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in Table 3, where '(7)' means the number of
MTMD units (
p
=7) installed.
The dash line and dot line in Figure 10 show
that a very small
σ
can significantly deteriorate
the control effectiveness of TMD and MTMD.
This is because the soft soil decreases the frequen-
cies and increases the damping of the SSI system
causes the detuning effect. So is a large
λ
h
. In
most cases, MTMD(7) has better control effective-
ness than TMD except when
σ
is smaller than
about 0.75 and
λ
h
= 5. This phenomenon indicates
that the sensitivity of MTMD to the variations in
system parameters is higher than that of TMD. In
order to reduce the detuning problem, enlarging
frequency spacing between MTMD units with
100% and the corresponding mean-square re-
sponse ratio,
R
x
p g
, is shown in Figure 10 (labeled
as MTMD(7)*). It is seen that although MTMD(7)*
is less effective than MTMD(7) for large
σ
, but
control effectiveness for small
σ
is significantly
improved. Figure10 also shows that Case 2 MTMD
controlling both two structural modes has better
performance than Case 1 MTMD in most situa-
tions.
The MTMD effectiveness in terms of dy-
namic responses is demonstrated using the 1995
Kobe earthquake as ground excitation. This ground
acceleration with peak value of 0.821g was re-
corded in the KJM000 component of the Japanese
KJMA station during the earthquake. To con-
Figure 10. Mean-square-response ratio of floor displacement with respect to free-field ground accel-
eration versus
σ
with and without TMD/MTMD in the cases of
λ
h
= 3
and
λ
h
=5
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