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Файл:Расчет переходных процессов в электроэнергетических системах методом интеграла Дюамеля. Учебное пособие
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– ɧɚ ɷɬɚɩɟ V ɜ ɢɧɬɟɪɜɚɥɟ t4 t t
ܷ
ሺݐሻ
݅
ହ
ܮ
ˇଷ
ˇସ
ʬ
ଶ
ܴ
ʬ
ܮ
ʬ
ଶ
ܴ
ʬ
+ܽ
+ܽ
ௗ
=
݁
൬
݁
൬
+ ܽ
ቈ
ܴ
ʬ
௧ି௧
య
ି
த
ʬ
െ݁
௧ି௧
ర
ି
த
ʬ
െ݁
ˇହ
ܮ
ʬ
ܴ
ʬ
௧ି௧
ି
த
ʬ
௧ି௧
ି
த
ʬ
1
െܽ
ˇହ
ሺ
ܴ
ʬ
ݐെݐ
ሻ
+ ݅
ସ
ɝɞɟ
ᇱᇱ
ሺ
݅
ݐ
ହ
ᇱᇱ
=
ሺ
݅
ݐ
ସ
ሻ
ସ
+ ݅
ܷ
ሻ
=
ସ
ܴ
ᇱᇱ
ሺ
ሻ
ݐ
݁
ଷ
ସ
൬
ଶ
మ
൰
య
൰
ௗ
ʬ
ି
1 െ݁
െܽ
െܽ
ᇱᇱ
ሺ
ହ
1 െ݁
൬
௧
రି௧య
த
ʬ
5
௧ି௧
ర
ି
த
ʬ
+
൰
1
ˇଷ
ܴ
ሺ
ʬ
ݐଷെݐ
ሻ
+
ଶ
(2.74)
1
ሺ
ˇସ
ݐ
ସ
ݐସെݐ
ܴ
ʬ
௧ି௧
ర
ି
த
ʬ
ሻ
݁
௧
రି௧య
ି
த
ʬ
ሻ
െ
ଷ
,
+
൰
(2.75)
.
– ɧɚ ɷɬɚɩɟ VI ɜ ɢɧɬɟɪɜɚɥɟ t
ܷ
ሺݐሻ
݅
ܮ
ˇଷ
ˇସ
ˇହ
ʬ
ଶ
ܴ
ʬ
ܮ
ʬ
ଶ
ܴ
ʬ
ܮ
ʬ
ଶ
ܴ
ʬ
+ܽ
+ܽ
+ܽ
ௗ
=
݁
൬
݁
൬
݁
൬
+ ܽ
ቈ
ܴ
ʬ
௧ି௧
య
ି
த
ʬ
െ݁
௧ି௧
ర
ି
த
ʬ
െ݁
௧ି௧
ఱ
ି
த
ʬ
െ݁
1
ˇ
ሺ
ݐെݐ
ܴ
ʬ
െܽ
ˇ
ି
ି
ି
ܴ
௧ି௧
௧ି௧
௧ି௧
ሻ
ହ
ܮ
த
த
த
t t6
5
ʬ
൬
ଶ
ʬ
మ
ʬ
െܽ
൰
య
ʬ
െܽ
൰
ర
ʬ
െܽ
൰
ᇱᇱ
+ ݅
71
1 െ݁
ˇଷ
ˇସ
ˇହ
ሺ
ሻ
ݐ
݁
ହ
ି
1
ܴ
1
ܴ
1
ܴ
ି
௧ି௧
ʬ
ʬ
ʬ
௧ି௧
த
ሺ
ሺ
ሺ
த
ʬ
ఱ
ʬ
+
൰
ݐଷെݐ
ݐସെݐ
ݐହെݐ
ఱ
,
ሻ
+
ଶ
ሻ
+
ଷ
ሻ
െ
ସ
(2.76)
ɝɞɟ
௧
ܷ
ᇱᇱ
ሺ
݅
ݐ
ହ
ᇱᇱ
=
ሺ
݅
ݐ
ହ
ହ
ᇱᇱ
+݅
ହ
ሻ
ௗ
ሻ
=
ሺ
ݐ
1 െ݁
൬
ܴ
ʬ
௧
ఱି௧ర
ି
ఛ
ʬ
ሻ
݁
ସ
ఱି௧ర
ି
ఛ
ʬ
+
൰
(2.77)
.
