Optimal Design and Practical Considerations of Tuned Mass Dampers for Structural Control - Design Optimization of Active and Passive Structural Control Systems - page 142

Figure 9. Optimal location of MTMD for three different uncoupled torsion/translation stiffness ratios:
k / k

x = , k / k

4

x = , k / k

1

x = .25

0

¸ ¸ ¸

Soil-Structure Interaction (SSI) Effect

Parameter σ is the relative stiffness of soil to
structure, whereas λ h is the height-to-base ratio
of structure. Small σ and large λ h represent sig-
nificant SSI effect.
The SSI effect on the MTMD control effective-
ness has been evaluated by Lin et al . (2005) with
the employment of a methodology developed by
Wu et al . (2001). With and without TMD/MTMD,
the mean-square-response ratio of floor translation
with respect to free-field ground acceleration,
R x p g

As mentioned previously, the building model
in Figure 8 has flexible foundation and the base
excitations are different from those of fixed-base
model. This is called the soil-structure interac-
tion (SSI) effect. It is well recognized that two
parameters govern the SSI effect:

V
h

h
r

σ =

s

and λ = (20)

ω

h

 , versus σ ranging from 0.5 to 5.0 for λ h = 3
and λ h =5 are shown in Figure 10. The design
parameters of TMD and MTMD(7) are presented

x

where V s = the shear wave velocity of the soil, h
= the height of the building, ω x

k m

= .

x p