Page 121 - 《应用声学》2020年第6期

第 39 卷 第 6 期 陈亮等： 四边简支含多孔材料双层板隔声特性 915

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附录A

矩阵表达式如下：
   
1
D 1
   
   1 
D 2
∗   ∗   (A-1)
1 . .  2 . . 
∆ =  , ∆ =  ,
 .   . 
   
1
D M
M ×M 2 M ×M 2
2
2
 
λ ∗1
1,1i
 
λ
 ∗1 
 1,2i 
. 
D i =  , i = 1, 2, · · · , M, (A-2)
 . . 
 
λ ∗1 M×M
1,Mi
4
4
2
2
λ ∗1 = (m/a) + (n/b) + 2(m/a) (n/b) . (A-3)
1,mn
常量f mn (k x , k y )表达如下：

ab(1 − cos mπ)(1 − cos nπ)


 2
 mnπ


 −ik y b ik y b
 abn e (1 − cos mπ)( e − cos nπ)



 2 2 2 2
 m(−k b + n π )
y
f mn (k x , k y ) = ,
abm e −ik x a (1 − cos nπ)( e ik x a − cos mπ)


 2 2 2 2
 n(−k a + m π )
 x


2

abmnπ e −i(k x a+k y b) ( e ik x a − cos mπ)( e ik y b − cos nπ)



2
2
2 2
2
2 2
(k a − m π )(k b − n π )
2
y
x
分别对应k x = 0、k y = 0，k x = 0、k y ̸= 0，k x ̸= 0、k y = 0，k x ̸= 0、k y ̸= 0。