɵɧɭɠɞɟɧɧɵɟ ɤɨɥɟɛɚɧɢɹ |
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ɉɨ ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ ɧɚ ɭɤɚɡɚɧɧɭɸ ɫɢɫɬɟɦɭ ɬɟɥ ɧɟ ɞɟɣɫɬɜɭɸɬ ɜɧɟɲɧɢɟ ɫɢɥɵ ɜɞɨɥɶ ɨɫɢ ɏ (ɫɢɥɚɦɢ ɬɪɟɧɢɹ ɢ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜɨɡɞɭɯɚ ɩɪɟɧɟɛɪɟɝɚɟɦ), ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫɨ ɜɬɨɪɵɦ ɡɚɤɨɧɨɦ ɇɶɸɬɨɧɚ ɭɫɤɨɪɟɧɢɟ ɰɟɧɬɪɚ ɦɚɫɫ ɪɚɜɧɨ ɧɭɥɸ:
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ɉɪɢ ɷɬɨɦ ɰɟɧɬɪ ɦɚɫɫ ɞɚɧɧɨɣ ɫɢɫɬɟɦɵ ɬɟɥ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɣ ɛɭɞɟɬ ɞɜɢɝɚɬɶɫɹ ɜɞɨɥɶ ɨɫɢ X ɫ ɩɨɫɬɨɹɧɧɨɣ ɫɤɨɪɨɫɬɶɸ ɢɥɢ ɩɨɤɨɢɬɶɫɹ.
Ⱦɢɮɮɟɪɟɧɰɢɪɭɹ (8.76) ɞɜɚɠɞɵ ɩɨ ɜɪɟɦɟɧɢ ɫ ɭɱɟɬɨɦ (8.75) ɢ (8.77), ɩɨɥɭɱɚɟɦ ɫɥɟɞɭɸɳɟɟ ɭɪɚɜɧɟɧɢɟ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɜɹɡɢ ɞɥɹ ɭɫɤɨɪɟɧɢɣ:
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sinD D cosD 0 . |
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ɉɪɢ ɦɚɥɵɯ ɭɝɥɚɯ ɨɬɤɥɨɧɟɧɢɹ ɦɚɹɬɧɢɤɚ ( sinD # D ) ɭɪɚɜɧɟɧɢɹ |
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(8.74), (8.75) ɢ (8.78) ɩɪɟɨɛɪɚɡɭɸɬɫɹ ɤ ɜɢɞɭ: |
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mglD mxM l , |
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xM (t) lD(t) , |
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(m M )xM mlD |
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ɉɨɥɭɱɟɧɧɚɹ ɫɢɫɬɟɦɚ ɭɪɚɜɧɟɧɢɣ (8.79) – (8.81) ɩɨɡɜɨɥɹɟɬ ɧɚɣ- |
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ɬɢ ɢɫɤɨɦɵɟ ɡɚɤɨɧɵ ɞɜɢɠɟɧɢɹ ɦɚɹɬɧɢɤɚ xm (t) |
ɢ ɬɟɥɟɠɤɢ xM (t) ɨɬ- |
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ɧɨɫɢɬɟɥɶɧɨ ɥɚɛɨɪɚɬɨɪɧɨɣ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ.
III. ɉɪɟɨɛɪɚɡɭɹ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ (8.79) – (8.81), ɩɨɥɭɱɚɟɦ ɭɪɚɜɧɟɧɢɟ ɝɚɪɦɨɧɢɱɟɫɤɢɯ ɤɨɥɟɛɚɧɢɣ (ɫɦ. ɮɨɪɦɭɥɭ (8.1) ɜ ɩ. 8.1.1. ɋɨɛɫɬɜɟɧɧɵɟ ɝɚɪɦɨɧɢɱɟɫɤɢɟ ɤɨɥɟɛɚɧɢɹ) ɦɚɹɬɧɢɤɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɟɥɟɠɤɢ:
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1 m / M D 0 . |
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ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɱɚɫɬɨɬɚ ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ ɦɚɹɬɧɢɤɚ Z0 |
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ɪɚɜɧɚ: |
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Z0 |
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1 m / M . |
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ɇɚ ɪɢɫ. 8.19 ɢɡɨɛɪɚɠɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶ ɱɚɫɬɨɬɵ ɤɨɥɟɛɚɧɢɣ ɦɚ- |
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ɹɬɧɢɤɚ |
Z0 |
ɨɬ ɨɬɧɨɲɟɧɢɹ ɦɚɫɫ |
m / M ɦɚɹɬɧɢɤɚ ɢ ɬɟɥɟɠɤɢ (ɩɪɢ |
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l = 2 ɦ). Ɉɬɦɟɬɢɦ, ɱɬɨ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɦɚɫɫɵ ɦɚɹɬɧɢɤɚ ɱɚɫɬɨɬɚ ɤɨɥɟɛɚɧɢɣ ɦɨɧɨɬɨɧɧɨ ɜɨɡɪɚɫɬɚɟɬ, ɚ ɩɪɢ ɞɨɫɬɚɬɨɱɧɨ ɦɚɥɨɣ ɦɚɫɫɟ ɦɚɹɬɧɢɤɚ m M ɱɚɫɬɨɬɚ ɟɝɨ ɤɨɥɟɛɚɧɢɣ ɫɨɜɩɚɞɚɟɬ ɫ ɱɚɫɬɨɬɨɣ ɤɨɥɟ-
292 ɆȿɏȺɇɂɄȺ. ɆȿɌɈȾɂɄȺ Ɋȿɒȿɇɂə ɁȺȾȺɑ
ɛɚɧɢɣ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɚɹɬɧɢɤɚ ɫ ɧɟɩɨɞɜɢɠɧɨɣ ɬɨɱɤɨɣ ɩɨɞɜɟɫɚ
(8.17) – Z0 |
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Ɋɢɫ. 8.19 |
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Ɋɟɲɟɧɢɟɦ ɭɪɚɜɧɟɧɢɹ (8.82) ɹɜɥɹɟɬɫɹ ɝɚɪɦɨɧɢɱɟɫɤɚɹ ɮɭɧɤɰɢɹ: |
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D(t) |
Acos(Z0t M0 ) . |
