Федоров М.П. и др. Информационно-компьютерные технологии в строительстве. Применение программы SCAD для расчета сооружений на динамические воздействия
Подождите немного. Документ загружается.
90
Ɇɚɬɪɢɰɵ (2.8) ɹɜɥɹɸɬɫɹ ɜɟɤɬɨɪɚɦɢ ɡɚɞɚɧɧɵɯ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɧɚɱɚɥɶɧɵɯ
ɩɟɪɟɦɟɳɟɧɢɣ ɢ ɫɤɨɪɨɫɬɟɣ ɜɫɟɯ ɦɚɫɫ.
Ɂɚɞɚɧɢɟ ɫɢɫɬɟɦɟ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɣ ɞɜɢɠɟɧɢɹ (2.7), ɹɜɥɹɸɳɢɯɫɹ
ɩɪɢɱɢɧɨɣ ɟɟ ɫɜɨɛɨɞɧɵɯ ɤɨɥɟɛɚɧɢɣ, ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɩɨɥɭɱɟɧɢɸ ɷɬɨɣ ɫɢɫɬɟɦɨɣ
ɧɟɤɨɬɨɪɨɣ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɭɩɪɭɝɨɣ ɞɟɮɨɪɦɚɰɢɢ
oɬooɬoo
)(5.0)(5.0 pDpuKu ɉ ,
ɝɞɟ
oo
pKp – ɜɟɤɬɨɪ ɧɚɱɚɥɶɧɵɯ ɡɧɚɱɟɧɢɣ ɫɢɥ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɜɟɤɬɨɪɭ
ɧɚɱɚɥɶɧɵɯ ɩɟɪɟɦɟɳɟɧɢɣ
o
u , ɢ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ
ooɬooo
)(5.0 uMu T .
ɉɨɥɧɚɹ ɧɚɱɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɫɢɫɬɟɦɵ 0
ooo
! Ɍ
ɉ
ɗ ɢ ɦɚɬɪɢɰɵ
MD
K
,, ɹɜɥɹɸɬɫɹ ɩɨɥɨɠɢɬɟɥɶɧɨ ɨɩɪɟɞɟɥɟɧɧɵɦɢ ɢ ɧɟɨɫɨɛɟɧɧɵɦɢ, ɬ.ɟ.
ɢɦɟɸɬ ɨɛɪɚɬɧɵɟ ɦɚɬɪɢɰɵ:
111
,,
MDK .
ɍɦɧɨɠɢɦ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ (2.1) ɧɚ
1
K
ɢ ɭɱɬɟɦ, ɱɬɨ E
K
K
1
, ɝɞɟ
E
ɹɜɥɹɟɬɫɹ ɟɞɢɧɢɱɧɨɣ ɦɚɬɪɢɰɟɣ. Ɍɨɝɞɚ ɩɨɥɭɱɢɦ:
)(
1
uMKu
.
(2.9)
ɋɨɩɨɫɬɚɜɥɹɹ (2.9) ɢ (2.2), ɨɬɦɟɬɢɦ, ɱɬɨ D
K
1
, ɢ ɦɚɬɪɢɱɧɨɟ ɭɪɚɜɧɟɧɢɟ
(2.1) ɭɦɧɨɠɟɧɢɟɦ ɟɝɨ ɧɚ ɦɚɬɪɢɰɭ
1
K
ɩɪɟɨɛɪɚɡɨɜɚɥɨɫɶ ɜ ɦɚɬɪɢɱɧɨɟ ɭɪɚɜɧɟɧɢɟ
(2.2).
Ⱥɧɚɥɨɝɢɱɧɨ, ɫɢɫɬɟɦɚ ɭɪɚɜɧɟɧɢɣ ɞɜɢɠɟɧɢɹ ɜ ɮɨɪɦɟ (2.2) ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɜ
ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ (2.1) ɭɦɧɨɠɟɧɢɟɦ (2.2) ɧɚ ɦɚɬɪɢɰɭ
1
D . ɉɪɢ ɷɬɨɦ
ɭɱɢɬɵɜɚɟɬɫɹ , ɱɬɨ EDD
1
ɢ
K
D
1
.
Ɂɚɩɢɫɶ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ ɜ ɦɚɬɪɢɱɧɨɦ ɜɢɞɟ ɩɪɢɦɟɧɢɦɚ ɢ ɞɥɹ ɫɢɫɬɟɦɵ ɫ
ɨɞɧɨɣ ɫɬɟɩɟɧɶɸ ɫɜɨɛɨɞɵ, ɤɨɝɞɚ 1 n . Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɜ ɷɬɨɦ ɫɥɭɱɚɟ:
kkuuuumm G G
1111111
;;;; KDuuM
,
G
1
k
;
k
G
1
; 1
G k
ɢ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ (2.1) ɢ (2.2) ɩɪɢɧɢɦɚɸɬ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɜɢɞ (1.8) ɢ (1.10).
2.2. Ɋɟɲɟɧɢɟ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ ɫɜɨɛɨɞɧɵɯ ɧɟɡɚɬɭɯɚɸɳɢɯ ɤɨɥɟɛɚɧɢɣ
ɦɟɬɨɞɨɦ ɪɚɡɥɨɠɟɧɢɹ ɜɟɤɬɨɪɚ ɢɫɤɨɦɵɯ ɩɟɪɟɦɟɳɟɧɢɣ ɦɚɫɫ
ɩɨ ɜɟɤɬɨɪɚɦ ɩɟɪɟɦɟɳɟɧɢɣ ɜ ɋɎɄ
ɉɪɢ ɪɚɫɱɟɬɟ ɫɨɨɪɭɠɟɧɢɣ ɨɬ ɪɚɡɥɢɱɧɵɯ ɜɨɡɞɟɣɫɬɜɢɣ, ɜɵɡɵɜɚɸɳɢɯ
ɞɢɧɚɦɢɱɟɫɤɢɣ ɯɚɪɚɤɬɟɪ ɢɯ ɇȾɋ, ɧɚɢɛɨɥɟɟ ɱɚɫɬɨ ɢɫɩɨɥɶɡɭɸɬ ɪɟɲɟɧɢɟ ɫɢɫɬɟɦɵ
ɭɪɚɜɧɟɧɢɣ, ɡɚɩɢɫɚɧɧɨɣ ɥɢɛɨ ɜ ɮɨɪɦɟ (2.1), ɥɢɛɨ ɜ ɮɨɪɦɟ (2.2), ɦɟɬɨɞɨɦ
91
ɪɚɡɥɨɠɟɧɢɹ ɢɫɤɨɦɵɯ ɩɟɪɟɦɟɳɟɧɢɣ ɜ ɪɹɞ ɩɨ ɫɨɛɫɬɜɟɧɧɵɦ ɮɨɪɦɚɦ ɤɨɥɟɛɚɧɢɣ
(ɦɨɞɚɥɶɧɚɹ ɫɭɩɟɪɩɨɡɢɰɢɹ):
)(
1
t
i
n
i
i
)
¦
uu .
