Page 127 - 《应用声学》2023年第4期

第 42 卷 第 4 期 丁栋等： 水中分层弹性球壳高频时域回波的声学编码研究 789

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附录A

待定系数矩阵 X 为 18 × 18 的矩阵，其中系数 d 31 = − xh ′(1) (x 1 ),
n
矩阵中不为0的待定系数如下： ′
d 32 = x L12 j (x L12 ),
n
ρ 0 2 (1)
d 11 = x T 12 n (x 1 ), d 33 = x L12 y (x L12 ),
h
′
n
ρ e
]j
d 12 = [2n(1 + n) − x 2 T 12 n (x L12 ) d 34 = n(n + 1)j n (x T 12 ),
′
− 4x L12 j (x L12 ), d 35 = n(n + 1)y n (x T 12 ),
n
d 13 = [2n(1 + n) − x 2 ]y n (x L12 ) d 36 = d 37 = · · · 0,
T 12
T 22 n (x L22 )
− 4x L12 y (x L12 ), d 42 = [2n(1 + n) − x 2 ]j
′
n
′
′
d 14 = 2n(n + 1)[x T 12 j (x T 12 ) − j n (x T 12 )], − 4x L2 j (x L22 ),
n
n
′
d 15 = 2n(n + 1)[x T 12 2y (x T 12 ) − y n (x T 12 )], d 43 = [2n(1 + n) − x 2 ]y n (x L22 )
T 22
n
′
′
d 22 = 2[j n (x L12 ) − x L12 j (x L12 )], − 4x L22 y (x L22 ),
n
n
′
d 23 = 2[y n (x L12 ) − x L12 y (x L12 )], d 44 = 2n(n + 1)[x T 22 j (x T 22 ) − j n (x T 22 )],
′
n
n
′
′
d 24 = 2x T 12 j (x T 12 ) d 45 = 2n(n + 1)[x T 22 y (x T 22 ) − y n (x T 22 )],
n
n
T 23 n (x L23 )
+ [x 2 T 12 − 2n(n + 1) + 2]j n (x T 12 ), d 46 = − {[2n(1 + n) − x 2 ]j
′
d 25 = 2x T 12 y (x T 12 ) − 4x L23 j (x L23 )},
′
n n
+ [x 2 T 12 − 2n(n + 1) + 2]y n (x T 12 ), d 47 = − {[2n(1 + n) − x 2 ]y n (x L23 )
T 23
′
d 26 = · · · d 218 = 0, − 4x L23 y (x L23 )},
n