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(8.84) |
Ⱥɦɩɥɢɬɭɞɚ |
A ɢ ɧɚɱɚɥɶɧɚɹ ɮɚɡɚ M0 |
ɜ (8.84) ɨɩɪɟɞɟɥɹɸɬɫɹ ɧɚɱɚɥɶ- |
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ɧɵɦɢ ɭɫɥɨɜɢɹɦɢ, ɤɨɬɨɪɵɟ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɭɫɥɨɜɢɹɦɢ ɡɚɞɚɱɢ ɡɚɩɢɫɵɜɚɸɬɫɹ ɜ ɜɢɞɟ:
D(t |
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0 , |
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(8.85) |
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V0 |
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0) |
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ȼ ɪɟɡɭɥɶɬɚɬɟ ɞɥɹ ɭɝɥɚ ɨɬɤɥɨɧɟɧɢɹ ɦɚɹɬɧɢɤɚ ɢɦɟɟɦ:
D(t) |
V0 |
cos(Z0t S / 2) |
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sin(Z0t) . |
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Ⱦɢɮɮɟɪɟɧɰɢɪɭɹ (8.87) ɞɜɚɠɞɵ ɩɨ ɜɪɟɦɟɧɢ ɢ ɩɨɞɫɬɚɜɥɹɹ D ɜ (8.81) ɩɨɥɭɱɚɟɦ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ ɞɥɹ ɤɨɨɪɞɢɧɚɬɵ ɬɟɥɟɠɤɢ xM :
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m / M |
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xM |
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ɂɧɬɟɝɪɢɪɭɹ (8.88) ɫ ɧɚɱɚɥɶɧɵɦɢ ɭɫɥɨɜɢɹɦɢ |
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xM (t |
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V0 , |
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ȽɅȺȼȺ 8. ɋɜɨɛɨɞɧɵɟ ɢ ɜɵɧɭɠɞɟɧɧɵɟ ɤɨɥɟɛɚɧɢɹ |
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ɧɚɯɨɞɢɦ ɢɫɤɨɦɵɣ ɡɚɤɨɧ ɞɜɢɠɟɧɢɹ ɬɟɥɟɠɤɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɥɚɛɨɪɚɬɨɪɧɨɣ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ:
xM |
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V0t AM sin(Z0t) , |
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ɝɞɟ |
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A |
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ɇɚ ɪɢɫ. 8.20 ɢɡɨɛɪɚɠɟɧɵ ɡɚɜɢɫɢɦɨɫɬɢ ɤɨɨɪɞɢɧɚɬɵ ɬɟɥɟɠɤɢ |
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xM (t) ɨɬ ɜɪɟɦɟɧɢ |
ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɹɯ ɨɬɧɨɲɟɧɢɹ |
ɦɚɫɫ |
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m / M ɦɚɹɬɧɢɤɚ ɢ ɬɟɥɟɠɤɢ. |
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Ɂɚɜɢɫɢɦɨɫɬɢ ɩɨɥɭɱɟɧɵ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (8.91) ɩɪɢ ɡɧɚɱɟɧɢɹɯ |
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ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɬɟɥɟɠɤɢ V0 1ɦ/ɫ ɢ ɞɥɢɧɵ ɦɚɹɬɧɢɤɚ l |
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Ʉɚɤ ɜɢɞɢɦ, ɩɨɫɬɭɩɚɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɬɟɥɟɠɤɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ
ɫɭɩɟɪɩɨɡɢɰɢɸ ɞɜɢɠɟɧɢɹ ɫ ɩɨɫɬɨɹɧɧɨɣ ɫɤɨɪɨɫɬɶɸ |
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ɝɚɪɦɨɧɢɱɟɫɤɢɯ ɤɨɥɟɛɚɧɢɣ ɫ ɱɚɫɬɨɬɨɣ Z0 ɢ ɚɦɩɥɢɬɭɞɨɣ |
AM (ɫɦ. |
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(8.91)). |
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Ɋɢɫ. 8.20 |
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Ɋɢɫ. 8.21 |
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ɆȿɏȺɇɂɄȺ. ɆȿɌɈȾɂɄȺ Ɋȿɒȿɇɂə ɁȺȾȺɑ |
Ɂɚɦɟɬɢɦ, ɱɬɨ ɩɪɢ ɞɨɫɬɚɬɨɱɧɨ ɦɚɥɨɣ ɦɚɫɫɟ ɦɚɹɬɧɢɤɚ m M ɤɨɥɟɛɚɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɬɟɥɟɠɤɢ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɡɚɦɟɬɧɨ, ɩɨɫɤɨɥɶɤɭ ɩɪɨɢɫɯɨɞɢɬ ɫ ɦɚɥɵɦɢ ɚɦɩɥɢɬɭɞɨɣ AM ɢ ɱɚɫɬɨɬɨɣ.