(2.10)
ɝɞɟ
ɬ
21
)...(
niiii
uuu u – ɜɟɤɬɨɪ ɩɟɪɟɦɟɳɟɧɢɣ i -ɣ ɫɨɛɫɬɜɟɧɧɨɣ ɮɨɪɦɵ ɤɨɥɟɛɚɧɢɣ
ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɫɨɨɪɭɠɟɧɢɹ, ɨɩɪɟɞɟɥɹɸɳɢɣ ɮɨɪɦɭ ɞɟɮɨɪɦɢɪɨɜɚɧɢɹ
ɫɨɨɪɭɠɟɧɢɹ ɩɪɢ ɟɝɨ ɫɜɨɛɨɞɧɵɯ ɤɨɥɟɛɚɧɢɹɯ ɫ ɧɟɤɨɬɨɪɨɣ ɫɨɛɫɬɜɟɧɧɨɣ ɱɚɫɬɨɬɨɣ,
ɤɨɬɨɪɚɹ ɛɭɞɟɬ ɞɚɥɟɟ ɨɩɪɟɞɟɥɟɧɚ;
)(˓ t
i
– ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɡɥɨɠɟɧɢɹ,
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɜɟɤɬɨɪɭ
i
u ɢ ɩɪɟɞɫɬɚɜɥɹɸɳɢɣ ɫɨɛɨɣ ɮɭɧɤɰɢɸ ɜɪɟɦɟɧɢ,
ɤɨɬɨɪɚɹ ɨɩɪɟɞɟɥɹɟɬ ɫɢɧɯɪɨɧɧɨɟ ɢɡɦɟɧɟɧɢɟ ɜɨ ɜɪɟɦɟɧɢ ɜɟɤɬɨɪɚ ɩɟɪɟɦɟɳɟɧɢɣ
i -ɣ ɫɨɛɫɬɜɟɧɧɨɣ ɮɨɪɦɵ ɤɨɥɟɛɚɧɢɣ:
»
»
»
»
»
»
»
¼
º
«
«
«
«
«
«
«
¬
ª
)(˓
)(˓
)(˓
)(˓
)(˓
2
1
t
t
t
t
t
ini
iki
ii
ii
iii
u
u
u
u
uu .
(2.11)
ɉɨɞɫɬɚɜɢɜ ɥɸɛɨɟ i -ɟ ɫɥɚɝɚɟɦɨɟ (2.11) ɫɭɦɦɵ (2.10) ɜ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ
ɞɜɢɠɟɧɢɹ, ɡɚɩɢɫɚɧɧɭɸ ɜ ɜɢɞɟ (2.1) ɢ ɜ ɜɢɞɟ (2.2), ɩɨɥɭɱɢɦ:
0uKuM )(˓)(˓ tt
iiii
;
)(˓)(˓ tt
iiii
uMDu .
ɢɥɢ
0uKuM
i
i
i
i
t
t
)(˓
)(˓
;
(2.12)
)(˓
)(˓
t
t
i
i
ii
uMDu
.
(2.13)
ɋɢɫɬɟɦɚ ɭɪɚɜɧɟɧɢɣ ɜ ɮɨɪɦɟ (2.12) ɢ ɜ ɮɨɪɦɟ (2.13) ɢɦɟɟɬ ɫɦɵɫɥ, ɤɨɝɞɚ
ɞɪɨɛɶ )(˓/)(˓ tt
ii
ɪɚɜɧɚ ɩɨɫɬɨɹɧɧɨɣ ɜɟɥɢɱɢɧɟ. ɉɪɢɪɚɜɧɹɜ )(˓/)(˓ tt
ii
ɜɟɥɢɱɢɧɟ
2
i
Z , ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɟ
0)(˓)(˓
2
Z tt
iii
,
(2.14)
ɢɡ ɤɨɬɨɪɨɝɨ ɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɭɧɤɰɢɹ ɜɪɟɦɟɧɢ
)(˓ t
i
.
ȼ ɪɟɡɭɥɶɬɚɬɟ ɜɵɩɨɥɧɟɧɧɨɝɨ ɞɟɣɫɬɜɢɹ ɩɪɨɢɡɨɲɥɨ ɨɬɞɟɥɟɧɢɟ ɮɭɧɤɰɢɢ
ɜɪɟɦɟɧɢ ɢɡ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ ɞɜɢɠɟɧɢɹ ɤɚɤ ɜ ɩɟɪɜɨɣ (2.12), ɬɚɤ ɢ ɜɨ ɜɬɨɪɨɣ
92
(2.13) ɮɨɪɦɚɯ ɟɟ ɡɚɩɢɫɢ. Ɍɟɩɟɪɶ ɞɜɭɦ ɮɨɪɦɚɦ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ ɞɜɢɠɟɧɢɹ
ɛɭɞɭɬ ɫɨɨɬɜɟɬɫɬɜɨɜɚɬɶ ɨɞɧɨɪɨɞɧɵɟ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ ɜ ɜɢɞɟ:
0uMK M
ii
)( ;
(2.15)
0uEA O
ii
)(
.
(2.16)
Ɂɞɟɫɶ ɜɜɟɞɟɧɵ ɨɛɨɡɧɚɱɟɧɢɹ:
2
ii
Z M ;
2
/1
ii
Z O ; MDA .
ɍɪɚɜɧɟɧɢɟ (2.14) ɢɦɟɟɬ ɬɚɤɨɣ ɠɟ ɜɢɞ, ɤɚɤ ɭɪɚɜɧɟɧɢɟ ɫɜɨɛɨɞɧɵɯ
ɧɟɡɚɬɭɯɚɸɳɢɯ ɤɨɥɟɛɚɧɢɣ (1.12) ɞɥɹ ɫɢɫɬɟɦɵ ɫ ɨɞɧɨɣ ɫɬɟɩɟɧɶɸ ɫɜɨɛɨɞɵ.
ɉɨɷɬɨɦɭ ɟɝɨ ɪɟɲɟɧɢɟ ɛɭɞɟɬ ɢɦɟɬɶ ɜɢɞ (1.15)
tAtAt
iiiii
ZZ sincos)(˓
21
,
(2.17)
ɢɥɢ (1.24), (1.27).
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɚɫɬɧɨɟ ɪɟɲɟɧɢɟ (2.11) ɫ ɮɭɧɤɰɢɟɣ ɜɪɟɦɟɧɢ (2.17)
ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɟɡɚɬɭɯɚɸɳɢɦ ɝɚɪɦɨɧɢɱɟɫɤɢɦ ɤɨɥɟɛɚɧɢɹɦ, ɩɪɨɢɫɯɨɞɹɳɢɦ ɫ
ɱɚɫɬɨɬɨɣ
i
Z ɢ ɢɦɟɸɳɢɦ ɮɨɪɦɭ ɤɨɥɟɛɚɧɢɣ, ɨɩɪɟɞɟɥɹɟɦɭɸ ɜɟɤɬɨɪɨɦ
i
u .
ɑɚɫɬɨɬɚ
i
Z
ɹɜɥɹɟɬɫɹ i -ɣ ɫɨɛɫɬɜɟɧɧɨɣ ɱɚɫɬɨɬɨɣ (i -ɣɋɑ) ɤɨɥɟɛɚɧɢɣ ɫɨɨɪɭɠɟɧɢɹ,
ɚ ɜɟɤɬɨɪ
i
u – ɜɟɤɬɨɪɨɦ ɩɟɪɟɦɟɳɟɧɢɣ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ i -ɨɣ ɫɨɛɫɬɜɟɧɧɨɣ
ɮɨɪɦɟ ɤɨɥɟɛɚɧɢɣ (i -ɣɋɎɄ). Ɍɚɤɢɯ ɋɑ ɢ ɋɎɄ ɛɭɞɟɬ ɫɬɨɥɶɤɨ, ɫɤɨɥɶɤɨ ɢɦɟɟɬɫɹ
ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɦɚɫɫ ɜ ɩɪɢɧɹɬɨɣ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ( ni ...,2,1 ).