– ɧɚ ɷɬɚɩɟ IV ɜ ɢɧɬɟɪɜɚɥɟ t t
ሺݐሻ
Ɂɧɚɱɟɧɢɟ ɜɪɟɦɟɧɢ t
݅
, ɩɪɢ ɤɨɬɨɪɨɦ ɬɨɤ ɫɬɚɧɨɜɢɬɫɹ ɪɚɜɧɵɦ
6
=0
6
.
(2.78)
ɧɭɥɸ, ɦɨɠɟɬ ɛɵɬɶ ɧɚɣɞɟɧɨ ɢɡ ɭɪɚɜɧɟɧɢɹ (2.76) ɨɬɧɨɫɢɬɟɥɶɧɨ t ɩɪɢ ɥɟɜɨɣ ɱɚɫɬɢ, ɪɚɜɧɨɣ ɧɭɥɸ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɨɫɰɢɥɥɨɝɪɚɦɦɵ ɬɨɤɨɜ ɨɬɤɥɸɱɚɟɦɨɣ
ɰɟɩɢ ɢ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɤɨɧɬɚɤɬɚɯ ɜɵɤɥɸɱɚɬɟɥɹ, ɩɨɥɭɱɟɧɧɵɟ
ɜ ɪɟɡɭɥɶɬɚɬɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ, ɩɪɢɧɢɦɚɸɬ ɜɢɞ ɧɚ ɪɢɫ. 2.9.
Ɋɢɫ. 2.9
72
Ɉɬɦɟɬɢɦ, ɱɬɨ ɱɟɦ ɛɥɢɠɟ ɤ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɤɪɢɜɨɣ
ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɞɭɝɟ ɟɟ ɭɫɪɟɞɧɟɧɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ, ɬɟɦ ɜɵɲɟ
ɫɯɨɞɢɦɨɫɬɶ ɮɨɪɦ ɤɪɢɜɵɯ ɬɨɤɚ, ɚ ɡɧɚɱɢɬ ɢ ɬɨɱɧɨɫɬɶ ɪɟɡɭɥɶɬɚɬɨɜ ɦɨɞɟɥɢɪɨɜɚɧɢɹ.
2.4. ȼɤɥɸɱɟɧɢɟ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶɧɨɣ
ɭɫɬɚɧɨɜɤɢ
ɉɪɟɨɛɪɚɡɨɜɚɧɢɟ ɷɥɟɤɬɪɨɷɧɟɪɝɢɢ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ ɜ
ɷɥɟɤɬɪɨɷɧɟɪɝɢɸ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶɧɵɯ ɭɫɬɚɧɨɜɨɤ.
Ɉɛɟɫɩɟɱɟɧɢɟ ɬɪɟɛɭɟɦɵɯ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɢ ɩɨɥɭɱɟɧɢɟ
ɨɩɬɢɦɚɥɶɧɵɯ ɡɧɚɱɟɧɢɣ ɜɵɯɨɞɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ ɧɟɜɨɡɦɨɠɧɨ ɛɟɡ ɝɥɭɛɨɤɨɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɩɪɨɰɟɫɫɨɜ.