ɂɫɤɨɦɵɣ ɡɚɤɨɧ ɞɜɢɠɟɧɢɹ ɦɚɹɬɧɢɤɚ xm (t) ɨɬɧɨɫɢɬɟɥɶɧɨ ɥɚ-
ɛɨɪɚɬɨɪɧɨɣ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ ɧɚɯɨɞɢɦ, ɢɫɩɨɥɶɡɭɹ ɩɪɢɧɰɢɩ ɫɭɩɟɪɩɨɡɢɰɢɢ ɞɜɢɠɟɧɢɣ (8.90) ɢ ɩɨɥɭɱɟɧɧɵɟ ɡɚɤɨɧɵ ɢɡɦɟɧɟɧɢɹ ɭɝɥɚ ɨɬɤɥɨɧɟɧɢɹ D(t) ɦɚɹɬɧɢɤɚ (8.87) ɢ ɞɜɢɠɟɧɢɹ xM (t)
ɬɟɥɟɠɤɢ (8.91):
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V0t |
Am sin(Z0t) , |
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1 m / M |
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ɝɞɟ |
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ɇɚ ɪɢɫ. 8.21 ɢɡɨɛɪɚɠɟɧɵ ɡɚɜɢɫɢɦɨɫɬɢ ɤɨɨɪɞɢɧɚɬɵ ɦɚɹɬɧɢɤɚ xm (t) ɨɬ ɜɪɟɦɟɧɢ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɹɯ ɨɬɧɨɲɟɧɢɹ ɦɚɫɫ m / M
ɦɚɹɬɧɢɤɚ ɢ ɬɟɥɟɠɤɢ. Ɂɚɜɢɫɢɦɨɫɬɢ ɩɨɥɭɱɟɧɵ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (8.93) ɩɪɢ ɬɟɯ ɠɟ ɡɧɚɱɟɧɢɹɯ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɬɟɥɟɠɤɢ ɢ ɞɥɢɧɵ ɦɚɹɬɧɢɤɚ, ɱɬɨ ɢ ɜ ɫɥɭɱɚɟ ɪɚɫɱɟɬɚ ɡɚɜɢɫɢɦɨɫɬɟɣ ɤɨɨɪɞɢɧɚɬɵ ɬɟɥɟɠɤɢ (ɫɦ. ɪɢɫ. 8.20). Ʉɚɤ ɜɢɞɢɦ, ɞɜɢɠɟɧɢɟ ɦɚɹɬɧɢɤɚ, ɤɚɤ ɢ ɜ ɫɥɭɱɚɟ ɬɟɥɟɠɤɢ, ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɭɩɟɪɩɨɡɢɰɢɸ ɞɜɢɠɟɧɢɹ ɫ ɬɨɣ ɠɟ ɩɨɫɬɨɹɧɧɨɣ
1
ɫɤɨɪɨɫɬɶɸ 1 m / M V0 ɢ ɝɚɪɦɨɧɢɱɟɫɤɢɯ ɤɨɥɟɛɚɧɢɣ ɫ ɬɨɣ ɠɟ ɱɚɫɬɨ-
ɬɨɣ Z0 , ɧɨ ɞɪɭɝɨɣ ɚɦɩɥɢɬɭɞɨɣ Am (ɫɦ. (8.94)). Ɂɚɦɟɬɢɦ, ɱɬɨ ɤɨɥɟ-
ɛɚɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɦɚɹɬɧɢɤɚ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɡɚɦɟɬɧɨ ɩɪɢ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɣ ɦɚɫɫɟ ɦɚɹɬɧɢɤɚ m !! M , ɩɨɫɤɨɥɶɤɭ ɩɪɨɢɫɯɨɞɢɬ ɫ ɦɚɥɨɣ ɚɦɩɥɢɬɭɞɨɣ Am .
ɇɚ ɪɢɫ. 8.22 ɢɡɨɛɪɚɠɟɧɵ ɡɚɜɢɫɢɦɨɫɬɢ ɚɦɩɥɢɬɭɞ ɤɨɥɟɛɚɧɢɣ ɬɟɥɟɠɤɢ AM ɢ ɦɚɹɬɧɢɤɚ Am ɨɬ ɫɨɨɬɧɨɲɟɧɢɹ ɢɯ ɦɚɫɫ ɩɪɢ ɭɤɚɡɚɧɧɵɯ ɜɵɲɟ ɡɧɚɱɟɧɢɹɯ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɬɟɥɟɠɤɢ ɢ ɞɥɢɧɵ ɦɚɹɬɧɢɤɚ. Ʉɚɤ ɜɢɞɢɦ, ɚɦɩɥɢɬɭɞɚ ɤɨɥɟɛɚɧɢɣ ɦɚɹɬɧɢɤɚ Am ɦɨɧɨɬɨɧɧɨ ɭɦɟɧɶɲɚɟɬɫɹ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɨɬɧɨɲɟɧɢɹ ɦɚɫɫ m / M . ɉɪɢ ɷɬɨɦ ɚɦɩɥɢɬɭɞɚ ɤɨɥɟɛɚɧɢɣ ɬɟɥɟɠɤɢ AM ɫɧɚɱɚɥɚ ɜɨɡɪɚɫɬɚɟɬ, ɞɨɫɬɢɝɚɹ ɦɚɤɫɢɦɭɦɚ, ɚ ɡɚɬɟɦ ɦɨɧɨɬɨɧɧɨ ɭɛɵɜɚɟɬ.
296 ɆȿɏȺɇɂɄȺ. ɆȿɌɈȾɂɄȺ Ɋȿɒȿɇɂə ɁȺȾȺɑ
Ɋɟɲɟɧɢɟ
I. ɇɚ ɬɟɥɨ ɜ ɩɪɨɰɟɫɫɟ ɞɜɢɠɟɧɢɹ ɞɟɣɫɬɜɭɸɬ ɫɢɥɚ ɬɹɠɟɫɬɢ mg , ɫɢɥɚ ɧɨɪɦɚɥɶɧɨɣ ɪɟɚɤɰɢɢ ɨɩɨɪɵ N ɢ ɫɢɥɚ ɬɪɟɧɢɹ ɩɨɤɨɹ Fɬɪ ɜ
ɬɨɱɤɟ ɫɨɩɪɢɤɨɫɧɨɜɟɧɢɹ ɬɟɥɚ ɫ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɶɸ (ɫɦ. ɪɢɫ. 8.23). ɋɢɥɨɣ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜɨɡɞɭɯɚ ɩɪɟɧɟɛɪɟɝɚɟɦ. Ɍɟɥɨ ɜɪɚɳɟɧɢɹ ɢ ɨɩɨɪɭ ɫɱɢɬɚɟɦ ɚɛɫɨɥɸɬɧɨ ɬɜɟɪɞɵɦɢ ɬɟɥɚɦɢ, ɩɨɷɬɨɦɭ ɬɪɟɧɢɟ ɤɚɱɟɧɢɹ ɧɟ ɭɱɢɬɵɜɚɟɦ.
Ɂɚɞɚɱɭ ɪɟɲɚɟɦ ɷɧɟɪɝɟɬɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ. Ɇɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɬɟɥɚ, ɤɚɬɚɸɳɟɝɨɫɹ ɛɟɡ ɩɪɨɫɤɚɥɶɡɵɜɚɧɢɹ ɩɨ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɫɨɯɪɚɧɹɟɬɫɹ, ɩɨɫɤɨɥɶɤɭ ɫɭɦɦɚɪɧɚɹ ɪɚɛɨɬɚ ɜɫɟɯ ɧɟɩɨɬɟɧɰɢɚɥɶɧɵɯ ɫɢɥ, ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɧɟɝɨ, ɪɚɜɧɚ ɧɭɥɸ (ɫɦ. ɩ. 3.1.3 ɜ Ƚɥɚɜɟ 3).
II. Ʉɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɬɟɥɚ ɩɨ ɬɟɨɪɟɦɟ Ʉɟɧɢɝɚ ɪɚɜɧɚ ɫɭɦɦɟ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɬɟɥɚ ɫɨ ɫɤɨɪɨɫɬɶɸ, ɪɚɜɧɨɣ ɫɤɨɪɨɫɬɢ ɰɟɧɬɪɚ ɦɚɫɫ V , ɢ ɷɧɟɪɝɢɢ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɫ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ Z ɜɨɤɪɭɝ ɨɫɢ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɰɟɧɬɪ ɦɚɫɫ (ɫɦ. (7.10) ɜ ɩ. 7.1. Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ ɜ Ƚɥɚɜɟ 7):
E k |
mV 2 |
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JZ2 |
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(8.95) |
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Ɂɞɟɫɶ J – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɬɟɥɚ, ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɰɟɧɬɪ ɦɚɫɫ, ɚ ɫɤɨɪɨɫɬɶ ɰɟɧɬɪɚ ɦɚɫɫ ɬɟɥɚ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫ. 8.22 ɪɚɜɧɚ
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(8.96) |
V (R r)D , |
ɝɞɟ D – ɭɝɨɥ, ɡɚɞɚɸɳɢɣ ɩɨɥɨɠɟɧɢɟ ɰɟɧɬɪɚ ɦɚɫɫ ɬɟɥɚ ɧɚ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ.
ȿɫɥɢ ɩɪɢɧɹɬɶ ɩɨɬɟɧɰɢɚɥɶɧɭɸ ɷɧɟɪɝɢɸ ɬɟɥɚ ɜ ɩɨɥɨɠɟɧɢɢ ɟɝɨ ɪɚɜɧɨɜɟɫɢɹ ɪɚɜɧɨɣ ɧɭɥɸ, ɬɨ ɩɪɢ ɨɬɤɥɨɧɟɧɢɢ ɰɟɧɬɪɚ ɦɚɫɫ ɧɚ ɭɝɨɥ D ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɫɬɚɧɨɜɢɬɫɹ ɪɚɜɧɨɣ (ɫɦ. ɪɢɫ. 8.23)
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E p |
mg(R r)(1 cosD) | |
mg |
(R r)D 2 . |
(8.97) |
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ɉɨɫɤɨɥɶɤɭ ɦɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɬɟɥɚ ɫɨɯɪɚɧɹɟɬɫɹ, ɬɨ |
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(8.98) |
