Environmental Engineering Reference
In-Depth Information
(
A
I
Pn
−
B
I
Pn
)
k
I
Pn
N
I
n
=
0
μ
n
W
I
n
(
y
)
−
χ
n
(
y
)
)
n
2
W
I
(
A
I
SVn
+
B
SVn
)(
I
+
−
χ
(
A
I
Pn
−
B
I
Pn
)
k
I
Pn
N
I
n
=
0
μ
n
W
I
I
n
(
y
)
+
−
χ
n
(
y
)
+
(
A
I
SVn
+
B
SVn
)(
k
SVn
)
2
I
χ
(
A
I
Pn
−
B
I
Pn
)
k
I
Pn
N
II
n
=
0
μ
W
II
n
II
n
(
y
)
=
−
χ
+
(
A
I
SVn
+
B
I
SVn
)(
−
)
n
W
II
2
II
χ
n
(
y
)
(
A
I
Pn
−
B
I
Pn
)
k
I
Pn
N
II
n
W
II
−
χ
II
+
0
μ
n
(
y
)
n
=
I
n
(
y
)
.
+
(
A
I
SVn
−
B
I
SVn
)(
k
I
SVn
)
2
χ
(4.75)
I
m
(
y
)and
χ
m
(
y
)inthe
Multiplying the transverse wave function
η
I
m
(
y
)in
the two sides of Eqs. 4.74 and 4.75, respectively, after integrating
I
m
(
y
)and
χ
twosidesofEqs.4.72and4.73, respectively, and
η
these equations and making use of
W
ξ
0
η
ξ
m
(
y
)
η
n
(
y
)
dy
=
δ
mn
and
W
ξ
0
χ
m
(
y
)
χ
n
(
y
)
dy
=
δ
mn
, wecan obtain
(
A
I
Pm
−
B
I
Pm
)
k
I
Pm
+
(
A
I
SVm
+
B
SVm
)
m
W
I
D
mn
(
A
I
Pn
−
B
I
Pn
)
k
I
Pn
+
(
A
I
SVn
+
B
I
SVn
)
n
W
II
, (4.76)
N
II
=
=
n
0
(
A
I
Pm
+
B
I
Pm
)
−
m
π
W
I
+
(
A
I
SVm
−
B
SVm
)
k
SVm
F
mn
(
A
I
Pn
+
B
I
SVn
)
k
I
SVn
, (4.77)
N
II
B
I
Pn
)
−
π
W
II
+
n
(
A
I
SVn
−
=
=
n
0