ȼɵɩɨɥɧɢɦ ɚɧɚɥɢɬɢɱɟɫɤɨɟ ɢɫɫɥɟɞɨɜɚɧɢɟ ɩɟɪɟɯɨɞɧɵɯ
ɩɪɨɰɟɫɫɨɜ ɜ ɫɢɫɬɟɦɟ, ɫɨɫɬɨɹɳɟɣ ɢɡ ɨɞɧɨɦɨɫɬɨɜɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ, ɫɝɥɚɠɢɜɚɸɳɟɝɨ ɪɟɚɤɬɨɪɚ ɢ ɧɚɝɪɭɡɤɢ ɧɚ
ɷ. ɞ. ɫ. (ɞɜɢɝɚɬɟɥɶ, ɚɤɤɭɦɭɥɹɬɨɪ ɢ ɞɪ.). ɉɪɢ ɷɬɨɦ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶ ɛɭɞɟɬ ɫɨɫɬɨɹɬɶ ɢɡ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ ɢ ɜɵɩɪɹɦɢɬɟɥɹ,
ɜɵɩɨɥɧɟɧɧɨɝɨ ɩɨ ɬɪɟɯɮɚɡɧɨɣ ɦɨɫɬɨɜɨɣ ɫɯɟɦɟ (ɪɢɫ. 2.10).
Ɂɚɞɚɱɟɣ ɢɫɫɥɟɞɨɜɚɧɢɹ ɛɭɞɟɬ ɪɚɫɱɟɬ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨɰɟɫɫɨɜ ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɫɢɫɬɟɦɟ, ɜɵɡɜɚɧɧɵɯ ɜɤɥɸɱɟɧɢɟɦ
ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ.
ɉɪɢ ɫɨɫɬɚɜɥɟɧɢɢ ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɫɯɟɦɵ ɛɭɞɟɦ ɫɱɢɬɚɬɶ,
ɱɬɨ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶ ɨɛɥɚɞɚɟɬ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɣ ɦɨɳɧɨɫɬɶɸ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ, ɤɚɤ ɢɡɜɟɫɬɧɨ, ɚɤɬɢɜɧɵɦɢ ɫɨɩɪɨɬɢɜɥɟɧɢɹɦɢ ɷɥɟɦɟɧɬɨɜ ɷɧɟɪɝɨɫɢɫɬɟɦɵ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ, ɚ ɨɫɧɨɜɧɨɟ ɜɥɢɹɧɢɟ ɢɡ ɜɫɟɯ ɩɚɪɚɦɟɬɪɨɜ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ ɧɚ
ɜɫɬɪɟɱɧɭɸ
73
ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɨɤɚɡɵɜɚɸɬ ɢɧɞɭɤɬɢɜɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɪɚɫɫɟɹɧɢɹ ɟɝɨ ɨɛɦɨɬɨɤ.
Ɋɢɫ. 2.10
Ɍɨɝɞɚ ɩɢɬɚɸɳɭɸ ɷɧɟɪɝɨɫɢɫɬɟɦɭ ɢ ɬɪɚɧɫɮɨɪɦɚɬɨɪ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ ɦɨɠɧɨ ɡɚɦɟɧɢɬɶ ɢɫɬɨɱɧɢɤɨɦ ɬɪɟɯɮɚɡɧɨɣ ɫɢɫɬɟɦɵ ɷ. ɞ. ɫ. ɟ
, ɟB, ɟC ɢ ɷɤɜɢɜɚɥɟɧɬɧɵɦ ɢɧɞɭɤɬɢɜɧɵɦ ɫɨ-
A
ɩɪɨɬɢɜɥɟɧɢɟɦ ɏȖ, ɜɤɥɸɱɟɧɧɵɦɢ ɜ ɤɚɠɞɭɸ ɮɚɡɭ ɢ ɩɪɢɜɟɞɟɧɧɵɦɢ ɤɨ ɜɬɨɪɢɱɧɨɣ ɫɬɨɪɨɧɟ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ (ɪɢɫ. 2.10).