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ɉɨɫɤɨɥɶɤɭ ɬɟɥɨ ɨɫɭɳɟɫɬɜɥɹɟɬ ɩɥɨɫɤɨɟ ɞɜɢɠɟɧɢɟ, ɪɚɫɫɦɨɬɪɢɦ ɷɬɨ ɞɜɢɠɟɧɢɟ ɤɚɤ ɜɪɚɳɟɧɢɟ ɜɨɤɪɭɝ ɦɝɧɨɜɟɧɧɨɣ ɨɫɢ ɫ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ Z . ɉɨ ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ ɤɚɱɟɧɢɟ ɩɪɨɢɫɯɨɞɢɬ ɛɟɡ ɩɪɨɫɤɚɥɶɡɵɜɚɧɢɹ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɦɝɧɨɜɟɧɧɚɹ ɨɫɶ ɜɪɚɳɟɧɢɹ ɩɪɨɯɨɞɢɬ ɱɟɪɟɡ
ȽɅȺȼȺ 8. ɋɜɨɛɨɞɧɵɟ ɢ ɜɵɧɭɠɞɟɧɧɵɟ ɤɨɥɟɛɚɧɢɹ |
297 |
ɬɨɱɤɢ ɫɨɩɪɢɤɨɫɧɨɜɟɧɢɹ ɬɟɥɚ ɫ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɶɸ ɢ ɫɤɨɪɨɫɬɶ ɰɟɧɬɪɚ ɦɚɫɫ ɬɟɥɚ ɪɚɜɧɚ:
V Zr . |
(8.99) |
ɉɪɢɪɚɜɧɢɜɚɹ ɩɪɚɜɵɟ ɱɚɫɬɢ ɜɵɪɚɠɟɧɢɣ (8.96) ɢ (8.99) ɞɥɹ ɫɤɨɪɨɫɬɢ ɰɟɧɬɪɚ ɦɚɫɫ, ɩɨɥɭɱɚɟɦ ɭɪɚɜɧɟɧɢɟ ɤɢɧɟɦɚɬɢɱɟɫɤɨɣ ɫɜɹɡɢ ɞɥɹ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ Z ɬɟɥɚ ɜɨɤɪɭɝ ɨɫɢ, ɩɪɨɯɨɞɹɳɟɣ
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ɱɟɪɟɡ ɰɟɧɬɪ ɦɚɫɫ, ɢ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ D ɰɟɧɬɪɚ ɦɚɫɫ ɜɨ- |
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ɤɪɭɝ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɨɫɢ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ: |
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(8.100) |
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III. Ɋɟɲɚɹ ɫɨɜɦɟɫɬɧɨ ɭɪɚɜɧɟɧɢɹ (8.95) – (8.98) ɢ (8.100), ɩɨ- |
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ɥɭɱɚɟɦ ɭɪɚɜɧɟɧɢɟ ɝɚɪɦɨɧɢɱɟɫɤɢɯ ɤɨɥɟɛɚɧɢɣ ɬɟɥɚ: |
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ɋɪɚɜɧɢɜɚɹ (8.101) ɫ (8.1), ɩɨɥɭɱɚɟɦ ɢɫɤɨɦɨɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɱɚɫɬɨɬɵ ɫɨɛɫɬɜɟɧɧɵɯ ɝɚɪɦɨɧɢɱɟɫɤɢɯ ɤɨɥɟɛɚɧɢɣ ɬɟɥɚ ɜɪɚɳɟɧɢɹ:
Z0 |
mgr 2 |
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(8.102) |
(R r)(mr |
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ȼ ɱɚɫɬɧɨɫɬɢ, ɞɥɹ ɫɩɥɨɲɧɨɝɨ ɰɢɥɢɧɞɪɚ |
¨ J |
ɰɢɥ |
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ɢ ɲɚɪɚ |
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¨ Jɲɚɪ |
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¸ ɩɨɥɭɱɟɧɧɨɟ ɜɵɪɚɠɟɧɢɟ ɩɪɢɧɢɦɚɟɬ ɜɢɞ: |
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Z0ɰɢɥ |
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2g |
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Z0ɲɚɪ |
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5g |
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Ɂɚɞɚɱɚ 8.5
(ɋɜɨɛɨɞɧɵɟ ɧɟɡɚɬɭɯɚɸɳɢɟ ɤɨɥɟɛɚɧɢɹ)
Ɉɩɪɟɞɟɥɢɬɶ ɱɚɫɬɨɬɭ Z0 ɦɚɥɵɯ ɫɨɛɫɬɜɟɧɧɵɯ ɝɚɪɦɨɧɢɱɟɫɤɢɯ
ɤɨɥɟɛɚɧɢɣ ɠɢɞɤɨɫɬɢ ɜ ɬɨɧɤɨɣ ɬɪɭɛɤɟ U-ɨɛɪɚɡɧɨɣ ɮɨɪɦɵ ɫ ɢɡɦɟɧɹɸɳɢɦɫɹ ɜɞɨɥɶ ɬɪɭɛɤɢ ɩɨɩɟɪɟɱɧɵɦ ɫɟɱɟɧɢɟɦ, ɩɨɦɟɳɟɧɧɨɣ ɜ ɩɨɥɟ ɫɢɥ ɬɹɠɟɫɬɢ Ɂɟɦɥɢ. ɋɱɢɬɚɬɶ ɡɚɞɚɧɧɨɣ ɡɚɜɢɫɢɦɨɫɬɶ ɩɥɨɳɚɞɢ ɩɨ-
298 |
ɆȿɏȺɇɂɄȺ. ɆȿɌɈȾɂɄȺ Ɋȿɒȿɇɂə ɁȺȾȺɑ |
ɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɬɪɭɛɤɢ S ɨɬ ɤɨɨɪɞɢɧɚɬɵ s ɜɞɨɥɶ ɬɪɭɛɤɢ, ɚ ɬɚɤɠɟ ɞɥɢɧɭ ɡɚɩɨɥɧɟɧɧɨɣ ɠɢɞɤɨɫɬɶɸ ɱɚɫɬɢ ɬɪɭɛɤɢ L.