ɉɨɫɬɨɹɧɧɵɟ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ
ii
AA
21
ɢ ɪɟɲɟɧɢɹ (2.17) ɭɪɚɜɧɟɧɢɹ (2.14)
ɨɩɪɟɞɟɥɹɸɬɫɹ ɢɡ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɣ ɞɜɢɠɟɧɢɹ (2.7) ɫ ɩɨɦɨɳɶɸ ɢɫɩɨɥɶɡɨɜɚɧɢɹ
ɫɜɨɣɫɬɜɚ ɨɪɬɨɝɨɧɚɥɶɧɨɫɬɢ ɋɎɄ, ɤɨɬɨɪɨɟ ɛɭɞɟɬ ɪɚɫɫɦɨɬɪɟɧɨ ɜ ɩɨɞɪɚɡɞɟɥɟ 2.3.
Ɉɩɪɟɞɟɥɟɧɢɟ ɫɨɛɫɬɜɟɧɧɵɯ ɱɚɫɬɨɬ. ɋɨɛɫɬɜɟɧɧɵɟ ɱɚɫɬɨɬɵ ɧɚɯɨɞɹɬɫɹ
ɪɟɲɟɧɢɟɦ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ
ɮɨɪɦɟ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ ((2.15) ɢɥɢ (2.16)), ɤɨɬɨɪɨɟ ɩɨɥɭɱɚɟɬɫɹ ɢɡ ɫɥɟɞɭɸɳɢɯ
ɫɨɨɛɪɚɠɟɧɢɣ.
ɉɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɜɟɤɬɨɪɨɜ ɩɟɪɟɦɟɳɟɧɢɣ ɜ ɋɎɄ ɪɟɲɟɧɢɟɦ ɫɢɫɬɟɦɵ
ɭɪɚɜɧɟɧɢɣ (2.15) ɢɥɢ (2.16) ɪɚɫɱɟɬɱɢɤɚ ɢɧɬɟɪɟɫɭɟɬ ɬɨɥɶɤɨ ɧɟɧɭɥɟɜɵɟ ɪɟɲɟɧɢɹ.
Ⱥ ɬɚɤ ɤɚɤ ɭɤɚɡɚɧɧɵɟ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ ɹɜɥɹɸɬɫɹ ɨɞɧɨɪɨɞɧɵɦɢ, ɬɨ ɧɟɧɭɥɟɜɨɟ
ɪɟɲɟɧɢɟ ɜɨɡɦɨɠɧɨ ɬɨɥɶɤɨ ɬɨɝɞɚ, ɤɨɝɞɚ ɨɩɪɟɞɟɥɢɬɟɥɶ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɫɢɫɬɟɦɵ
ɪɚɜɟɧ ɧɭɥɸ:
0 M MK
i
;
(2.18)
0 O EA
i
.
(2.19)
Ɋɚɫɤɪɵɜɚɹ ɨɩɪɟɞɟɥɢɬɟɥɢ, ɩɨɥɭɱɢɦ ɚɥɝɟɛɪɚɢɱɟɫɤɢɟ ɭɪɚɜɧɟɧɢɹ n -ɨɣ
ɫɬɟɩɟɧɢ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɜ ɜɢɞɟ:
0...
1
1
1
MMM
o
n
n
n
n
bbbb ;
(2.20)
93
0...
1
1
1
OOO
o
n
n
n
n
aaaa .
(2.21)
Ɍɚɤ ɤɚɤ ɦɚɬɪɢɰɵ MDK ,, ɹɜɥɹɸɬɫɹ ɫɢɦɦɟɬɪɢɱɧɵɦɢ ɩɨɥɨɠɢɬɟɥɶɧɨ
ɨɩɪɟɞɟɥɟɧɧɵɦɢ, ɬɨ ɪɟɲɟɧɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɢɯ ɭɪɚɜɧɟɧɢɣ ɞɚɟɬ n
ɜɟɳɟɫɬɜɟɧɧɵɯ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɤɨɪɧɟɣ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ
O
M
ɢ , ɩɨ ɤɨɬɨɪɵɦ
ɨɩɪɟɞɟɥɹɸɬɫɹ ɫɨɛɫɬɜɟɧɧɵɟ ɱɚɫɬɨɬɵ
i
Z
ɧɟɡɚɬɭɯɚɸɳɢɯ ɤɨɥɟɛɚɧɢɣ:
iii
O M Z /1 , ( ni ,...,2,1 ).
(2.22)
ɋɩɟɤɬɪ ɫɨɛɫɬɜɟɧɧɵɯ ɱɚɫɬɨɬ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɭɩɪɭɝɨɣ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ
ɩɪɟɞɫɬɚɜɥɹɸɬ ɜ ɜɢɞɟ:
n
ZZZ ...
21
,
(2.23)
ɝɞɟ ɩɟɪɜɚɹ ɋɑ ɹɜɥɹɟɬɫɹ ɧɢɡɲɟɣ ɫɨɛɫɬɜɟɧɧɨɣ ɱɚɫɬɨɬɨɣ.
Ɉɩɪɟɞɟɥɟɧɢɟ ɜɟɤɬɨɪɨɜ
i
u i - ɣɋɎɄ. Ʉɚɠɞɨɣ ɧɚɣɞɟɧɧɨɣ ɱɚɫɬɨɬɟ
i
Z
ɢɡ
ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ (2.15) ɩɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱɢ ɜ ɮɨɪɦɟ ɦɟɬɨɞɚ ɩɟɪɟɦɟɳɟɧɢɣ,
ɢɥɢ ɢɡ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ (2.16) ɩɪɢ ɪɟɲɟɧɢɢ ɜ ɮɨɪɦɟ ɦɟɬɨɞɚ ɫɢɥ,
ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɜɟɤɬɨɪ ɩɟɪɟɦɟɳɟɧɢɣ
i
u
.
Ɍɚɤ ɤɚɤ ɭɤɚɡɚɧɧɵɟ ɫɢɫɬɟɦɵ
n ɭɪɚɜɧɟɧɢɣ ɹɜɥɹɸɬɫɹ ɨɞɧɨɪɨɞɧɵɦɢ, ɬɨ
ɧɟɡɚɜɢɫɢɦɵɦɢ ɹɜɥɹɸɬɫɹ ɬɨɥɶɤɨ 1
n ɭɪɚɜɧɟɧɢɟ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɚɛɫɨɥɸɬɧɵɟ
ɡɧɚɱɟɧɢɹ ɩɟɪɟɦɟɳɟɧɢɣ ɜ ɜɟɤɬɨɪɟ
i
u
ɧɚɣɬɢ ɧɟɥɶɡɹ. ȼɨɡɦɨɠɧɨ ɨɩɪɟɞɟɥɟɧɢɟ
ɬɨɥɶɤɨ ɢɯ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɡɧɚɱɟɧɢɣ.
Ɋɚɫɫɦɨɬɪɢɦ, ɧɚɩɪɢɦɟɪ, ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ (2.15) ɜ ɤɚɧɨɧɢɱɟɫɤɨɦ ɜɢɞɟ:
°
°
¿
°
°
¾
½
M
M
M
0
:
0
0
)(...
:::::::
...)(
...)(
2211
22222121
12121111
nininninin
niniii
niniii
umkukuk
ukumkuk
ukukumk
.
