Geology Reference
In-Depth Information
INTRODUCTION
this approach, the dynamic behaviour of a single
damper is described by a set of differential equa-
tions. The rheological properties of VE dampers
could be also described using the fractional
calculus and the fractional mechanical models.
This approach has received considerable attention
and has been used in modelling the rheological
behaviour of VE materials and dampers (Bagley
and Torvik, 1989; Rossikhin and Shitikova, 2001;
Chang and Singh, 2002). The fractional models
have an ability to correctly describe the behaviour
of VE materials and dampers using a small number
of model parameters. A single equation is enough
to describe the VE damper dynamics, which is
an important advantage of the discussed model.
However, in this case, the VE damper equation
of motion is the fractional differential equation.
An optimal distribution of the damping prop-
erties of dampers and optimal positioning of
dampers are important from the designer's point
of view. The optimal positioning of a single viscous
damper based on the energy criterion was con-
sidered by Gurgoze and Muller (1992). Take-
waki (2009) used a gradient-based approach for
the optimal placement of passive, mainly viscous,
dampers and modelled by the simple Maxwell
model by minimizing the norm of the response
transfer function calculated for the undamped
fundamental frequency of structure. Singh and
Moreschi (2001) used a gradient-based optimiza-
tion procedure to obtain the optimal distribution
of viscous dampers. Moreover, the genetic algo-
rithm was used by Singh and Moreschi (2002) to
find the optimal size and location of viscous and
viscoelastic dampers. Tsuji and Nakamura (1996)
described a method to find the optimal storey
stiffness distribution and the optimal damper
distribution for structures subjected to a set of
earthquakes. A sequential search algorithm was
presented by Zhang and Soong (1992) and by
Garcia and Soong (2002) for the design of an
optimal damper configuration. Aydin et al. (2007)
considered the optimal distribution of viscous
dampers, as used for the rehabilitation of an exist-
Passive damping systems consist of various me-
chanical devices which are mounted on structures
and dissipate a portion of the energy introduced
by excitation forces affecting the structures.
Different kinds of mechanical devices, such as
viscous dampers, viscoelastic dampers, tuned
mass dampers, or base isolation systems, can
be used as passive systems. In contrast with the
active and semi-active systems, the passive ones
require no amount of energy to operate. Online
measurements of the dynamical state of the
structure are not necessary. Topics by Soong and
Dargush (1997), by Constantinou et al. (1998), and
Hanson and Soong (2001) contain important basic
information concerning many aspects of passive
control of civil structures. Moreover, fundamental
information concerning passive control systems
can be found in topics by Mead ((1998), by Jones
D.I.G. (2001), and De Silva (2007).
In civil engineering, VE dampers are suc-
cessfully applied to reduce excessive vibrations
of buildings caused by winds and earthquakes.
It was found that incorporation of VE dampers
in a structure leads to a significant reduction of
unwanted vibrations; see the paper by Soong and
Spencer (2002). A number of applications of VE
dampers in civil engineering are listed in a topic
by Christopoulos and Filiatrault (2006).
The VE dampers' behaviour depends mainly
on the rheological properties of the VE material
and the dampers are made of. In the past, several
rheological models were proposed to describe the
dynamic behaviour of VE materials and dampers.
Both the classical and the so-called fractional-
derivative models of dampers and VE materials
are available. In the classical approach, the me-
chanical models consisting of springs and dashpots
are used to describe the rheological properties of
VE dampers, see, for example the paper by Park
(2001). A good description of the VE dampers
requires mechanical models consisting of a set of
appropriately connected springs and dashpots. In
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