Ɋɟɲɟɧɢɟ
I. ɉɨɫɤɨɥɶɤɭ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ ɧɟ ɨɝɨɜɚɪɢɜɚɟɬɫɹ ɢɧɨɟ, ɠɢɞɤɨɫɬɶ ɛɭɞɟɦ ɫɱɢɬɚɬɶ ɧɟɜɹɡɤɨɣ ɢ ɧɟɫɠɢɦɚɟɦɨɣ. Ɂɚɞɚɱɭ ɪɟɲɚɟɦ ɷɧɟɪɝɟɬɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ. ɉɪɢɦɟɦ ɡɚ ɧɨɥɶ ɨɬɫɱɟɬɚ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɠɢɞɤɨɫɬɢ ɟɟ ɩɨɥɨɠɟɧɢɟ ɪɚɜɧɨɜɟɫɢɹ. ɉɨ ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ ɫɨɨɛɳɚɸɳɢɟɫɹ ɫɨɫɭɞɵ ɢɦɟɸɬ ɧɟɩɪɚɜɢɥɶɧɭɸ ɮɨɪɦɭ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɫɦɟɳɟɧɢɟ ɪɚɡɥɢɱɧɵɯ ɱɚɫɬɢɰ ɠɢɞɤɨɫɬɢ ɩɪɢ ɤɨɥɟɛɚɧɢɹɯ ɛɭɞɟɬ ɪɚɡɥɢɱɧɨ, ɜ ɨɬɥɢɱɢɟ ɨɬ ɤɨɥɟɛɚɧɢɣ ɜ ɬɪɭɛɤɟ ɫ ɩɨɫɬɨɹɧɧɵɦ ɩɨɩɟɪɟɱɧɵɦ ɫɟɱɟɧɢɟɦ. ȼɜɟɞɟɦ ɨɛɨɡɧɚɱɟɧɢɹ: A1 – ɚɦɩɥɢɬɭɞɚ ɦɚɥɵɯ ɝɚɪɦɨɧɢɱɟɫɤɢɯ ɤɨɥɟɛɚɧɢɣ ɠɢɞɤɨɫɬɢ ɜ ɥɟɜɨɦ ɤɨɥɟɧɟ ɬɪɭɛɤɢ, A2 – ɚɦɩɥɢɬɭɞɚ ɦɚɥɵɯ ɝɚɪɦɨɧɢɱɟɫɤɢɯ ɤɨɥɟɛɚɧɢɣ ɜ ɩɪɚɜɨɦ ɤɨɥɟɧɟ, ȡ – ɩɥɨɬɧɨɫɬɶ ɠɢɞɤɨɫɬɢ.
II. ɉɭɫɬɶ ɩɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɬɪɭɛɤɢ ɟɫɬɶ ɢɡɜɟɫɬɧɚɹ ɮɭɧɤɰɢɹ ɤɨɨɪɞɢɧɚɬɵ ɜɞɨɥɶ ɬɪɭɛɤɢ S(s). Ɇɚɫɫɚ ɜɫɟɣ ɠɢɞɤɨɫɬɢ
L
ɪɚɜɧɚ m ³USds (L – ɞɥɢɧɚ ɡɚɩɨɥɧɟɧɧɨɣ ɠɢɞɤɨɫɬɶɸ ɱɚɫɬɢ ɬɪɭɛɤɢ).
0
Ʉɨɥɟɛɚɧɢɹ ɫɱɢɬɚɟɦ ɦɚɥɵɦɢ, ɩɨɷɬɨɦɭ ɩɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɬɪɭɛɤɢ ɧɚ ɪɚɫɫɬɨɹɧɢɢ ɞɜɨɣɧɨɣ ɚɦɩɥɢɬɭɞɵ ɤɨɥɟɛɚɧɢɣ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɧɟɢɡɦɟɧɧɨɣ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɟɫɥɢ S1 ɢ S2 – ɩɥɨɳɚɞɢ ɫɟɱɟ-
ɧɢɹ ɩɪɚɜɨɣ ɢ ɥɟɜɨɣ ɫɜɨɛɨɞɧɵɯ ɩɨɜɟɪɯɧɨɫɬɟɣ ɧɟɫɠɢɦɚɟɦɨɣ ɠɢɞɤɨɫɬɢ ɜ ɬɪɭɛɤɟ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɬɨ
A1S1 A2 S2 . |
(8.105) |
Ȼɭɞɟɦ ɨɬɫɱɢɬɵɜɚɬɶ ɤɨɨɪɞɢɧɚɬɭ s ɨɬ ɥɟɜɨɣ ɫɜɨɛɨɞɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɠɢɞɤɨɫɬɢ ɜ ɩɨɥɨɠɟɧɢɢ ɪɚɜɧɨɜɟɫɢɹ. Ʉɨɨɪɞɢɧɚɬɚ ɩɪɚɜɨɣ ɫɜɨɛɨɞɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɜ ɩɨɥɨɠɟɧɢɢ ɪɚɜɧɨɜɟɫɢɹ ɪɚɜɧɚ ɞɥɢɧɟ ɫɬɨɥɛɚ ɠɢɞɤɨɫɬɢ s L . Ⱥɦɩɥɢɬɭɞɭ ɤɨɥɟɛɚɧɢɣ A ɜ ɫɟɱɟɧɢɢ ɫ ɩɪɨɢɡɜɨɥɶɧɨɣ ɤɨɨɪɞɢɧɚɬɨɣ 0 d s d L ɩɥɨɳɚɞɶɸ S ɧɚɯɨɞɢɦ ɢɡ ɭɫɥɨɜɢɹ A1S1 AS ,
ɚɧɚɥɨɝɢɱɧɨɝɨ (8.105). Ɍɨɝɞɚ ɜ ɫɥɭɱɚɟ ɝɚɪɦɨɧɢɱɟɫɤɢɯ ɤɨɥɟɛɚɧɢɣ ɚɦɩɥɢɬɭɞɚ V ɤɨɥɟɛɚɧɢɣ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰ ɠɢɞɤɨɫɬɢ ɜ ɫɟɱɟɧɢɢ ɬɪɭɛɤɢ ɫ ɤɨɨɪɞɢɧɚɬɨɣ s ɪɚɜɧɚ
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Ɂɚɩɢɲɟɦ |
ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɜɫɟɣ ɠɢɞɤɨɫɬɢ ɜ ɦɨɦɟɧɬ |
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ɩɪɨɯɨɠɞɟɧɢɹ ɟɸ ɩɨɥɨɠɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ:
ȽɅȺȼȺ 8. ɋɜɨɛɨɞɧɵɟ ɢ ɜɵɧɭɠɞɟɧɧɵɟ ɤɨɥɟɛɚɧɢɹ |
299 |
Emaxk |
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U S ds V 2 |
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UZ2 A2 S 2 L ds |
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ɑɟɪɟɡ ɱɟɬɜɟɪɬɶ ɩɟɪɢɨɞɚ ɜɫɹ ɷɧɟɪɝɢɹ ɛɭɞɟɬ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɢ |
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ɨɩɪɟɞɟɥɹɬɶɫɹ ɪɚɛɨɬɨɣ ɫɢɥ ɬɹɠɟɫɬɢ ɩɨ ɩɟɪɟɦɟɳɟɧɢɸ ɨɛɴɟɦɚ ɠɢɞɤɨ-
ɫɬɢ A S |
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Emax |
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ɉɨɫɤɨɥɶɤɭ ɫɢɥɚɦɢ ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ ɢ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜɨɡɞɭɯɚ |
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ɩɪɟɧɟɛɪɟɝɚɟɦ, ɦɟɯɚɧɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɠɢɞɤɨɫɬɢ ɫɨɯɪɚɧɹɟɬɫɹ: |
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III. ɉɨɞɫɬɚɜɥɹɹ (8.107) ɢ (8.108) ɜ (8.109), ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɱɚɫɬɨɬɵ ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ ɠɢɞɤɨɫɬɢ Z0 :
2 |
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ɂɡ (8.110) ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɫɥɟɞɭɟɬ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɢɫɤɨɦɨɣ ɱɚɫɬɨɬɵ ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ ɠɢɞɤɨɫɬɢ ɜ ɬɪɭɛɤɟ:
Z0 |
g S1 S2 |
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(8.111) |
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ɉɨɥɭɱɟɧɧɨɟ ɜɵɪɚɠɟɧɢɟ (8.111) ɩɪɢ S = const ɩɟɪɟɯɨɞɢɬ ɜ ɢɡɜɟɫɬɧɭɸ ɮɨɪɦɭɥɭ ɞɥɹ ɱɚɫɬɨɬɵ ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ ɠɢɞɤɨɫɬɢ ɜ U-ɨɛɪɚɡɧɨɣ ɬɪɭɛɤɟ ɫ ɩɨɫɬɨɹɧɧɵɦ ɩɨɩɟɪɟɱɧɵɦ ɫɟɱɟɧɢɟɦ:
Z0 |
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Ɂɚɞɚɱɚ 8.6
(ɋɜɨɛɨɞɧɵɟ ɡɚɬɭɯɚɸɳɢɟ ɤɨɥɟɛɚɧɢɹ)
ɋɬɭɩɟɧɱɚɬɵɣ ɰɢɥɢɧɞɪɢɱɟɫɤɢɣ ɛɥɨɤ ɦɨɠɟɬ ɜɪɚɳɚɬɶɫɹ ɛɟɡ ɬɪɟɧɢɹ ɜɨɤɪɭɝ ɡɚɤɪɟɩɥɟɧɧɨɣ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɨɫɢ, ɫɨɜɩɚɞɚɸɳɢɣ ɫ ɨɫɶɸ ɫɢɦɦɟɬɪɢɢ ɛɥɨɤɚ. Ɋɚɞɢɭɫɵ ɰɢɥɢɧɞɪɨɜ ɛɥɨɤɚ – R ɢ r . Ɇɨɦɟɧɬ ɢɧɟɪɰɢɢ ɛɥɨɤɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɭɤɚɡɚɧɧɨɣ ɨɫɢ ɪɚɜɟɧ J . ɇɚ ɰɢɥɢɧɞɪɵ ɧɚɦɨɬɚɧɵ ɞɜɟ ɧɟɜɟɫɨɦɵɟ ɧɟɪɚɫɬɹɠɢɦɵɟ ɧɢɬɢ, ɧɚɱɚɥɚ ɤɨɬɨɪɵɯ ɡɚɤɪɟɩɥɟɧɵ ɧɚ ɪɚɡɧɵɯ ɰɢɥɢɧɞɪɚɯ. ɇɚ ɤɨɧɰɟ ɩɪɚɜɨɣ ɧɢɬɢ ɜɢɫɢɬ
300 |
ɆȿɏȺɇɂɄȺ. ɆȿɌɈȾɂɄȺ Ɋȿɒȿɇɂə ɁȺȾȺɑ |
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ɬɟɥɨ ɦɚɫɫɨɣ m . Ʉɨɧɟɰ ɥɟɜɨɣ ɧɢɬɢ ɩɪɢɤɪɟ- |
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ɩɥɟɧ ɤ ɥɟɝɤɨɣ ɩɪɭɠɢɧɟ ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦ |
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ɠɟɫɬɤɨɫɬɢ |
k , ɧɢɠɧɢɣ ɤɨɧɟɰ ɤɨɬɨɪɨɣ ɡɚ- |
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ɤɪɟɩɥɟɧ ɬɚɤ, ɱɬɨ ɨɫɶ ɩɪɭɠɢɧɵ ɜɟɪɬɢɤɚɥɶɧɚ |
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(ɪɢɫ. 8.24). Ɍɟɥɨ ɫɨɜɟɪɲɚɟɬ ɦɚɥɵɟ ɜɟɪɬɢ- |
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ɤɚɥɶɧɵɟ ɤɨɥɟɛɚɧɢɹ ɜ ɠɢɞɤɨɫɬɢ ɫ ɤɨɷɮɮɢ- |
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ɰɢɟɧɬɨɦ ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ K . Ɉɩɪɟɞɟɥɢɬɶ |
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ɡɚɤɨɧ ɞɜɢɠɟɧɢɹ ɬɟɥɚ, ɟɫɥɢ ɜ ɩɨɥɨɠɟɧɢɢ |
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ɪɚɜɧɨɜɟɫɢɹ ɟɦɭ ɫɨɨɛɳɢɥɢ ɫɤɨɪɨɫɬɶ V0 . |
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Ɋɟɲɟɧɢɟ |
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I. Ɂɚɞɚɱɭ ɪɟɲɚɟɦ ɞɢɧɚɦɢɱɟɫɤɢɦ ɦɟ- |
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ɬɨɞɨɦ ɜ ɥɚɛɨɪɚɬɨɪɧɨɣ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫ- |
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Ɋɢɫ. 8.24 |