Ɋɚɡɞɟɥɢɦ ɟɟ ɧɚ ɜɟɥɢɱɢɧɭ
i
u
1
ɢ ɜɜɟɞɟɦ ɧɨɜɵɟ ɨɬɧɨɫɢɬɟɥɶɧɵɟ ɩɟɪɟɦɟɳɟɧɢɹ
ijiji
uuy
1
/ , ɝɞɟ nj ,...,2,1 ; ni ,...,2,1 .
Ɍɚɤ ɤɚɤ
1/
111
iii
uuy , ɬɨ ɧɟɢɡɜɟɫɬɧɵɦɢ ɹɜɥɹɸɬɫɹ 1n ɨɬɧɨɫɢɬɟɥɶɧɵɟ
ɩɟɪɟɦɟɳɟɧɢɹ
ijiji
uuy
1
/ , ɝɞɟ nj ,...,2 ; ni ,...,3,2,1 . ɂɯ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ
ɪɟɲɟɧɢɟɦ ɫɢɫɬɟɦɵ ɥɸɛɵɯ 1n ɭɪɚɜɧɟɧɢɣ:
°
°
¿
°
°
¾
½
M
M
M
.
:
;
);(
)(...
:::::::
...)(
...
1
21
211
3322
23232222
1313212
n
i
nininninin
niniij
ninii
k
k
mk
ymkykyk
ykykymk
ykykyk
.
(2.24)
94
ȼ ɪɟɡɭɥɶɬɚɬɟ ɞɥɹ n ɫɨɛɫɬɜɟɧɧɵɯ ɱɚɫɬɨɬ ɩɨɥɭɱɢɦ n ɜɟɤɬɨɪɨɜ:
ɬ
32
),...,,1(
niiii
yyy y
.
(2.25)
ɂɦ ɛɭɞɭɬ ɫɨɨɬɜɟɬɫɬɜɨɜɚɬɶ ɢɫɤɨɦɵɟ ɜɟɤɬɨɪɵ ɋɎɄ, ɨɩɪɟɞɟɥɟɧɧɵɟ ɫ
ɬɨɱɧɨɫɬɶɸ ɞɨ ɩɨɫɬɨɹɧɧɨɝɨ ɦɧɨɠɢɬɟɥɹ
i
u
1
:
iii
u yu
1
.
(2.26)
Ɉɩɪɟɞɟɥɟɧɢɟ ɫɢɥ ɢɧɟɪɰɢɢ, ɪɚɡɥɨɠɟɧɧɵɯ ɩɨ ɋɎɄ. ɉɪɢ ɫɜɨɛɨɞɧɵɯ
ɧɟɡɚɬɭɯɚɸɳɢɯ ɤɨɥɟɛɚɧɢɹɯ ɤɚɠɞɨɦɭ ɜɟɤɬɨɪɭ ɩɟɪɟɦɟɳɟɧɢɣ
)(˓ t
iii
uu (2.11)
ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɜɟɤɬɨɪ ɭɫɤɨɪɟɧɢɣ
)(˓ t
iii
uu ɢ (ɫ ɭɱɟɬɨɦ (2.14)) ɜɟɤɬɨɪ ɫɢɥ
ɢɧɟɪɰɢɢ
)(˓)(˓ tt
iiiiii
juMuMj
.
(2.27)
Ɂɞɟɫɶ
iii
uMj
2
Z
(2.28)
ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɜɟɤɬɨɪ ɚɦɩɥɢɬɭɞɧɵɯ ɡɧɚɱɟɧɢɣ ɫɢɥ ɢɧɟɪɰɢɢ,
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɜɟɤɬɨɪɭ
i
u . ȼɟɤɬɨɪ ɷɬɢɯ ɫɢɥ ɢɧɟɪɰɢɢ ɢ ɜɵɡɵɜɚɟɬ
ɞɟɮɨɪɦɚɰɢɸ ɫɨɨɪɭɠɟɧɢɹ ɩɨ ɣ
i ɋɎɄ.
ɉɪɢɦɟɪ 1. ȼ ɩɪɢɦɟɪɟ 1, ɪɚɫɫɦɨɬɪɟɧɧɨɦ ɜ ɩɨɞɪɚɡɞɟɥɟ 1.4, ɪɚɫɱɟɬɧɚɹ ɫɯɟɦɚ
ɠɟɥɟɡɨɛɟɬɨɧɧɨɣ ɛɚɥɤɢ ɫ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɟɦ, ɪɚɫɩɨɥɨɠɟɧɧɵɦ ɜ ɫɟɪɟɞɢɧɟ ɩɪɨɥɟɬɚ
(ɫɦ. ɪɢɫ. 1.24), ɛɵɥɚ ɩɪɟɞɫɬɚɜɥɟɧɚ ɤɚɤ ɫɢɫɬɟɦɚ ɫ ɨɞɧɨɣ ɫɬɟɩɟɧɶɸ ɫɜɨɛɨɞɵ.
ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɩɪɨɝɪɚɦɦɵ SCAD ɷɬɨ ɛɵɥɨ ɞɨɫɬɢɝɧɭɬɨ ɪɚɡɞɟɥɟɧɢɟɦ ɛɚɥɤɢ ɧɚ ɞɜɚ
ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɚ ɬɢɩɚ 2 «ɋɬɟɪɠɟɧɶ ɩɥɨɫɤɨɣ ɪɚɦɵ» ɢ ɡɚɦɟɧɨɣ ɪɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ
ɦɚɫɫɵ ɤɚɠɞɨɝɨ ɷɥɟɦɟɧɬɚ ɞɜɭɦɹ ɬɨɱɟɱɧɵɦɢ ɦɚɫɫɚɦɢ ɩɨ ɤɨɧɰɚɦ ɷɥɟɦɟɧɬɨɜ.
ȼ ɪɟɡɭɥɶɬɚɬɟ ɬɚɤɨɝɨ ɞɟɣɫɬɜɢɹ ɛɚɥɤɚ ɫɬɚɥɚ ɧɟɜɟɫɨɦɨɣ («ɛɟɡɦɚɫɫɨɜɨɣ») ɩɨ ɞɥɢɧɟ, ɚɟɟ
ɦɚɫɫɚ ɨɤɚɡɚɥɚɫɶ ɫɨɫɪɟɞɨɬɨɱɟɧɧɨɣ ɜ ɬɪɟɯ ɭɡɥɚɯ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɆɄɗ (ɫɦ. ɪɢɫ. 1.8, ɛ). ɉɪɢ
ɷɬɨɦ ɬɨɱɟɱɧɵɟ ɦɚɫɫɵ, ɩɨɩɚɜɲɢɟ ɜ ɨɩɨɪɧɵɟ ɭɡɥɵ 1 ɢ 3, ɨɤɚɡɚɥɢɫɶ ɧɟɩɨɞɜɢɠɧɵɦɢ ɩɪɢ
ɪɚɫɫɦɨɬɪɟɧɢɢ ɩɨɩɟɪɟɱɧɵɯ ɤɨɥɟɛɚɧɢɣ ɩɨɥɭɱɟɧɧɨɣ ɫɢɫɬɟɦɵ. ɉɪɢɜɟɞɟɧɧɚɹ ɬɨɱɟɱɧɚɹ ɦɚɫɫɚ
ɛɚɥɤɢ, ɨɤɚɡɚɜɲɚɹɫɹ ɜ ɭɡɥɟ 2, ɫɨɜɩɚɥɚ ɫ ɦɚɫɫɨɣ ɞɜɢɝɚɬɟɥɹ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɱɟɝɨ ɨɛɪɚɡɨɜɚɥɚɫɶ
ɫɭɦɦɚɪɧɚɹ ɦɚɫɫɚ
ɫ2
m , ɤɨɬɨɪɚɹ ɩɪɢ ɩɨɩɟɪɟɱɧɵɯ ɤɨɥɟɛɚɧɢɹɯ ɛɚɥɤɢ ɢɦɟɟɬ ɨɞɧɭ ɫɬɟɩɟɧɶ
ɫɜɨɛɨɞɵ.
