Geology Reference
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Figure 8. (a) An irregular building-soil interaction model before and after deformation (Wu et al., 2001),
(b) Top-view of floor equipped with MTMD (c) Top-view of foundation with ground reaction forces
The mass and stiffness matrices of the fixed-
base building can be given by
where
m
p
and
J
p
are the mass and polar moment
of inertia of the floor, respectively.
k
x
and
k
θ
are
the uncoupled lateral stiffness and torsional stiff-
ness, respectively;
e
is the one-way eccentricity
of the C.R. from the C.M. The displacement vec-
tor is represented by
U
p
m
0
M
p
and
=
0
J
p
p
(12)
T
k
ek
=
{
θ
, which can
also be expressed by the product of mode shape
matrix and modal displacement vector as
x
−
x
p
p
θ
K
=
2
2 2
p
−
ek
k
+
e k
θ
θ
x
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