Page 237 - 《应用声学》2025年第3期

第 44 卷 第 3 期 苏娜娜等： 孔隙度检测长骨骨质疏松的超声导波传播特性 771

{ [ 2 2 2 2 ]
′
m 44 = iω 2r 1 λ γ Sls1 Z 1 (γ Sls1 r 1 ) − r (2γ − (γ + k )(A + Qη 2 )/N)Z 0 (γ Sls1 r 1 ) N
1 1 Sls1 Sls1
2 2 2 }
− r (γ Sls1 + k )(Q + Rη 2 )Z 0 (γ Sls1 r 1 ) ,
1
2
m 45 = iω(−2ikr λ 2 γ St1 Z 0 (γ St1 r 1 ) + 2ikr 1 Z 1 (γ St1 r 1 )),
1
{ [ 2 2 2 2 ]
m 46 = iω 2r 1 λ 1 γ Slf1 W 1 (γ Slf1 r 1 ) − r (2γ − (γ + k )(A + Qη 1 )/N)W 0 (γ Slf1 r 1 ) N
1 Slf1 Slf1
2 2 2 }
− r (γ Slf1 + k )(Q + Rη 1 )W 0 (γ Slf1 r 1 ) ,
1
{ [ 2 2 2 2 ]
′
m 47 = iω 2r 1 λ γ Sls1 W 1 (γ Sls1 r 1 ) − r (2γ − (γ + k )(A + Qη 2 )/N)W 0 (γ Sls1 r 1 ) N
1 1 Sls1 Sls1
}
2
2
− r (γ 2 + k )(Q + Rη 2 )W 0 (γ Sls1 r 1 ) ,
1 Sls1
2
m 48 = iω(−2ikr λ 2 γ St1 W 0 (γ St1 r 1 ) + 2ikr 1 W 1 (γ St1 r 1 )),
1
2
2
2
m 51 = −2ikr λ L1 γ Ll1 H (1) (γ Ll1 r 1 ), m 52 = r (k − γ 2 )H (1) (γ Lt1 r 1 ),
1 1 1 Lt1 1
2
2 ′
m 53 = ωN(2kr λ 1 γ Slf1 Z 1 (γ Slf1 r 1 )), m 54 = ωN(2kr λ γ Sls1 Z 1 (γ Sls1 r 1 )),
1 1 1
2 2 2 2
m 55 = −iωNr (γ St1 − k )Z 1 (γ St1 r 1 ), m 56 = ωN(2kr λ 1 γ Slf1 W 1 (γ Slf1 r 1 )),
1
1
2
2
2 ′
m 57 = ωN(2kr λ γ Sls1 W 1 (γ Sls1 r 1 )), m 58 = −iωNr (γ 2 − k )W 1 (γ St1 r 1 ),
1 1 1 St1
m 61 = −λ L1 γ Ll1 H (1) (γ Ll1 r 1 ), m 62 = −ikH (1) (γ Lt1 r 1 ),
1 1
m 63 = iω(1 − β + βη 1 )(−λ 1 γ Slf1 Z 1 (γ Slf1 r 1 )), m 64 = iω(1 − β + βη 2 )(−λ γ Sls1 Z 1 (γ Sls1 r 1 )),
′
1
m 65 = iω(1 − β + βη 2 )(−ikZ 1 (γ St1 r 1 ), m 66 = iω(1 − β + βη 1 )(−λ 1 γ Slf1 W 1 (γ Slf1 r 1 )),
′
m 67 = iω(1 − β + βη 2 )(−λ γ Sls1 W 1 (γ Sls1 r 1 )), m 68 = iω(1 − β + βη 2 )(−ikW 1 (γ St1 r 1 ),
1
2
2
m 71 = β[r (−iωρ L + 2µ L k )H (1) (γ Ll1 r 1 ) + 2r 1 λ L1 µ L γ Ll1 H (1) (γ Ll1 r 1 )],
0
1
1
2
m 72 = β(−2ikr λ L2 µ L γ Lt1 H (1) (γ Lt1 r 1 ) + 2r 1 µ L ikH (1) (γ Lt1 r 1 )),
1 0 1
2
2
2
2
m 73 = iω(−r (γ 2 + k )(Q + Rη 1 )Z 0 (γ Slf1 r 1 )), m 74 = iω(−r (γ 2 + k )(Q + Rη 2 )Z 0 (γ Sls1 r 1 )),
1 Slf1 1 Sls1
2
2
m 75 = 0, m 76 = iω(−r (γ 2 + k )(Q + Rη 1 )W 0 (γ Slf1 r 1 )),
Slf1
1
2
2
m 77 = iω(−r (γ 2 + k )(Q + Rη 2 )W 0 (γ Sls1 r 1 )), m 78 = 0,
1 Sls1
m 81 = ikH (1) (γ Ll1 r 1 ), m 82 = λ L2 γ Lt1 H (1) (γ Lt1 r 1 ), m 83 = −ωkZ 0 (γ Slf1 r 1 ),
0 0
m 84 = −ωkZ 0 (γ Sls1 r 1 )), m 85 = iωλ 2 γ St1 Z 0 (γ St1 r 1 ), m 86 = −ωkW 0 (γ Slf1 r 1 ),
m 87 = −ωkW 0 (γ Sls1 r 1 )), m 88 = iωλ 2 γ St1 W 0 (γ St1 r 1 ).
附录 B

0 m 13 m 14 m 16 m 17

0 m 23 m 24 m 26 m 27 0 m 35 m 38

L 1 = m 41 m 43 m 44 m 46 m 47 , L 2 = m 52 m 55 m 58 .

m 61 m 63 m 64 m 66 m 67 m 82 m 85 m 88

m 71 m 73 m 74 m 76 m 77