ȿɫɥɢ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɆɄɗ ɪɚɫɫɦɚɬɪɢɜɚɟɦɭɸ ɛɚɥɤɭ ɪɚɡɛɢɬɶ ɧɟ ɧɚ ɞɜɚ, ɚ ɧɚ ɱɟɬɵɪɟ
ɪɚɜɧɵɯ ɷɥɟɦɟɧɬɚ (ɪɢɫ. 2.2, ɚ) ɢ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɚɤɨɣ ɠɟ ɫɩɨɫɨɛ ɡɚɦɟɧɵ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɦɚɫɫɵ
ɬɨɱɟɱɧɵɦɢ ɦɚɫɫɚɦɢ ɩɨ ɤɨɧɰɚɦ Ʉɗ, ɬɨ ɩɪɢ ɩɨɩɟɪɟɱɧɵɯ ɤɨɥɟɛɚɧɢɹɯ ɛɚɥɤɢ ɩɨɥɭɱɢɦ ɫɢɫɬɟɦɭ ɫ
ɬɪɟɦɹ ɫɬɟɩɟɧɹɦɢ ɫɜɨɛɨɞɵ (ɪɢɫ. 2.2, ɛ).
Ɍɚɤɚɹ ɫɢɫɬɟɦɚ ɢɦɟɟɬ ɬɪɢ ɋɑ ɢ ɬɪɢ ɋɎɄ (ɬɪɢ «ɦɨɞɵ» ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ),
ɩɪɟɞɫɬɚɜɥɟɧɧɵɯ ɩɪɢ ɪɚɫɱɟɬɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɜɟɤɬɨɪɚɦɢ ɩɨɩɟɪɟɱɧɵɯ ɩɟɪɟɦɟɳɟɧɢɣ ɦɚɫɫ ɜ
ɤɚɠɞɨɣ ɋɎɄ ɛɚɥɤɢ.
Ɋɟɲɢɦ ɡɚɞɚɱɭ ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ ɋɑ ɢ ɋɎɄ ɫ ɩɨɦɨɳɶɸ ɩɪɨɝɪɚɦɦɵ SCAD. ɗɬɚ
ɞɢɧɚɦɢɱɟɫɤɚɹ ɡɚɞɚɱɚ ɜ ɩɪɨɝɪɚɦɦɟ SCAD ɧɚɡɵɜɚɟɬɫɹ «ɦɨɞɚɥɶɧɵɦ ɚɧɚɥɢɡɨɦ».
95
Ɋɢɫ. 2.2
ɋ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ ɩɪɨɝɪɚɦɦɚ SCAD ɭɠɟ ɧɟɨɞɧɨɤɪɚɬɧɨ ɢɫɩɨɥɶɡɨɜɚɥɚɫɶ ɭɱɚɳɢɦɢɫɹ
ɞɥɹ ɪɟɲɟɧɢɹ ɪɚɡɥɢɱɧɵɯ ɫɬɚɬɢɱɟɫɤɢɯ ɡɚɞɚɱ [1, 2, 3] ɢ ɞɢɧɚɦɢɱɟɫɤɢɯ ɡɚɞɚɱ ɜ ɞɚɧɧɨɦ ɩɨɫɨɛɢɢ,
ɪɚɫɫɦɨɬɪɢɦ ɩɪɨɰɟɞɭɪɭ ɪɚɫɱɟɬɚ ɜ ɫɨɤɪɚɳɟɧɧɨɦ ɜɢɞɟ.
ɂɧɫɬɪɭɤɰɢɹ ɩɨ ɪɟɲɟɧɢɸ ɞɢɧɚɦɢɱɟɫɤɨɣ ɡɚɞɚɱɢ «Ɇɨɞɚɥɶɧɵɣ ɚɧɚɥɢɡ»
ɫ ɩɨɦɨɳɶɸ ɩɪɨɝɪɚɦɦɵ SCAD
ɗɬɚɩɵ 1 ɢ 2. ȼɵɩɨɥɧɢɦ ɷɬɚɩɵ 1 ɢ 2 ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɪɚɫɱɟɬɚ, ɩɪɢɜɟɞɟɧɧɨɣ ɜ ɍɆɄ ɩɨ
ɫɬɪɨɢɬɟɥɶɧɨɣ ɦɟɯɚɧɢɤɟ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ [1, 2], ɢ ɫɨɡɞɚɞɢɦ ɪɚɫɱɟɬɧɭɸ ɫɯɟɦɭ ɛɚɥɤɢ ɜ ɜɢɞɟ
ɫɢɫɬɟɦɵ ɱɟɬɵɪɟɯ Ʉɗ ɬɢɩɚ 2 «ɋɬɟɪɠɟɧɶ ɩɥɨɫɤɨɣ ɪɚɦɵ».
ɗɬɚɩ 3. ɋɨɡɞɚɞɢɦ ɡɚɝɪɭɠɟɧɢɟ ɞɥɹ ɞɢɧɚɦɢɱɟɫɤɨɣ ɡɚɞɚɱɢ «Ɇɨɞɚɥɶɧɵɣ ɚɧɚɥɢɡ». Ⱦɥɹ
ɷɬɨɝɨ ɧɚɠɦɟɦ ɤɧɨɩɤɭ «Ⱦɢɧɚɦɢɱɟɫɤɢɟ ɜɨɡɞɟɣɫɬɜɢɹ» ɧɚ ɢɧɫɬɪɭɦɟɧɬɚɥɶɧɨɣ ɩɚɧɟɥɢ,
ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɪɚɡɞɟɥɭ Ɂɚɝɪɭɠɟɧɢɹ. ɉɨɹɜɢɜɲɢɣɫɹ ɩɪɢ ɷɬɨɦ ɜɢɞ ɞɢɚɥɨɝɨɜɨɝɨ ɨɤɧɚ
ɡɚɜɢɫɢɬ ɨɬ ɢɫɩɨɥɶɡɭɟɦɨɣ ɜɟɪɫɢɢ ɩɪɨɝɪɚɦɦɵ SCAD. Ɉɞɧɚɤɨ, ɩɪɢɧɰɢɩɢɚɥɶɧɨɝɨ ɪɚɡɥɢɱɢɹ ɜ
ɩɪɨɰɟɞɭɪɟ ɡɚɞɚɧɢɹ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ ɜ ɪɚɡɧɵɯ ɜɟɪɫɢɹɯ ɧɟɬ.
ɇɢɠɟ ɩɨɤɚɡɚɧɚ ɱɚɫɬɶ ɜɚɪɢɚɧɬɚ ɜɢɞɚ ɞɢɚɥɨɝɨɜɨɝɨ ɨɤɧɚ «ɉɚɪɚɦɟɬɪɵ ɞɢɧɚɦɢɱɟɫɤɢɯ
ɜɨɡɞɟɣɫɬɜɢɣ», ɝɞɟ ɧɚ ɫɬɪ. 1 «ȼɜɨɞ ɩɚɪɚɦɟɬɪɨɜ ɞɢɧɚɦɢɱɟɫɤɨɣ ɧɚɝɪɭɡɤɢ» ɧɚ ɩɨɥɟ «ȼɢɞ
ɜɨɡɞɟɣɫɬɜɢɹ» ɜɵɛɢɪɚɟɦ «ɉɪɨɱɢɟ ɜɨɡɞɟɣɫɬɜɢɹ», ɚ ɡɚɬɟɦ «Ɇɨɞɚɥɶɧɵɣ ɚɧɚɥɢɡ». ɇɚ ɷɬɨɣ ɠɟ
ɫɬɪɚɧɢɰɟ ɜ ɨɤɧɟ «ɂɦɹ ɡɚɝɪɭɠɟɧɢɹ» ɡɚɩɢɫɵɜɚɟɦ ɢɦɹ «ɦɨɞ-3».
