ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
188
beg
, , 0
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T z r
T
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@
w
flat
( , 0),
,
z z r z

*
w
*
cyl
0,
, 0 ,
0 ;
0,
,
0 .
r z
z z
r
r
z z
­
ª
º d
¬
¼
° ®
ª
º t
° ¬
¼
¯
(8)
ȼ ɮɨɪɦɭɥɚɯ (1)—(8):
U
—
ɩɥɨɬɧɨɫɬɶ, ɤɝ/ɦ
3
;
c
—
ɭɞɟɥɶɧɚɹ ɬɟɩ-
ɥɨɟɦɤɨɫɬɶ, Ⱦɠ/(ɤɝ
˜
K); ,
z r
—
ɨɫɢ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢ-
ɧɚɬ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɜɞɨɥɶ ɨɫɢ ɫɢɦɦɟɬɪɢɢ ɬɟɥɚ ɢ ɩɨ
ɧɨɪɦɚɥɢ ɤ ɧɟɣ, ɜ ɞɨɥɹɯ ɨɬ ɯɚɪɚɤɬɟɪɧɨɝɨ ɥɢɧɟɣɧɨɝɨ ɪɚɡɦɟɪɚ ɬɟɥɚ;
s
—
ɯɚɪɚɤɬɟɪɧɵɣ ɥɢɧɟɣɧɵɣ ɪɚɡɦɟɪ ɬɟɥɚ, ɦ;
, ,
T z r
W
—
ɬɟɦɩɟɪɚɬɭɪɚ, K;
W
—
ɜɪɟɦɟɧɧáɹ ɤɨɨɪɞɢɧɚɬɚ, ɫ;
cyl
r
—
ɪɚɞɢɭɫ ɰɢɥɢɧɞɪɚ;
end
W
—
ɜɟɪɯ-
ɧɹɹ ɝɪɚɧɢɰɚ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɜɪɟɦɟɧɧɨɝɨ ɢɧɬɟɪɜɚɥɚ, ɫ;
O
—
ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ, ȼɬ/(ɦ
˜
K);
-
—
ɭɝɨɥ ɦɟɠɞɭ ɤɚɫɚɬɟɥɶɧɨɣ ɤ ɨɛɪɚ-
ɡɭɸɳɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɬɟɥɚ ɢ ɨɫɶɸ
z
,
ɪɚɞ;
Q
—
ɭɞɟɥɶɧɵɣ ɬɟɩɥɨɜɨɣ
ɩɨɬɨɤ, ɩɨɞɜɨɞɢɦɵɣ ɩɨ ɧɨɪɦɚɥɢ ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɬɟɥɚ, ȼɬ/ɦ
2
;
beg
T
—
ɬɟɦɩɟɪɚɬɭɪɚ ɬɟɥɚ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ, K.
Ɉɫɶ
z
ɧɚɩɪɚɜɥɟɧɚ ɜɧɭɬɪɶ ɬɟɥɚ, ɚ ɟɟ ɧɭɥɟɜɨɟ ɡɧɚɱɟɧɢɟ ɫɨɜɦɟɳɟɧɨ
ɫ ɬɨɱɤɨɣ ɩɟɪɟɫɟɱɟɧɢɹ ɨɫɢ ɫɢɦɦɟɬɪɢɢ ɬɟɥɚ ɫ ɩɨɜɟɪɯɧɨɫɬɶɸ ɟɝɨ ɡɚɬɭɩ-
ɥɟɧɧɨɣ ɱɚɫɬɢ ɜ ɧɭɥɟɜɨɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ. ɂɧɞɟɤɫ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ
ɭɤɚɡɵɜɚɟɬ ɨɫɶ, ɜɞɨɥɶ ɤɨɬɨɪɨɣ ɨɧɚ ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɤɨɧ-
ɞɭɤɬɢɜɧɨɝɨ ɬɟɩɥɨɩɟɪɟɧɨɫɚ.
