Geology Reference
In-Depth Information
Figure 1. Modified Bouc-Wen model for MR
damper
is the mass matrix,
c c c
c c c c
c c
+
−
0
1
2
2
C
=
−
+
−
(28)
2
2
3
3
−
0
3
3
is the damping matrix,
k k k
k k k k
k k
+
−
0
1
2
2
K
=
−
+
−
(29)
2
2
3
3
−
0
3
3
is the stiffness matrix,
nonlinearly although the structure itself is usu-
ally assumed to remain linear.
(
)
f
t x x v
,
,
,
MR
1
1
1
(
)
=
f
MR
t x x v
,
,
,
0
0
(30)
1
1
1
5.2. Building-MR Damper System
To demonstrate the effectiveness of the HRC
MIMO ARX-TS fuzzy model proposed in this
study, a 3-story shear planar frame structure em-
ploying an MR damper is investigated. An example
of a building structure employing an MR damper
is depicted in Figure 2. The associated equation
of motion is given by
is the MR damper force vector;
w
g
denotes the
ground acceleration, mi are the mass of the ith
floor, ki is the stiffness of the ith floor columns,
ci is the damping of the ith floor columns, the
vector x is the displacement relative to the ground,
x
is the velocity,
x
is the acceleration,
x
1
and
x
1
are the displacement and the velocity at the 1st
floor level relative to the ground, respectively,
v
1
is the voltage level to be applied, and
“
and
›
are location matrices of control forces and distur-
bance signal, respectively. The second order
differential equation can be converted into a set
of first order differential equations in state space
as
(
)
−
Mx Cx Kx
+
+
=
“
f
t x x v
,
,
,
M w
›
,
MR
1
1
1
g
(26)
where the system matrices are;
m
0
0
1
M
=
m
(27)
0
0
2
m
0
0
3
(
)
−
*
*
*
z
=
A z
+
B f
t z z v
,
,
,
E w
6 1
6 1 6 1
6 3
MR
1
4
1
3 1
6 3
g
3 1
×
×
×
×
×
×
×
(
)
+
*
*
y
=
C
z
+
D f
t z z v
,
,
,
n
,
9 1
×
9 6 6 1
×
×
9 3
×
MR
1
4
1
3 1
9 1
×
×
(31)
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