ȼɫɟ ɨɫɬɚɥɶɧɵɟ ɜɨɡɦɨɠɧɨɫɬɢ ɷɬɨɝɨ ɨɤɧɚ ɩɨɤɚ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɧɟ ɛɭɞɟɦ ɢ ɧɚɠɚɬɢɟɦ ɜɟɪɯɧɟɣ
ɫɬɪɨɤɟ «ɦɨɞɚɥɶɧɵɣ ɚɧɚɥɢɡ» ɩɟɪɟɣɞɟɦ ɧɚ ɜɬɨɪɭɸ ɫɬɪɚɧɢɰɭ ɞɢɚɥɨɝɨɜɨɝɨ ɨɤɧɚ, ɧɚ ɤɨɬɨɪɨɣ
ɜɜɨɞɢɦ ɱɢɫɥɨ ɭɱɢɬɵɜɚɟɦɵɯ ɮɨɪɦ ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ (ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ – 3).
ɛ
q
m
4
m
3
5
4
2 2
2
2
ɞ
G
ɚ
)
m
2
3
2
1
ɛ
)
96
ɉɨɞɬɜɟɪɞɢɜ ɜɜɟɞɟɧɧɭɸ ɢɧɮɨɪɦɚɰɢɸ ɧɚɠɚɬɢɟɦ ɤɧɨɩɤɢ «ɈɄ», ɡɚɤɪɨɟɦ ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ ɢ
ɧɚ ɢɧɫɬɪɭɦɟɧɬɚɥɶɧɨɣ ɩɚɧɟɥɢ ɪɚɡɞɟɥɚ Ɂɚɝɪɭɠɟɧɢɹ ɧɚɠɦɟɦ ɤɧɨɩɤɭ «ɂɧɟɪɰɢɨɧɧɵɟ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ». ȼ ɨɬɤɪɵɜɲɟɦɫɹ ɫɩɢɫɤɟ ɜɵɛɟɪɟɦ «Ɂɚɞɚɧɢɟ ɦɚɫɫ». Ɉɬɤɪɨɟɬɫɹ ɨɤɧɨ «Ɇɚɫɫɵ».
Ɋɚɫɫɦɨɬɪɢɦ ɜɧɚɱɚɥɟ, ɩɪɢɜɟɞɟɧɧɭɸ ɧɢɠɟ, ɟɝɨ ɱɚɫɬɶ «ɂɧɟɪɰɢɨɧɧɵɟ ɫɜɨɣɫɬɜɚ ɭɡɥɨɜ». Ɂɞɟɫɶ
ɜɜɟɞɟɧ ɜɟɫ ɞɜɢɝɚɬɟɥɹ 1.5 ɬɫ, ɨɬɧɟɫɟɧɧɵɣ ɤ ɭɡɥɭ 3 ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɆɄɗ ɛɚɥɤɢ ɢ ɭɤɚɡɚɧɨ
ɧɚɩɪɚɜɥɟɧɢɟ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ ɷɬɨɣ ɦɚɫɫɵ:
.
Ɉɤɧɨ ɡɚɤɪɵɜɚɟɬɫɹ ɢ ɫ ɩɨɦɨɳɶɸ ɤɭɪɫɨɪɚ ɫɞɟɥɚɧɧɵɣ ɜɜɨɞ ɨɬɧɨɫɢɬɫɹ ɤ ɭɡɥɭ 3 ɧɚ ɪɚɫɱɟɬɧɨɣ
ɫɯɟɦɟ ɆɄɗ ɛɚɥɤɢ ɢ ɩɨɞɬɜɟɪɠɞɚɟɬɫɹ ɧɚɠɚɬɢɟɦ ɤɧɨɩɤɢ «ɈɄ» ɧɚ ɢɧɫɬɪɭɦɟɧɬɚɥɶɧɨɣ ɩɚɧɟɥɢ.
ɉɪɢ ɧɚɠɚɬɵɯ ɧɚ ɮɢɥɶɬɪɟ ɨɬɨɛɪɚɠɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɤɧɨɩɚɯ ɜ ɭɡɥɟ 3 ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ
ɩɨɥɭɱɢɦ ɢɧɮɨɪɦɚɰɢɸ ɨ ɫɞɟɥɚɧɧɨɦ ɜɜɨɞɟ (ɪɢɫ. 2.3).
Ⱦɥɹ ɜɜɨɞɚ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɦɚɫɫɵ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɷɥɟɦɟɧɬɚ ɧɚ ɩɪɢɜɟɞɟɧɧɨɦ ɧɢɠɟ
ɩɨɥɟ «ɦɚɫɫɵ ɜ ɷɥɟɦɟɧɬɚɯ» ɜɜɨɞɢɬɫɹ ɜɟɫ ɨɞɧɨɝɨ ɦɟɬɪɚ ɞɥɢɧɵ ɷɥɟɦɟɧɬɚ (ɜ ɩɪɢɦɟɪɟ: 0.6 ɬɫ).
ɉɨɫɥɟ ɡɚɤɪɵɬɢɹ ɨɤɧɚ ɧɚɠɚɬɢɟɦ ɤɧɨɩɤɢ «ɈɄ» ɷɥɟɦɟɧɬɵ ɧɚ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ, ɢɦɟɸɳɢɟ
ɭɤɚɡɚɧɧɭɸ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɜɟɫɚ, «ɨɬɦɟɱɚɸɬɫɹ» (ɷɬɚ ɩɪɨɰɟɞɭɪɚ ɧɟɨɞɧɨɤɪɚɬɧɨ ɨɬɦɟɱɚɥɚɫɶ ɜ
ɪɚɡɥɢɱɧɵɯ ɩɪɢɦɟɪɚɯ ɪɚɫɱɟɬɚ). ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɭɱɢɦ ɫɯɟɦɭ ɡɚɝɪɭɠɟɧɢɹ 1 ɫɢɦɟɧɟɦ «ɦɨɞ-3» ɜ
ɜɢɞɟ, ɩɪɢɜɟɞɟɧɧɨɦ ɧɚ ɪɢɫ. 2.3, ɤɨɬɨɪɭɸ ɧɟɨɛɯɨɞɢɦɨ ɫɨɯɪɚɧɢɬɶ.
Ɋɢɫ. 2.3
ɗɬɚɩ 4. ȼɵɩɨɥɧɹɟɦ ɥɢɧɟɣɧɵɣ ɪɚɫɱɟɬ ɢ ɩɪɢɜɨɞɢɦ ɟɝɨ ɪɟɡɭɥɶɬɚɬɵ. Ɋɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɚ
ɞɢɧɚɦɢɱɟɫɤɨɣ ɡɚɞɚɱɢ «Ɇɨɞɚɥɶɧɵɣ ɚɧɚɥɢɡ» ɜɵɞɚɸɬɫɹ ɜ ɬɚɛɥɢɰɟ «Ɉɮɨɪɦɥɟɧɢɟ ɪɟɡɭɥɶɬɚɬɨɜ
ɪɚɫɱɟɬɚ» ɜ ɪɚɡɞɟɥɟ «Ⱦɢɧɚɦɢɤɚ» ɜ ɜɢɞɟ ɫɥɟɞɭɸɳɢɯ ɬɪɟɯ ɬɚɛɥɢɰ.
------------------------------------------------------------------
| ɊȺɋɉɊȿȾȿɅȿɇɂȿ ȼȿɋɈȼ ɆȺɋɋ, ɬɫ |
------------------------------------------------------------------
| 1 2 3 4 5 |
------------------------------------------------------------------
| 1 - ( ɦɨɞ-3) |
| Z 1.2 2.7 1.2 |
------------------------------------------------------------------
D0.6
1
D0.6
D0.6
3
2
4
5
D0.6
D1.5
97
ȼ ɬɚɛɥɢɰɟ ɞɚɧ ɜɟɫ ɬɨɱɟɱɧɵɯ ɦɚɫɫ ɜ ɭɡɥɚɯ 2, 3, 4 ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɛɚɥɤɢ ɩɨɫɥɟ ɩɪɢɜɟɞɟɧɢɹ
ɜ ɩɪɨɝɪɚɦɦɟ SCAD ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɦɚɫɫɵ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɤ ɭɤɚɡɚɧɧɵɦ ɭɡɥɚɦ.
-----------------------------------------------------------------
Ɂɚɝpɭ: N COȻCTB.: ɑ A C T O T ɕ: ɉEPɂOȾɕ |
| : ɉ/ɉ : :-----------------------------:----------
|ɠɟɧɢɟ: : ɁHAɑEHɂə : 1/C : Ƚɐ : C |
------------------------------------------------------------------
| 1 1 .0137914 72.50864 11.54596 .0866103 |
| 2 .0027208 367.5373 58.52505 .0170867 |
| 3 .0015063 663.8773 105.7129 .0094595 |
------------------------------------------------------------------
------------------------------------------------------------------
| ɎɈɊɆɕ ɄɈɅȿȻȺɇɂɃ, ɦ (ɪɢɫ. 2.4) |
------------------------------------------------------------------
| 1 2 3 4 5 |
------------------------------------------------------------------
| 1 - 1 ( ɦɨɞ-3) |
| Z 0.6994 1. 0.6994 |
| 1 - 2 |
| Z 1. 0 -1. |
| 1 - 3 |
| Z 1. -0.6216 1. |
------------------------------------------------------------------
ɉɪɢɦɟɱɚɧɢɟ ɤ ɬɚɛɥ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɪɟɲɟɧɢɹ ɜ ɩɪɨɝɪɚɦɦɟ SCAD ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ (2.15)
ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɩɨɫɬɨɹɧɧɨɣ ɜɟɥɢɱɢɧɵ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɟɪɟɦɟɳɟɧɢɹ ɦɚɫɫ ɜ ɭɡɥɚɯ 2, 3 ɢ 4,
ɹɜɥɹɸɳɢɟɫɹ ɤɨɦɩɨɧɟɧɬɚɦɢ ɜɟɤɬɨɪɨɜ
i
u , 4,3,2 i . ɉɨɫɬɨɹɧɧɚɹ ɜɟɥɢɱɢɧɚ
ki
u
(2.26) ɜ ɤɚɠɞɨɣ
ɋɎɄ ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɜɧɨɣ ɡɧɚɱɟɧɢɸ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɩɟɪɟɦɟɳɟɧɢɹ ɭɡɥɚ k ɜ ɷɬɨɣ ɋɎɄ. Ɍɚɤɢɦ
ɨɛɪɚɡɨɦ, ɜ ɬɚɛɥɢɰɟ ɩɪɢɜɟɞɟɧɵ ɡɧɚɱɟɧɢɹ ɜɟɤɬɨɪɚ
i
y (2.26).
ɉɪɢ ɨɬɤɪɵɬɢɢ ɧɚ ɞɟɪɟɜɟ ɩɪɨɟɤɬɚ ɪɚɡɞɟɥɚ «Ƚɪɚɮɢɱɟɫɤɢɣ ɚɧɚɥɢɡ», ɦɨɝɭɬ ɛɵɬɶ
ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɨɬɤɪɵɬɵ ɢ ɫɨɯɪɚɧɟɧɵ ɢɡɨɛɪɚɠɟɧɢɹ ɋɎɄ (ɪɢɫ. 2.4).
Ɋɢɫ. 2.4
1 2 3 4 5
1-ɹɋɎɄ
12 345
2-ɹɋɎɄ
1 2 3 4 5
3-ɹɋɎɄ
98
Ɉɛɪɚɬɢɦ ɜɧɢɦɚɧɢɟ ɜɨ ɜɬɨɪɨɣ ɬɚɛɥɢɰɟ ɧɚ ɡɧɚɱɟɧɢɟ ɩɟɪɜɨɣ ɱɚɫɬɨɬɵ. Ɉɧɚ ɩɨɥɭɱɢɥɚɫɶ
ɩɪɢɦɟɪɧɨ ɧɚ 5 ɩɪɨɰɟɧɬɨɜ ɜɵɲɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɫɨɛɫɬɜɟɧɧɨɣ ɱɚɫɬɨɬɵ ɜ ɫɢɫɬɟɦɟ ɫ ɨɞɧɨɣ
ɫɬɟɩɟɧɶɸ ɫɜɨɛɨɞɵ (ɫɦ. ɩɪɢɦɟɪ 4 ɜ ɩɨɞɪɚɡɞɟɥɟ 1.1).
ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɛɨɥɟɟ ɬɨɱɧɚɹ ɚɩɩɪɨɤɫɢɦɚɰɢɹ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɦɚɫɫɵ ɛɚɥɤɢ
ɞɢɫɤɪɟɬɧɵɦɢ ɦɚɫɫɚɦɢ, ɭɦɟɧɶɲɚɹ ɩɪɢɜɟɞɟɧɧɭɸ ɦɚɫɫɭ, ɨɬɧɨɫɹɳɭɸɫɹ ɤ ɫɪɟɞɧɟɦɭ ɭɡɥɭ,
ɫɩɨɫɨɛɫɬɜɭɟɬ ɭɜɟɥɢɱɟɧɢɸ ɩɟɪɜɨɣ ɫɨɛɫɬɜɟɧɧɨɣ ɱɚɫɬɨɬɵ (ɜ ɫɢɫɬɟɦɟ ɫ ɨɞɧɨɣ ɫɬɟɩɟɧɶɸ ɫɜɨɛɨɞɵ
ɷɬɨ ɜɢɞɧɨ ɢɡ ɮɨɪɦɭɥ (1.14)).
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɱɢɫɥɚ ɷɥɟɦɟɧɬɨɜ, ɧɚ ɤɨɬɨɪɵɟ ɪɚɡɞɟɥɟɧɚ ɛɚɥɤɚ,
ɫɨɛɫɬɜɟɧɧɵɟ ɱɚɫɬɨɬɵ ɢ ɮɨɪɦɵ ɤɨɥɟɛɚɧɢɣ ɛɭɞɭɬ ɭɬɨɱɧɹɬɶɫɹ.
ɇɢɠɟ ɩɪɢɜɟɞɟɧɵ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɬɚɛɥɢɰɵ ɩɪɢ ɪɚɡɞɟɥɟɧɢɢ ɛɚɥɤɢ ɧɚ 8 ɷɥɟɦɟɧɬɨɜ.
