Civil Engineering Reference
In-Depth Information
2
⎫
⎪
∫
m x
φ
zz
2
L
mM
/
∫
x
=
φ
=
⎪
⎪
⎪
⎬
⎪
⎪
z
z
z
2
∫
dx
φ
L
z
L
(6.27)
2
∫
m x
φ
θθ
2
L
mM
/
∫
x
=
φ
=
⎪
⎪
⎭
θ
θ
θ
2
∫
dx
φ
L
θ
L
and where the joint acceptance functions are given by
⎛
(
)
⎧
⎪
Sx
Δω
,
( ) ( )
(
)
2
ˆ
⎜
uu
()
J
∫∫
x
x
2
C I
ω
=
φ
⋅
φ
⋅
⎨
z
z
1
z
2
L
u
⎜
2
σ
⎪
⎩
L
u
⎝
exp
(6.28)
12
2
⎞
(
)
⎫
Sx
,
Δω
⎡
CCI
⎤
⎛
⎞
⎪
ww
2
⎟
′
dx dx
∫
dx
+
+
φ
⎬
⎜
⎟
⎢
⎥
L
D
w
12
z
2
B
⎟
σ
⎣
⎝
⎠
⎦
⎪
⎭
w
⎠
L
⎛
(
)
⎧
⎪
Sx
,
Δω
2
( ) ( )
(
)
ˆ
()
⎜
uu
J
∫∫
x
x
2
C
I
ω
=
φ
⋅
φ
⋅
⎨
θ
θ
1
θ
2
Mu
⎜
2
σ
⎪
⎩
L
u
⎝
exp
(6.29)
12
(
)
⎫
⎪
⎞
Sx
Δω
,
2
(
)
ww
2
C
′
I
dx dx
∫
dx
+
⎟
φ
⎬
Mw
12
θ
2
⎟
σ
⎪
⎭
⎠
w
L
The corresponding frequency response functions (see Eqs. 4.24, 4.68 and 4.69) are given
by
1
−
⎫
⎡
2
⎤
⎛
⎞
ω
ω
(
)
⎪
ˆ
()
H
⎢
1
2
i
⎥
ω
=−
κ
−
+
ζ
−
ζ
⋅
⎜⎟
z
ae
z
ae
⎪
z
z
⎢
ω
ω
⎥
⎝⎠
z
z
⎣
⎦
⎪
⎬
⎪
(6.30)
−
1
2
⎡
⎤
⎛
⎞
ω
ω
(
)
ˆ
()
⎢
⎥
⎪
H
1
2
i
ω
=−
κ
−
+
ζ
−
ζ
⋅
⎜ ⎟
θ
ae
θ
ae
θ
θ
⎪
⎢
ω
ω
⎥
⎝ ⎠
θ
θ
⎣
⎦
⎭
where:
