Page 129 - 《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 791

]j
d 1210 = [2n(1 + n) − x 2 T 44 n (x L44 ) + [x 2 T 44 − 2n(n + 1) + 2]y n (x T 44 ),
′
− 4x L44 j (x L44 ), d 1514 = − 2[j n (x L45 ) − x L45 j (x L45 )],
′
n
n
2
′
d 1211 = [2n(1 + n) − x T 44 ]y n (x L44 ) d 1515 = − 2[y n (x L45 ) − x L45 y (x L45 )],
n
′
− 4x L44 y (x L44 ), d 1516 = − {2x T 45 j (x T 45 )
′
n
n
′
d 1212 = 2n(n + 1)[x T 44 j (x T 44 ) − j n (x T 44 )], 2
n + [x T 45 − 2n(n + 1) + 2]j n (x T 45 ),
′
d 1213 = 2n(n + 1)[x T 44 y (x T 44 ) − y n (x T 44 )], ′
n d 1517 = − {2x T 45 y (x T 45 )
n
]j
d 1214 = − {[2n(1 + n) − x 2 T 45 n (x L45 ) + [x 2 − 2n(n + 1) + 2]y n (x T 45 )},
T 45
− 4x L45 j (x L45 )}, d 1614 = [2n(1 + n) − x 2 ]j
′
T 55 n (x L55 )
n
2
d 1215 = − {[2n(1 + n) − x T 45 ]y n (x L45 ) − 4x L55 j (x L55 ),
′
n
′
− 4x L45 y (x L45 )}, d 1615 = [2n(1 + n) − x 2 ]y n (x L55 )
n
T 55
′
d 1216 = − 2n(n + 1)[x T 45 j (x T 45 ) − j n (x T 45 )],
n − 4x L55 y (x L55 ),
′
n
d 1217 = − 2n(n + 1)[x T 45 y (x T 45 ) − y n (x T 45 )],
′
′
n d 1616 = 2n(n + 1)[x T 55 j (x T 55 ) − j n (x T 55 )],
n
d 1310 = x L44 j (x L44 ),
′
n d 1617 = 2n(n + 1)[x T 55 y (x T 55 ) − y n (x T 55 )],
′
n
d 1311 = x L44 y (x L44 ), ρ 6 2
′
n
j
d 1618 = x T 55 n (x 6 ),
d 1312 = n(n + 1)j n (x T 44 ), ρ 5
′
d 1714 = 2[j n (x L55 ) − x L55 j (x L55 )],
n
d 1313 = n(n + 1)j n (x T 44 ),
′
d 1715 = 2[y n (x L55 ) − x L55 y (x L55 )],
n
′
d 1314 = − x L45 j (x L45 ),
n
d 1716 = 2x T 55 j (x T 55 )
′
n
′
d 1315 = − x L45 y (x L45 ),
n 2
+ [x − 2n(n + 1) + 2]j n (x T 55 ),
d 1316 = − n(n + 1)j n (x T 45 ), T 55
′
d 1717 = 2x T 55 y (x T 55 )
d 1317 = − n(n + 1)j n (x T 45 ), n
+ [x 2 − 2n(n + 1) + 2]y n (x T 55 ),
d 1410 = j n (x L4 ), T 55
′
d 1814 = x L55 j (x L55 ),
d 1411 = y n (x L4 ), n
′
′
d 1412 = j n (x T 44 ) + x T 44 j (x T 44 ), d 1815 = x L55 y (x L55 ),
n
n
′
d 1413 = y n (k T 44 ) + x T 44 y (x T 44 ), d 1816 = n(n + 1)j n (x T 55 ),
n
d 1414 = − j n (x L45 ), d 1817 = n(n + 1)y n (x T 55 ),
′
d 1415 = − y n (x L45 ), d 1818 = − x 6 j (x 6 ),
n
j
∗
′
d 1416 = − {j n (x T 45 ) + x T 45 j (x T 45 )}, A = x 2 T 12 n (x 1 ) ρ 1 ,
1
n
ρ 2
′
d 1417 = − {y n (x T 45 ) + x T 45 y (x T 45 )}, A = x 1 j (x 1 ),
∗
′
n
2
n
′
d 1510 = 2[j n (x L44 ) − x L44 j (x L44 )],
n
其 中， 下 标 xy 表 示 第 x 行 第 y 列； x 1 = k 1 r 1 、
′
d 1511 = 2[y n (x L44 ) − x L4 y (x L44 )],
n
x 6 = k 6 r 6 分别表示区域 1 和区域 6 中的归一化
d 1512 = 2x T 44 j (x T 44 )
′
n 频率；x T ij = k T j r i 、x Lij = k Lj r i 分别表示第j 个区
+ [x 2 − 2n(n + 1) + 2]j n (x T 44 ), 域第 i 个边界处剪切波和压力波波速对应的归一化
T 44
′
d 1513 = 2x T 44 y (x T 44 ) 频率。
n