------------------------------------------------------------------
| ɊȺɋɉɊȿȾȿɅȿɇɂȿ ȼȿɋɈȼ ɆȺɋɋ, ɬɫ |
------------------------------------------------------------------
| 1 2 3 4 5 6 7 8 9 |
------------------------------------------------------------------
| 1 - (ɦɨɞ-7) |
| Z .6 .6 .6 2.1 .6 .6 .6 |
------------------------------------------------------------------
------------------------------------------------------------------
Ɂɚɝpɭ: N : COȻCTB. ɑ A C T O T ɕ : ɉEPɂOȾɕ |
: ɉ/ɉ : :-----------------------------:----------------
|ɠɟɧɢɟ: : ɁHAɑEHɂə: 1/C : Ƚɐ : C |
------------------------------------------------------------------
| 1 1 .013788 72.52652 11.5488 .086589 |
| 2 .0027018 370.1119 58.93501 .0169678|
| 3 .0014249 701.7884 111.7497 .0089485|
| 4 .0006802 1470.149 234.1002 .0042716|
| 5 .0005024 1990.379 316.9394 .0031551|
| 6 .0003203 3121.445 497.0455 .0020118|
| 7 .0002825 3539.174 563.5627 .0017744|
------------------------------------------------------------------
------------------------------------------------------------------
| ɎɈɊɆɕ ɄɈɅȿȻȺɇɂɃ, ɦ |
------------------------------------------------------------------
| 1 2 3 4 5 6 7 8 |
------------------------------------------------------------------
| 1 - 1 ( ɦɨɞ-7) |
| Z .3766 .6994 .92 1. .92 .6994 .3766 |
| 1 - 2 |
| Z -.7071 -1. -.7071 .7071 1. .7071 |
| 1 - 3 |
| Z .827 .8046 .0207 -.5104 .0207 .8046 .827 |
| 1 - 4 |
| Z .6666 -.6666 .6666 -.6666 |
| 1 - 5 |
| Z .5785 -.3111 -.4655 .2446 -.4655 -.3111 .5785 |
| 1 - 6 |
| Z .4309 -.6094 .4309 -.4309 .6094 -.4309 |
| 1 - 7 |
| Z .388 -.6463 .7246 -.2061 .7246 -.6463 .388 |
------------------------------------------------------------------
99
Ⱦɥɹ ɢɥɥɸɫɬɪɚɰɢɢ ɜɢɞɚ ɋɎɄ ɜ ɩɨɫɥɟɞɧɟɦ ɪɚɡɛɢɟɧɢɢ ɛɚɥɤɢ ɧɚ Ʉɗ ɩɪɢɜɟɞɟɧɵ ɟɳɟ ɞɜɟ
ɋɎɄ: ɱɟɬɜɟɪɬɚɹ ɢ ɩɹɬɚɹ (ɪɢɫ. 2.5).
ɋ ɭɜɟɥɢɱɟɧɢɟɦ ɱɢɫɥɚ Ʉɗ ɫɨɛɫɬɜɟɧɧɵɟ ɱɚɫɬɨɬɵ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɢɦ ɋɎɄ ɭɬɨɱɧɹɸɬɫɹ.
ɇɟɨɛɯɨɞɢɦɨɫɬɶ ɪɚɡɛɢɟɧɢɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɫɢɫɬɟɦɵ ɧɚ ɛɨғɥɶɲɟɟ ɱɢɫɥɨ ɷɥɟɦɟɧɬɨɜ
ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɪɚɤɬɢɱɟɫɤɨɣ ɧɟɨɛɯɨɞɢɦɨɫɬɶɸ ɩɨɥɭɱɟɧɢɹ ɡɚɞɚɧɧɨɣ ɬɨɱɧɨɫɬɢ ɪɚɫɱɟɬɚ.
Ɋɢɫ. 2.5
ɑɢɫɥɨ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɞɨɥɠɧɨ ɛɵɬɶ ɜɵɛɪɚɧɨ ɬɚɤɢɦ, ɱɬɨɛɵ ɧɭɠɧɵɟ ɋɑ ɢ ɋɎɄ
ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɢɡɦɟɧɹɥɢɫɶ ɛɵ ɩɪɢ ɞɚɥɶɧɟɣɲɟɦ ɭɜɟɥɢɱɟɧɢɢ ɱɢɫɥɚ Ʉɗ.
2.3. ɋɜɨɣɫɬɜɨ ɨɪɬɨɝɨɧɚɥɶɧɨɫɬɢ ɫɨɛɫɬɜɟɧɧɵɯ ɮɨɪɦ ɤɨɥɟɛɚɧɢɣ
ɋɨɛɫɬɜɟɧɧɵɟ ɮɨɪɦɵ ɤɨɥɟɛɚɧɢɣ ɨɛɥɚɞɚɸɬ ɫɜɨɣɫɬɜɨɦ ɨɪɬɨɝɨɧɚɥɶɧɨɫɬɢ,
ɡɚɤɥɸɱɚɸɳɢɦɫɹ ɜ ɬɨɦ, ɱɬɨ ɫɨɛɥɸɞɚɟɬɫɹ ɪɚɜɟɧɫɬɜɨ ɧɭɥɸ ɫɥɟɞɭɸɳɟɝɨ
ɩɪɨɢɡɜɟɞɟɧɢɹ ɦɚɬɪɢɰ:
ij
ij
z ɩɪɢ0)(
ɬ
uMu .
(2.29)
Ⱦɥɹ ɞɨɤɚɡɚɬɟɥɶɫɬɜɚ ɪɚɫɫɦɨɬɪɢɦ ɞɜɟ ɥɸɛɵɟ ɋɎɄ (j - ɸɢi – ɸ), ɤɨɬɨɪɵɟ
ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɧɟɤɨɬɨɪɵɦ ɞɜɭɦ ɧɟ ɪɚɜɧɵɦ ɞɪɭɝ ɞɪɭɝɭ ɫɨɛɫɬɜɟɧɧɵɦ ɱɚɫɬɨɬɚɦ
(
ij
ZzZ ).
ɉɪɟɞɫɬɚɜɢɦ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ (2.16) ɜ ɜɢɞɟ
)(
2
iii
uMDu Z .
(2.30)
ɍɱɢɬɵɜɚɹ ɫɦɵɫɥ ɦɚɬɪɢɰɵ
D
, ɤɚɤ ɦɚɬɪɢɰɵ ɜɥɢɹɧɢɹ ɫɢɥ ɧɚ ɩɟɪɟɦɟɳɟɧɢɹ
ɩɨ ɢɯ ɧɚɩɪɚɜɥɟɧɢɹɦ, ɡɚɤɥɸɱɚɟɦ, ɱɬɨ
2
iii
uMj
Z
ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɜɟɤɬɨɪ
ɫɢɥ, ɫɬɚɬɢɱɟɫɤɢ ɩɪɢɥɨɠɟɧɧɵɯ ɤ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɭɩɪɭɝɨɣ ɫɢɫɬɟɦɟ ɢ
ɜɵɡɵɜɚɸɳɢɯ ɟɟ ɩɟɪɟɦɟɳɟɧɢɹ ɜ ɜɢɞɟ ɜɟɤɬɨɪɚ
i
u . ɗɬɨ ɛɵɥɨ ɩɨɤɚɡɚɧɨ ɢ ɜ
ɜɵɪɚɠɟɧɢɹɯ (2.27) ɢ (2.28).