ɉɟɪɟɯɨɞ ɤ ɩɨɞɜɢɠɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ.
ȼ ɩɨɞɚɜɥɹɸɳɟɦ
ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ ɱɢɫɥɟɧɧɨɟ ɪɟɲɟɧɢɟ ɡɚɞɚɱ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ
ɤɥɚɫɫɚ ɧɚɯɨɞɹɬ ɜ ɢɫɯɨɞɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ (ɧɚɡɨɜɟɦ ɟɟ ɧɟɩɨɞɜɢɠ-
ɧɨɣ) ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɹɜɧɵɯ ɢɥɢ ɧɟɹɜɧɵɯ ɪɚɫɱɟɬɧɵɯ ɫɯɟɦ; ɜ ɩɨ-
ɫɥɟɞɧɟɦ ɫɥɭɱɚɟ ɨɛɵɱɧɨ ɩɪɢɦɟɧɹɸɬ ɦɟɬɨɞ ɩɟɪɟɦɟɧɧɵɯ ɧɚɩɪɚɜɥɟɧɢɣ
[2].
Ʉ ɧɟɞɨɫɬɚɬɤɚɦ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɬɚɤɢɯ ɩɨɞɯɨɞɨɜ ɤ ɪɟɲɟɧɢɸ ɡɚɞɚɱ,
ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɯɫɹ ɞɨɫɬɚɬɨɱɧɨ ɫɥɨɠɧɨɣ ɮɨɪɦɨɣ ɪɚɫɱɟɬɧɨɣ ɨɛɥɚɫɬɢ,
ɨɬɧɨɫɹɬ:
x
ɫɥɨɠɧɨɫɬɶ ɮɨɪɦɢɪɨɜɚɧɢɹ ɤɨɧɟɱɧɨ-ɪɚɡɧɨɫɬɧɵɯ ɨɩɟɪɚɬɨɪɨɜ ɜ
ɨɤɪɟɫɬɧɨɫɬɢ ɝɪɚɧɢɰ ɷɬɨɣ ɨɛɥɚɫɬɢ, ɨɛɥɚɞɚɸɳɢɯ ɜɬɨɪɵɦ ɩɨɪɹɞɤɨɦ
ɬɨɱɧɨɫɬɢ ɚɩɩɪɨɤɫɢɦɚɰɢɢ (ɨɫɨɛɟɧɧɨ ɩɪɢ ɩɨɞɜɢɠɧɨɫɬɢ ɱɚɫɬɢ ɢɡ ɭɤɚ-
ɡɚɧɧɵɯ ɝɪɚɧɢɰ);
x
ɫɥɨɠɧɨɫɬɶ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɧɟɪɚɜɧɨɦɟɪɧɵɯ ɫɟɬɨɤ ɩɪɢ ɢɡɦɟɧɟɧɢɢ
ɪɚɡɦɟɪɨɜ ɨɛɥɚɫɬɢ ɨɩɪɟɞɟɥɟɧɢɹ ɢɫɤɨɦɨɣ ɮɭɧɤɰɢɢ ɫ ɬɟɱɟɧɢɟɦ ɜɪɟɦɟɧɢ.
Ɉɞɧɢɦ ɢɡ ɜɨɡɦɨɠɧɵɯ ɩɭɬɟɣ ɪɟɲɟɧɢɹ ɭɤɚɡɚɧɧɵɯ ɩɪɨɛɥɟɦ ɹɜɥɹɟɬ-
ɫɹ ɩɟɪɟɯɨɞ ɨɬ ɧɟɩɨɞɜɢɠɧɨɣ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ
^ `
, ,
z r
W
ɤ ɩɨɞɜɢɠɧɨɣ
ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ
^
`
, ,
x y
W
c
,
ɤɨɬɨɪɚɹ ɞɥɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɡɚɞɚɱɢ
ɢɦɟɟɬ ɜɢɞ
w
,
,
z z r
x
W
'
,
y r
.
W
W
c