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ɬɟɦɟ ɨɬɫɱɟɬɚ. ɇɚɩɪɚɜɢɦ ɨɫɶ X ɞɟɤɚɪɬɨɜɨɣ |
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ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ ɜɟɪɬɢɤɚɥɶɧɨ ɜɧɢɡ (ɫɦ.
ɪɢɫ. 8.25). ɇɚ ɬɟɥɨ ɦɚɫɫɨɣ m ɞɟɣɫɬɜɭɸɬ ɱɟɬɵɪɟ ɫɢɥɵ – ɫɢɥɚ ɬɹɠɟɫɬɢ mg, ɫɢɥɚ Ⱥɪɯɢɦɟɞɚ FAɪɯ, ɫɢɥɚ ɧɚɬɹɠɟɧɢɹ ɧɢɬɢ T1 ɢ ɫɢɥɚ ɜɹɡɤɨɝɨ ɬɪɟɧɢɹ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚɹ ɫɤɨɪɨɫɬɢ ɬɟɥɚ Fɬɪ K x (ɫɦ. (2.12) ɜ ɩ. 2.1.2.ȼ Ƚɥɚɜɵ 2). ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɭɤɚɡɚɧɧɵɯ ɫɢɥ ɬɟɥɨ ɫɨɜɟɪɲɚɟɬ
ɜɟɪɬɢɤɚɥɶɧɵɟ ɡɚɬɭɯɚɸɳɢɟ ɤɨɥɟɛɚɧɢɹ. |
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II. Ɂɚɩɢɲɟɦ ɭɪɚɜɧɟɧɢɟ |
ɞɜɢɠɟɧɢɹ |
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ɬɟɥɚ ɜ ɩɪɨɟɤɰɢɢ ɧɚ ɨɫɶ ɏ: |
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mg FȺɪɯ |
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(8.113) |
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mx |
T1 K x . |
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Ɂɚɩɢɲɟɦ ɬɚɤɠɟ ɭɪɚɜɧɟɧɢɟ ɦɨɦɟɧɬɨɜ |
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ɞɥɹ ɛɥɨɤɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɡɚɤɪɟɩɥɟɧɧɨɣ ɨɫɢ, |
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ɫɨɜɩɚɞɚɸɳɟɣ ɫ ɨɫɶɸ ɫɢɦɦɟɬɪɢɢ ɛɥɨɤɚ ɢ |
T2 |
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ɧɚɩɪɚɜɥɟɧɧɨɣ ɡɚ |
ɩɥɨɫɤɨɫɬɶ |
ɱɟɪɬɟɠɚ |
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T1 |
xɩɪ |
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(ɪɢɫ. 8.25): |
T1r T2 R . |
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(8.114) |
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T1 |
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JD |
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FȺɪɯ |
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Ɂɞɟɫɶ D – ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɛɥɨɤɚ, T1 ɢ T2 – |
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x |
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ɫɢɥɵ ɧɚɬɹɠɟɧɢɹ ɩɪɚɜɨɣ ɢ ɥɟɜɨɣ ɧɢɬɟɣ, |
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Fɬɪ |
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X |
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ɞɟɣɫɬɜɭɸɳɢɟ ɧɚ ɛɥɨɤ. |
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ɇɢɬɶ |
ɫɱɢɬɚɟɦ |
ɧɟɜɟɫɨɦɨɣ, |
ɫɥɟɞɨɜɚ- |
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mg |
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ɬɟɥɶɧɨ, ɫɢɥɚ ɧɚɬɹɠɟɧɢɹ ɥɟɜɨɣ ɧɢɬɢ ɪɚɜɧɚ |
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ɫɢɥɟ ɭɩɪɭɝɨɫɬɢ, ɫ ɤɨɬɨɪɨɣ ɩɪɭɠɢɧɚ ɞɟɣɫɬ- |
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Ɋɢɫ. 8.25 |
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ɜɭɟɬ ɧɚ ɧɢɬɶ: |
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T2 k (xɩɪ xɩɪ,0 ) , |
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(8.115) |
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