Page 88 - 201901

84 2019 年 1 月

附录A

图A1为BB布局计算实例示意图。
Ρ
θ
x W t W p
y
L
C ~C 

图 A1 BB 结构算例
Fig. A1 Example of BB structure
边界条件如下：
h p1 dW t1
在y = 0时：(1) v 1y = jωW t1 , (2) u y = W t1 , (3) U y = W t1 , (4) u x = W p1 − ,
2 dx
2 2 4 2 h p1 τ xy 。
(5) (D p1 k − ω m s1 )W p1 = τ yx , (6) (D 1 k − ω m s1 )W t1 = P 1 + σ y + s − jk x 2
x
x
在y = L时：(7) u y = 0, (8) U y = 0, (9) u x = 0。
[A] 9×9 [C] 9×1 = [B] 9×1
[
]
T
其中，[C] = C 1 C 2 C 3 C 4 C 5 C 6 W t1 W p2 R 。
k 1y k 1y k 2y k 2y
A(1, 7) = ω, A(1, 9) = k y , A(2, 1) = , A(2, 2) = − , A(2, 3) = , A(2, 4) = − ,
k 2 k 2 k 2 k 2
1 1 2 2
k x k x k 1y k 1y k 2y
A(2, 5) = , A(2, 6) = , A(2, 7) = j, A(3, 1) = b 1 , A(3, 2) = −b 1 , A(3, 3) = b 2 ,
k 2 t k 2 t k 2 1 k 2 1 k 2 2
k 2y k x k x k x k x
A(3, 4) = − b 2 2 , A(3, 5) = g 2 , A(3, 6) = g 2 , A(3, 7) = j, A(4, 1) = 2 , A(4, 2) = 2 ,
k k k k k
2 t t 1 1
k x k x k ty k ty h p1
A(4, 3) = , A(4, 4) = , A(4, 5) = − , A(4, 6) = , A(4, 7) = −k x , A(4, 8) = j,
k 2 k 2 k 2 k 2 2
2 2 t t
2
k − k 2
2k x k 1y 2k x k 1y 2k x k 2y 2k x k 2y x ty
A(5, 1) = , A(5, 2) = − , A(5, 3) = , A(5, 4) = − , A(5, 5) = ,
k 1 2 k 2 1 k 2 2 k 2 2 k t 2
2
2
2
k − k 2 ty m s1 ω − D p1 k 2 k 2 1y k k 1y
x
A(5, 6) = , A(5, 8) = x , A(6, 1) = 2N + A + Q + b 1 E 2 − jNh p1 x ,
k 2 N k 2 k 2
t 1 1
2
2
k 1y k k 1y k 2y k k 2y
2
2
A(6, 2) = 2N 2 + A + Q + b 1 E 2 − jNh p1 x 2 , A(6, 3) = 2N 2 + A + Q + b 2 E 2 − jNh p1 x 2 ,
k k k k
1 1 2 2
2
2
2
k 2y k k 2y k x k ty k − k 2 ty h p1
x
A(6, 4) = 2N + A + Q + b 2 E 2 − jNh p1 x , A(6, 5) = 2N − jNk x ,
k 2 k 2 k 2 k 2 2
2 2 t t
2
k − k 2
k x k ty x ty h p1 4 2
A(6, 6) = − 2N 2 − jNk x 2 , A(6, 7) = −D 1 k + m s1 ω , A(6, 9) = jωρ 0 ,
x
k t k t 2
k 1y −jk 1y L k 1y jk 1y L k 2y −jk 2y L k 2y jk 2y L
A(7, 1) = 2 e , A(7, 2) = − 2 e , A(7, 3) = 2 e , A(7, 4) = − 2 e ,
k k k k
1 1 2 2
k x −jk ty L k x jk ty L k 1y −jk 1y L k 1y jk 1y L
A(7, 5) = e , A(7, 6) = e , A(8, 1) = b 1 e , A(8, 2) = −b 1 e ,
k 2 k 2 k 2 k 2
t t 1 1
k 2y −jk 2y L k 2y jk 2y L k x −jk ty L k x jk ty L
A(8, 3) = b 2 2 e , A(8, 4) = −b 2 2 e , A(8, 5) = g 2 e , A(8, 6) = g 2 e ,
k 2 k 2 k t k t
k x −jk 1y L k x jk 1y L k x −jk 2y L k x jk 2y L
A(9, 1) = 2 e , A(9, 2) = 2 e , A(9, 3) = 2 e , A(9, 4) = 2 e ,
k k k k
1 1 2 2
k ty −jk ty L k ty jk ty L
A(9, 5) = − e , A(9, 6) = e , B(1) = k y , B(6) = −jωρ 0 ,
k 2 k 2
t t
其余全为零。