Biomedical Engineering Reference
In-Depth Information
3)[1, 1, 1]
T
. Recall from (
9.8
) the formula for
will generate quasi-waves,
n
¼
(1/
√
Z
d
, thus
Z
d
¼ C
d
Þ¼C
d
ðA
A
992 GPa
U
U
þ
M
þ
0
:
:
[1, 0, 0]
T
,from(
9.27
)wenotethatfor
n
[1,0,0]
T
,
Proceedwith the first case,
n
¼
¼
Z
i
1
k
1
;
Q
ik
¼
C
ik
¼
M
i
1
n
k
or
2
4
3
5
¼
2
4
3
5
¼
2
4
3
5
Z
11
Z
16
Z
15
Z
11
00
0
Z
66
0
00
Z
55
Z
1111
Z
1121
Z
1131
Z
1121
Z
2121
Z
2131
Z
1131
Z
2131
Z
3131
Z
16
Z
66
Z
56
Q ¼
Z
15
Z
56
Z
55
2
3
4
:
32
0
0
4
5
GPa
¼
02
:
32
0
;
0
0
1
:
58
2
3
2
3
M
11
00
M
21
00
M
31
00
1
:
322 0 0
000
000
4
5
¼
4
5
GPa
C
¼
:
The solution to the problem is the solution of the 6 by 6 system of equations
given by (
9.30
), thus the values of the tensors
J
,
R
,
C
, and
Q
in the coordinate
system of the principal axes of material symmetry and at the vector
n
[1, 0, 0]
T
are determined first. The specified numerical values of
J
,
R
,
C
, and
Q
, the four 3 by
3 submatrices that form the 6 by 6 matrix in equation (
9.30
), are given by (compare
(
9.39
)to(
9.41
))
¼
2
4
3
5
;
3
:
48
10
6
1
:
5
v
2
0
0
v
2
1
Q
r
¼
1
;
000
2
:
32
10
6
1
:
5
v
2
0
0
10
6
5
v
2
0
0
1
:
58
1
:
is calculated above to be 1,500 kg/m
3
,
where
r
2
4
3
5
;
1
:
322
10
6
v
2
0
0
r
f
v
2
1
C
T
r
f
v
2
1
v
2
C
¼
¼
1
;
000
0
0
v
2
0
0
2
3
10
6
2
v
2
1
:
76
0
0
i
m
o
4
5
:
v
2
Mn
n
r
f
J
þ
R
¼
1
;
000
2
v
2
0
0
2
v
2
0
0
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