Civil Engineering Reference
In-Depth Information
t
23
t
26
p
1
jωZ
s
−
t
21
u
s
x
+
t
23
)u
s
z
+
0
=
(t
22
−
t
24
+
(10.143)
t
33
t
36
p
1
jωZ
s
−
t
31
u
s
x
+
t
33
)u
s
z
+
0
=
(t
32
−
t
34
+
(10.144)
The components
u
s
x
,u
s
z
,
and
p
are different from 0 only if the determinant of the
previous system of three equations is equal to 0. This leads to
2
jω
1
Z
s
=−
(10.145)
with
t
11
t
12
−
t
13
t
16
−
t
14
1
=
t
21
t
22
t
24
t
31
t
32
−
t
33
t
36
−
t
34
−
t
23
t
26
−
(10.146)
t
11
t
12
−
t
13
t
13
t
21
t
22
−
t
23
t
23
t
31
t
32
−
2
=
(10.147)
t
33
t
33
Examples of applications can be found in Khurana
et al
. (2009) using a variant of
the presented transfer matrix representation.
Appendix 10.A: Coefficients
T
i
in Equation (10.46)
Similar coefficients are given in the work by Vashishth and Khurana (2004).
C
1
B
5
(B
7
−
T
0
=
B
4
B
8
)
(10.A.1)
T
12
/c
2
T
1
=
T
11
+
(10.A.2)
T
22
/c
2
T
23
/c
4
T
2
=
T
21
+
+
(10.A.3)
T
3
=
T
31
+
T
32
/c
2
+
T
33
/c
4
+
T
34
/c
6
(10.A.4)
B
7
)ρ
T
11
=
C
1
(B
4
B
8
−
+
C
1
ρB
5
B
8
(10.A.5)
ρ
0
(B
4
B
8
B
7
)
+
2
C
1
ρ
0
B
5
B
7
+
C
1
C
3
B
4
B
5
−
−
T
12
=
C
1
(
2
B
1
+
B
2
)(B
7
−
B
4
B
8
)
−
C
3
B
4
B
5
B
8
+
C
3
B
5
B
7
+
C
1
(B
3
B
8
+
2
B
3
B
5
B
8
)
−
(10.A.6)
C
1
B
6
(
2
B
3
B
7
+
2
B
5
B
7
−
B
4
B
6
)
C
1
ρ
2
B
8
−
2
C
1
ρρ
0
B
7
−
T
21
=−
C
3
C
1
ρ(B
4
+
B
5
)
(10.A.7)
C
1
ρ
0
B
5
+
C
3
ρ
0
B
4
+
ρρ
0
B
8
+
2
B
7
ρ
0
+
