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26
()
()
()
;
I
288,60
943,29447,12500,7136,3847,4415,2
I
1
2736,2
3
2
736,22
2
1
I
1
2764,1
3
2
764,12
2
1
I
1
764,129,1229,129,12764,1764,12
6
6
I
1
446,1
3
2
3446,1
2
1
I
1
182,1764,12182,1
182,12764,1764,12
6
6
I
1
554,1
3
2
3554,1
2
1
I
1
dx
EJ
MM
1
13
32
21
1
6
1
l
0
11
11
=
=+++++=⋅⋅⋅⋅⋅⋅+
+⋅⋅⋅⋅⋅⋅+⋅⋅−⋅⋅+⋅⋅⋅+
+⋅⋅⋅⋅⋅+⋅⋅−⋅⋅+⋅⋅⋅⋅+
+⋅⋅⋅⋅⋅=
⋅
=δ
∑
∫
()
()
()
;
I
886,12
052,6292,0351,0710,2739,0742,2
I
1
223,1
3
2
23,12
2
1
I
1
227,0
3
2
27,02
2
1
I
1
114,027,02114,0114,0227,027,02
6
6
I
1
344,1
3
2
344,13
2
1
I
1
426,027,0227,0
27,02426,0426,02
6
6
I
1
656,1
3
2
656,13
2
1
I
1
dx
EJ
MM
1
13
32
21
1
6
1
l
0
22
22
=
=+++++=⋅⋅⋅⋅⋅⋅+
+⋅⋅⋅⋅⋅⋅+⋅⋅+⋅⋅+⋅⋅⋅+
+⋅⋅⋅⋅⋅+⋅⋅+⋅⋅+⋅⋅⋅⋅+
+⋅⋅⋅⋅⋅=
⋅
=δ
∑
∫
l
()
()
()
.
I
22
462,13905,1768,0915,2378,0573,2
I
1
2736,2
3
2
23,12
2
1
I
1
2764,1
3
2
27,02
2
1
I
1
27,029,1114,0764,129,1114,02764,127,02
6
6
I
1
446,1
3
2
344,13
2
1
I
1
182,127,0426
,0764,1426,0182,1227,0764,12
6
6
I
1
554,1
3
2
656,13
2
1
I
1
dx
EJ
MM
113
32
21
1
6
1
0
21
12
=+++++=⋅⋅⋅⋅⋅⋅+
+⋅⋅⋅⋅⋅⋅+⋅−⋅+⋅⋅−⋅⋅⋅+
+⋅⋅⋅⋅⋅+⋅−⋅+⋅⋅−⋅⋅⋅⋅+
+⋅⋅⋅⋅⋅=
⋅
=δ
∑
∫
l
4.3. Записываем вековое уравнение в развернутом виде, т. е.
()
(
)
0mmδδδλmδmδλ
21
2
1211222111
2
22
=⋅−+⋅+−
или
0
I
68,109826
λ
I
49,1700
λ
2
11
2
=+−
.
Отсюда:
6 l
M1 ⋅ M1 1 1 2
δ 11 = ∑ ∫ dx = ⋅ ⋅ 1,554 ⋅ 3 ⋅ ⋅ 1,554 +
1 0 EJ I1 2 3
1 6 1 1 2
+ ⋅ ⋅ (2 ⋅ 1,764 ⋅ 1,764 + 2 ⋅ 1,182 ⋅ 1,182 − 2 ⋅ 1,764 ⋅ 1,182 ) + ⋅ ⋅ 1, 446 ⋅ 3 ⋅ ⋅ 1, 446 +
I1 6 I2 2 3
1 6 1 1 2
+ ⋅ (2 ⋅ 1,764 ⋅ 1,764 + 2 ⋅ 1, 29 ⋅ 1, 29 − 2 ⋅ 1,29 ⋅ 1,764 ) + ⋅ ⋅ 2 ⋅ 1,764 ⋅ ⋅ 1,764 ⋅ 2 +
I2 6 I3 2 3
1 1 2 1
+ ⋅ ⋅ 2 ⋅ 2,736 ⋅ ⋅ 2,736 ⋅ 2 = (2, 415 + 4,847 + 3,136 + 7 ,500 + 12 , 447 + 29 ,943 ) =
I3 2 3 I1
60 , 288
= ;
I1
6 ll
M2 ⋅M2 1 1 2
δ 22 = ∑∫ 1 EJ
dx = ⋅ ⋅ 3 ⋅ 1, 656 ⋅ ⋅ 1, 656 +
I1 2 3
0
1 6 1 1 2
+ ⋅ ⋅ (2 ⋅ 0 , 426 ⋅ 0 , 426 + 2 ⋅ 0 , 27 ⋅ 0 , 27 + 2 ⋅ 0 , 27 ⋅ 0 , 426 ) + ⋅ ⋅ 3 ⋅ 1,344 ⋅ ⋅ 1,344 +
I1 6 I2 2 3
1 6 1 1 2
+ ⋅ (2 ⋅ 0 , 27 ⋅ 0 , 27 + 2 ⋅ 0 ,114 ⋅ 0 ,114 + 2 ⋅ 0 , 27 ⋅ 0 ,114 ) + ⋅ ⋅ 2 ⋅ 0 , 27 ⋅ ⋅ 0 , 27 ⋅ 2 +
I2 6 I3 2 3
1 1 2 1
+ ⋅ ⋅ 2 ⋅ 1, 23 ⋅ ⋅ 1, 23 ⋅ 2 = (2 ,742 + 0 ,739 + 2 ,710 + 0 ,351 + 0 , 292 + 6 ,052 ) =
I3 2 3 I1
12 ,886
= ;
I1
6 l
M1 ⋅ M 2 1 1 2
δ 12 = ∑ ∫ dx = ⋅ ⋅ 3 ⋅ 1,656 ⋅ ⋅ 1,554 +
1 0 EJ I1 2 3
1 6 1 1 2
+ ⋅ ⋅ (2 ⋅ 1,764 ⋅ 0,27 − 2 ⋅ 1,182 ⋅ 0,426 + 1,764 ⋅ 0,426 − 0,27 ⋅ 1,182 ) + ⋅ ⋅ 3 ⋅ 1,344 ⋅ ⋅ 1,446 +
I1 6 I2 2 3
1 6 1 1 2
+ ⋅ (2 ⋅ 0,27 ⋅ 1,764 − 2 ⋅ 0,114 ⋅ 1,29 + 1,764 ⋅ 0,114 − 1,29 ⋅ 0,27 ) + ⋅ ⋅ 2 ⋅ 0,27 ⋅ ⋅ 1,764 ⋅ 2 +
I2 6 I3 2 3
1 1 2 1 22
+ ⋅ ⋅ 2 ⋅ 1,23 ⋅ ⋅ 2,736 ⋅ 2 = (2,573 + 0,378 + 2,915 + 0,768 + 1,905 + 13,462 ) = .
I3 2 3 I1 I1
4.3. Записываем вековое уравнение в развернутом виде, т. е.
λ2 − (δ11m1 + δ22m2 ) ⋅ λ + (δ11δ − δ122 ) ⋅ m1m2 = 0
22
или
1700,49 109826,68
λ2 − λ+ = 0.
I1 I12
Отсюда:
26
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