ȼ ɏȖ ɜɯɨɞɹɬ ɷɤɜɢɜɚɥɟɧɬɧɨɟ ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ
ɷɧɟɪɝɨɫɢɫɬɟɦɵ ɧɚ ɮɚɡɭ ɢ ɢɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɮɚɡɵ
ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ, ɩɪɢɜɟɞɟɧɧɵɟ ɤ ɜɬɨɪɢɱɧɨɣ ɫɬɨɪɨɧɟ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ.
ɇɚ ɫɬɨɪɨɧɟ ɜɵɩɪɹɦɥɟɧɧɨɝɨ ɬɨɤɚ (ɪɢɫ. 2.10) ɛɭɞɟɦ ɭɱɢɬɵɜɚɬɶ ɜɫɬɪɟɱɧɭɸ ɷ. ɞ. ɫ. ɧɚɝɪɭɡɤɢ E ɢ ɢɧɞɭɤɬɢɜɧɨɫɬɶ ɪɟɚɤɬɨɪɚ
74
X, ɤ ɤɨɬɨɪɨɣ ɬɚɤɠɟ ɦɨɠɟɬ ɛɵɬɶ ɞɨɛɚɜɥɟɧɚ ɢɧɞɭɤɬɢɜɧɨɫɬɶ
ɧɚɝɪɭɡɤɢ.
ɉɪɢ ɚɧɚɥɢɡɟ ɪɚɛɨɬɵ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ ɞɥɹ ɛɨɥɶɲɟɣ ɨɛɳɧɨɫɬɢ ɛɭɞɟɦ ɫɱɢɬɚɬɶ, ɱɬɨ ɜɟɧɬɢɥɢ ɜɵɩɪɹɦɢɬɟɥɹ ɹɜɥɹɸɬɫɹ
ɭɩɪɚɜɥɹɟɦɵɦɢ. Ʉɪɨɦɟ ɬɨɝɨ, ɩɪɢɧɢɦɚɟɦ ɜɨ ɜɧɢɦɚɧɢɟ ɬɨɥɶɤɨ
ɢɞɟɚɥɶɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɜɟɧɬɢɥɟɣ, ɩɪɢ ɤɨɬɨɪɨɣ ɨɧɢ
ɢɦɟɸɬ ɛɟɫɤɨɧɟɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜ ɡɚɩɟɪɬɨɦ ɫɨɫɬɨɹɧɢɢ ɢ
ɩɨɫɬɨɹɧɧɨɟ, ɧɟ ɡɚɜɢɫɹɳɟɟ ɨɬ ɬɨɤɚ, ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɜ
ɩɪɨɜɨɞɹɳɟɦ ɫɨɫɬɨɹɧɢɢ (Uɩɪ = const). ɉɪɢ ɷɬɨɦ, ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɜɨ ɜɪɟɦɹ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɭɝɨɥ ɤɨɦɦɭɬɚɰɢɢ Ȗ
ɩɪɢ ɧɚɢɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɹɯ ɬɨɤɚ ɧɟ ɞɨɫɬɢɝɚɟɬ 60°, ɚ ɭɝɨɥ ɪɟɝɭɥɢɪɨɜɚɧɢɹ Į ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ.
Ɋɚɫɫɦɨɬɪɢɦ ɢɡɦɟɧɟɧɢɟ ɷ. ɞ. ɫ. ɢ ɬɨɤɚ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ ɜ
ɩɟɪɟɯɨɞɧɨɦ ɩɪɨɰɟɫɫɟ ɩɨɫɥɟ ɟɝɨ ɜɤɥɸɱɟɧɢɹ (ɪɢɫ. 2.11).
Ɋɢɫ. 2.11
75
ȼ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɢɦɩɭɥɶɫɚɦɢ ɨɬɩɢɪɚɸɬɫɹ
ɞɜɚ ɫɦɟɠɧɵɯ ɩɨ ɧɨɦɟɪɚɦ ɜɟɧɬɢɥɹ, ɧɚɩɪɢɦɟɪ ɜɟɧɬɢɥɢ 1 ɢ 2,
ɱɟɪɟɡ ɤɨɬɨɪɵɟ ɩɪɨɯɨɞɢɬ ɬɨɤ ɜ ɬɟɱɟɧɢɟ მ ɩɟɪɢɨɞɚ (60°). ɉɨɫɥɟ ɷɬɨɝɨ ɨɬɩɢɪɚɟɬɫɹ ɜɟɧɬɢɥɶ 3, ɢ ɩɪɨɢɫɯɨɞɢɬ ɤɨɦɦɭɬɚɰɢɹ
ɬɨɤɚ ɫ ɨɞɧɨɝɨ ɜɟɧɬɢɥɹ ɧɚ ɞɪɭɝɨɣ (ɫ ɜɟɧɬɢɥɹ 1 ɧɚ ɜɟɧɬɢɥɶ 3)
ɢ ɨɞɧɨɜɪɟɦɟɧɧɨ ɫ ɨɞɧɨɣ ɮɚɡɵ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ ɧɚ ɞɪɭɝɭɸ (ɫ
ɮɚɡɵ B
ɧɚ ɮɚɡɭ C). Ʉɨɦɦɭɬɚɰɢɹ ɬɨɤɚ ɩɪɨɢɫɯɨɞɢɬ ɜ ɩɪɟɞɟɥɚɯ
ɭɝɥɚ Ȗ, ɚ ɞɚɥɶɲɟ ɞɨ ɤɨɧɰɚ ɢɧɬɟɪɜɚɥɚ ɜɪɟɦɟɧɢ, ɨɬɫɱɢɬɵɜɚɟɦɨɝɨ ɦɟɠɞɭ ɦɨɦɟɧɬɚɦɢ ɩɨɞɚɱɢ ɢɦɩɭɥɶɫɚ ɧɚ ɨɱɟɪɟɞɧɨɣ ɜɟɧɬɢɥɶ, ɬɨɤ ɩɪɨɩɭɫɤɚɸɬ ɜɟɧɬɢɥɢ 2 ɢ 3.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɢɧɬɟɪɜɚɥ ɩɨɜɬɨɪɹɟɦɨɫɬɢ ɧɚɱɢɧɚɹ ɫɨ ɜɬɨɪɨɝɨ, ɫɨɞɟɪɠɢɬ ɞɜɚ ɩɪɨɦɟɠɭɬɤɚ: ɤɨɦɦɭɬɚɰɢɨɧɧɵɣ ɞɥɢɬɟɥɶɧɨɫɬɶɸ Ȗ, ɤɨɝɞɚ ɬɨɤ ɩɪɨɩɭɫɤɚɸɬ ɬɪɢ ɜɟɧɬɢɥɹ, ɢ ɦɟɠɤɨɦɦɭɬɚɰɢɨɧɧɵɣ, ɤɨɝɞɚ ɬɨɤ ɩɪɨɩɭɫɤɚɸɬ ɞɜɚ ɜɟɧɬɢɥɹ. ɉɪɢ ɷɬɨɦ
ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɢɧɬɟɪɜɚɥɚ ɩɨɜɬɨɪɹɟɦɨɫɬɢ, ɨɩɪɟɞɟɥɹɟɦɚɹ ɩɨɞɚɱɟɣ ɢɦɩɭɥɶɫɚ ɧɚ ɫɥɟɞɭɸɳɢɣ ɜɟɧɬɢɥɶ, ɪɚɜɧɚ 60°,
ɬ.ɤ. ɭɝɨɥ Į ɞɥɹ ɜɫɟɯ ɜɟɧɬɢɥɟɣ ɨɞɢɧɚɤɨɜ. ȼɟɥɢɱɢɧɚ ɠɟ ɭɝɥɚ
ɤɨɦɦɭɬɚɰɢɢ ɢɡɦɟɧɹɟɬɫɹ, ɭɜɟɥɢɱɢɜɚɹɫɶ ɫ ɪɨɫɬɨɦ ɬɨɤɚ.
ɇɚɣɞɟɦ ɢɡɦɟɧɟɧɢɟ ɜɵɩɪɹɦɥɟɧɧɨɝɨ ɬɨɤɚ ɿ ɜ ɧɟɤɨɬɨɪɨɦ
ɢɧɬɟɪɜɚɥɟ ɩɨɜɬɨɪɹɟɦɨɫɬɢ (ɪɢɫ. 2.11), ɤɨɬɨɪɵɣ ɞɥɹ ɨɩɪɟɞɟɥɟɧɧɨɫɬɢ ɜɨɡɶɦɟɦ ɥɟɠɚɳɢɦ, ɧɚɩɪɢɦɟɪ, ɜ ɩɪɟɞɟɥɚɯ ɨɬ
ș = 4ʌ/3 ɞɨ ș = 5ʌ/3 (5-ɣ ɢɧɬɟɪɜɚɥ).
ȼ ɤɨɦɦɭɬɚɰɢɨɧɧɨɦ ɩɪɨɦɟɠɭɬɤɟ ɷɬɨɝɨ ɢɧɬɟɪɜɚɥɚ ɬɨɤ ɩɪɨɩɭɫɤɚɸɬ ɜɟɧɬɢɥɢ 4, 5 ɢ 6, ɚ ɜ ɦɟɠɤɨɦɦɭɬɚɰɢɨɧɧɨɦ – ɜɟɧɬɢɥɢ
5 ɢ 6.
ɋɨɫɬɚɜɢɦ ɢɫɯɨɞɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɞɥɹ
ɤɨɦɦɭɬɚɰɢɨɧɧɨɝɨ ɩɪɨɦɟɠɭɬɤɚ, ɤɨɝɞɚ 4ʌ/3 ș 4ʌ/3 + Ȗ4.
ɉɪɨɯɨɞɹ ɩɨ ɤɨɧɬɭɪɭ ɱɟɪɟɡ ɜɟɧɬɢɥɢ 4 ɢ 5 (ɪɢɫ. 2.12), ɩɨɥɭɱɚɟɦ ɩɟɪɜɨɟ ɢɫɯɨɞɧɨɟ ɭɪɚɜɧɟɧɢɟ
76
ܺ
൫ܺ+
ஓ
൯
݀݅ሺɅ
݀Ʌ
ሻ
+ ܺ
ሺɅሻ
݀݅
ସ
ஓ
+ ܧ+2ܷ˒˓= ݁െ݁
݀Ʌ
. (2.79)
Ɋɚɡɧɨɫɬɶ ɷ. ɞ. ɫ., ɜɯɨɞɹɳɭɸ ɜ ɩɪɚɜɭɸ ɱɚɫɬɶ ɭɪɚɜɧɟɧɢɹ, ɡɚɩɢɲɟɦ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɚɱɚɥɚ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ
െ݁= ܧ
݁
െܧ
sin
Ʌ+
൬
+ Ƚെ
6
Ɏ
sin
Ʌെ
൬
+ Ƚെ
2
Ɏ
3
ܧ
cos
5Ɏ
=
Ʌ+
ξ
൬
+ Ƚെ
6
4Ɏ
3
൰
4Ɏ
3
=
4Ɏ
3
൰
െ
൰
(2.80)
,
ɝɞɟ ȿm – ɚɦɩɥɢɬɭɞɚ ɮɚɡɧɨɣ ɷ. ɞ. ɫ.
