Geology Reference
In-Depth Information
assessment of physical systems across multiple
domains, (3) rapid qualitative identification of
damage locations, (4) the ability to identify sensor
faults, (5) the ability to perform online diagnosis
based on continuous monitoring, (6) reduction of
data processing errors due to absence of transfor-
mation to frequency domain or approximations in
feature selection, and (7) rapid quantification of
damage size since only the substructure containing
damage is analyzed. Finally, it may be noted that
the research carried out in this chapter represents
a novel application of bond graphs and structural
optimization to the health assessment of frame
structures under earthquake loads. The next section
provides a brief overview on bond graph theory.
sure and volume flow, and for thermodynamic
systems, they are temperature and entropy flow.
Bond graph elements consist of five primitives
(passive elements), two ideal sources (active ele-
ments), and two junctions (see Figure 1). The five
primitives are the Capacitance (C), the Inertance
(I), the Resistor (R), the transformer (TF) and the
Gyrator (GY). The source elements are the effort
source
S
e
and the flow source
S
f
, which produce
energy. The two junctions are the serial junction
(1-J) and the parallel junction (0-J), which connect
various elements together. Bonds are energy
transfer pathways that connect elements and junc-
tions and are represented as half arrows. This half
arrow defines the positive direction of energy
flow. Effort and flow signals are the information
transferred through these pathways. Figure 2
shows the tetrahedron state demonstrating the
relations related by C-, I-, and R-elements in
structural engineering setting (Paynter 1961). The
vertices represent the pair, effort and momentum
and the pair, flow and displacement. The associ-
ated directed arrows imply that momentum and
displacement are computed by integrating effort
and flow, respectively. I- and C-elements represent
the state variables of the system that accumulate
net flow (I-element stores momentum and C-el-
ement stores displacement). Brief descriptions of
bond graph elements are provided below with
emphasis on translating concepts to structural
engineering (see Table 1 and Figure 1).
2. BOND GRAPH THEORY
AND TERMINOLOGY
Bond graph is a graphical domain-independent
framework capable of modeling dynamic systems
across multiple domains (e.g. structural, electrical,
mechanical, and hydraulic), thus providing a uni-
fied framework for dynamic analysis and SI of
multidisciplinary systems. For instance, a hydrau-
lic actuator composed of electrical, hydraulic and
mechanical components can be modeled easily
using bond graphs. Bond graph is a domain-in-
dependent framework. For instance, a SDOF
mechanical system and an electrical circuit can
be represented using the same bond graph model
(an example is given later). The BG theory is
based on the energy conservation and energy
exchange among system components. Irrespective
of the domain, power is the product of the two
conjugate variables effort
e
and flow
f
. In struc-
tural and mechanical systems,
e
and f describe
the force and velocity (for translation) or torque
and angular velocity (for rotation) at a point in
the system. In each domain there is such a com-
bination of variables for which a physical inter-
pretation exists. In electrical networks,
e
and
f
are
voltage and current. In hydraulics, they are pres-
1.
C-element (Figure a(1)):
C-element relates
effort to time integral of flow (i.e., displace-
ment) and is used to model linear or rotational
springs, or stiffness of a structural member.
The constitutive relation for a spring mod-
t
∫
eled as a C-element is
e
=
1 /
C
f dt
,
−∞
where
e
is the force in the spring,
f
is the
velocity and
C
is a constant
(
k
1 / stiffness
). The C-element
receives flow (cause) and produces effort
=
C
=
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