Civil Engineering Reference
In-Depth Information
33
ˆ
() () (
)
()
¦¦
xt G
=
ω
⋅
2
S
ω ω
Δ ⋅
cos
ω ψ
t
+
3
3
nj xj
j j
nj
==
11
ˆ
ˆ
ˆ
() (
)
( )
(
)
()
(
)
Ga
cos
t Ga
cos
t Ga
cos
t
=
ω
ω ψ
+
+
ω
ω ψ
+
+
ω
⋅ ⋅
ω ψ
+
31
1
1
1
11
31
2
2
2
12
31
3
3
3
13
ˆ
ˆ
ˆ
() (
)
( )
(
)
( )
(
)
+
Ga
ω
cos
ω ψ
t Ga
+
+
ω
cos
ω ψ
t Ga
+
+
ω
⋅ ⋅
cos
ω ψ
t
+
32
1
1
1
21
32
2
2
2
22
32
3
3
3
23
ˆ
ˆ
ˆ
() (
)
() (
)
()
(
)
Ga
cos
t Ga
cos
t G
a
cos
t
+
ω
ω ψ
+
+
ω
ω ψ
+
+
ω
⋅ ⋅
ω ψ
+
33
1
1
1
31
33
2
2
2
32
33
3
3
3
33
(
)
(
)
(
)
=
0.646 cos 0.3
⋅
t
+
ψ
+
0.228 cos 0.7
⋅
t
+
ψ
+
0.039 cos 1.1
⋅
t
+
ψ
11
12
13
(
)
(
)
(
)
0.86 cos 0.3
t
0.713 cos 0.7
t
0.236 cos 1.1
t
+⋅
++ ⋅
ψ
++ ⋅
ψ
+
ψ
21
22
23
(
)
(
)
(
)
+
1.431 cos 0.3
⋅
t
+
ψ
+
2.343 cos 0.7
⋅
t
+
ψ
+
1.532 cos 1.1
⋅
t
+
ψ
31
32
33
What then remains is to ascribe arbitrary values (between 0 and
2
π ) to the phase angles,
ψ
.
nj
The following is chosen:
0.7
0.6
0.3
ª
º
«
»
2
0.1
0.4
0.2
ȥ
=⋅
«
π
»
«
»
0.1
0.7
0.8
¬
¼
Fig. A.5
Simulated time series