Ɋɢɫ. 2.12
ɉɨɞɫɬɚɜɥɹɹ ɜ (2.79) ɜɦɟɫɬɨ (ɟB – ɟA) ɡɚɩɢɫɚɧɧɨɟ ɜɵɲɟ ɜɵɪɚɠɟɧɢɟ, ɩɨɥɭɱɚɟɦ
77
൫
ܺ+ܺ
ܺ
ܺ
൯
ஓ
=ξ3
݀݅ሺɅ
݀Ʌ
ܧ
+ ܺ
cos
൬
ሻ
݀݅
ஓ
Ʌ+
ସ
݀Ʌ
Ɏ
6
ሺɅሻ
+ Ƚെ
+ ܧ+2ܷ
4Ɏ
൰
3
=
˒˓
(2.81)
.
Ⱦɥɹ ɭɩɪɨɳɟɧɢɹ ɞɚɥɶɧɟɣɲɢɯ ɜɵɤɥɚɞɨɤ ɢ ɩɨɥɭɱɟɧɢɹ ɛɨɥɟɟ
ɨɛɳɢɯ ɪɟɡɭɥɶɬɚɬɨɜ ɜɜɟɞɟɦ ɨɬɧɨɫɢɬɟɥɶɧɵɟ ɜɟɥɢɱɢɧɵ, ɩɪɢɧɹɜ ɡɚ ɛɚɡɢɫɧɵɟ
ܷ˄= ܧ
ܫ
˄
ܺ˄= ܺ
=
;
ܧ
;
ஓ
.
ஓ
(2.82)
ȼɟɥɢɱɢɧɵ, ɜɵɪɚɠɟɧɧɵɟ ɜ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɟɞɢɧɢɰɚɯ, ɩɨɥɭɱɚɬ ɫɥɟɞɭɸɳɢɟ ɨɛɨɡɧɚɱɟɧɢɹ
ሻ
˄
=
=
݅
=
ܧ
ܧ+2ܷ
ܧ
ܺ
.
ܺ
ஓ
ஓ
;
˒˓
;
(2.83)
ሺɅሻ
݅
=
כ
ܧ+2ܷ
݁
=
כ
ܷ
ܫ
˒˓
˄
ܺ
ݔ
=
כ
ܺ
˄
݅ሺɅ
ɉɟɪɟɯɨɞɹ ɤ ɨɬɧɨɫɢɬɟɥɶɧɵɦ ɜɟɥɢɱɢɧɚɦ, ɭɪɚɜɧɟɧɢɟ (2.81)
ɩɪɢɧɢɦɚɟɬ ɜɢɞ
ሺɅሻ
݀݅
ሺ
ݔ
+1
כ
=ξ3 cos
כ
ሻ
+
݀Ʌ
Ʌ+
൬
݀݅
Ɏ
+ Ƚെ
6
78
ସכ
݀Ʌ
ሺɅሻ
+ ݁
4Ɏ
3
=
כ
.
൰
(2.84)
ɉɪɨɯɨɞɹ ɩɨ ɤɨɧɬɭɪɭ ɱɟɪɟɡ ɜɟɧɬɢɥɢ 6 ɢ 5 (ɪɢɫ. 2.12), ɧɚɯɨ-
ܺ
ܺ+ܺ
ɞɢɦ ɜɬɨɪɨɟ ɢɫɯɨɞɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɤɨɦɦɭɬɚɰɢɨɧɧɨɝɨ ɩɪɨɦɟɠɭɬɤɚ
൫ܺ+
ஓ
൯
݀݅ሺɅ
݀Ʌ
ሻ
+ ܺ
ሺɅሻ
݀݅
ஓ
+ ܧ+2ܷ˒˓= ݁െ݁
݀Ʌ
. (2.85)
Ɋɚɡɧɨɫɬɶ ɷ. ɞ. ɫ. ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ (2.85) ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɚɱɚɥɚ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ ɪɚɜɧɚ
݁െ݁= ܧ
sin
Ʌ+
൬
+ Ƚെ
6
Ɏ
Ɏ
െܧ
sin
Ʌെ
൬
+ Ƚെ
2
Ɏ
=
3ܧ
cos
Ʌെ
ξ
൬
+ Ƚെ
6
4Ɏ
3
൰
4Ɏ
3
4Ɏ
3
=
൰
െ
൰
(2.86)
.
ɉɨɞɫɬɚɜɥɹɹ (2.86) ɜ (2.85), ɧɚɯɨɞɢɦ
ሻ
=
ஓ
൯
ξ
݀݅ሺɅ
݀Ԃ
3ܧ
+ ܺ
cos
൬
൫
݀݅
ஓ
Ʌെ
݀Ԃ
Ɏ
6
ሺɅሻ
+ Ƚെ
+ ܧ+2ܷ
4Ɏ
൰
3
=
˒˓
(2.87)
,
ɢɥɢ, ɩɟɪɟɯɨɞɹ ɤ ɨɬɧɨɫɢɬɟɥɶɧɵɦ ɜɟɥɢɱɢɧɚɦ
ሺɅሻ
݀݅
ሺ
ݔ
+1
כ
=ξ3 cos
כ
ሻ
+
݀Ԃ
Ʌെ
൬
݀݅
Ɏ
+ Ƚെ
6
כ
݀Ԃ
ሺɅሻ
+ ݁
4Ɏ
3
=
כ
.
൰
(2.88)
79
ɋɤɥɚɞɵɜɚɹ (2.84) ɢ (2.88) ɢ ɭɱɢɬɵɜɚɹ, ɱɬɨ
ሺɅሻ
݅
ସכ
+ ݅
כ
ሺɅሻ
= ݅
ሺɅሻ
,
(2.89)
כ
ɩɨɥɭɱɚɟɦ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ
ɜɵɩɪɹɦɥɟɧɧɨɝɨ ɬɨɤɚ ɜ ɤɨɦɦɭɬɚɰɢɨɧɧɨɦ ɩɪɨɦɟɠɭɬɤɟ
൬
3
+
ݔ
כ
2
ሺɅሻ
݀݅
כ
൰
݀Ʌ
=
3
2
cos
Ʌ+ Ƚെ
൬
4Ɏ
3
൰
. (2.90)
െ݁
כ
Ɂɚɩɢɲɟɦ ɬɟɩɟɪɶ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɦɟɠɤɨɦɦɭɬɚɰɢɨɧɧɨɝɨ ɩɪɨɦɟɠɭɬɤɚ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɢɧɬɟɪɜɚɥɚ, ɤɨɝɞɚ 4ʌ/3 + Ȗ4 ș 5ʌ/3. Ɍɚɤ ɤɚɤ ɜ ɷɬɨ ɜɪɟɦɹ ɩɪɨɩɭɫɤɚɸɬ ɬɨɤ ɜɟɧɬɢɥɢ 5 ɢ 6 (ɪɢɫ. 2.13), ɬɨ ɩɪɢɯɨɞɢɦ ɤ ɭɪɚɜɧɟɧɢɸ
ሺɅሻ
൫ܺ+2ܺஓ൯
݀݅
+ ܧ+2ܷ˒˓= ݁െ݁
݀Ʌ
, (2.91)
ɢɥɢ, ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɚɱɚɥɚ ɩɟɪɟɯɨɞɧɨɝɨ ɩɪɨɰɟɫɫɚ
ሻ
݀݅ሺɅ
൫ܺ+2ܺ
൯
ஓ
=
3ܧ
ξ
cos
݀Ʌ
Ʌെ
൬
+ ܧ+2ܷ
Ɏ
+ Ƚെ
6
˒˓
4Ɏ
3
൰
=
(2.92)
,
ɝɞɟ Ȗ4 – ɭɝɨɥ ɤɨɦɦɭɬɚɰɢɢ ɧɚ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ 5-ɦ ɢɧɬɟɪɜɚɥɟ ɩɨɜɬɨɪɹɟɦɨɫɬɢ.
80
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