Health Assessment of Engineering Structures Using Graphical Models - Structural Seismic Design Optimization and Earthquake Engineering - page 345

Figure 1. Bond graph elements: (a) passive elements (b) active sources (c) junctions

(effect). The small vertical line in Figure
a(1) is the causal stroke representing the
integral causality relation (constitutive equa-
tion). The half arrow defines the direction
of power flow ( power = e f ).
2. I-element (Figure 1(a2)): I-element models
inertial effects in structural systems, and
inductance effects in electrical or fluid sys-
tems. For a mass m subjected to a force p ,

damper, e and f are related through a linear
relation ( e = f ). R-elements can have
the causal stroke at either ends.
4. TF-element (Figure 1(a4)): TF-element
can represent an ideal electrical transformer
or a massless lever. It can also represent the
mode shape at a point in the structure. TF-
element does not store or absorb energy. It
conserves power and transmits the factors
of power with power scaling as defined by
the transformer modulus r. The balance rela-
tion between the power variables for the
transformer of Figure 1(a4) is e f

t t

∫ ∫

f ( / 1 m ) e dt ( / 1 m ) p dt

= = .

−∞ −∞

This relation represents the Newton's second
law of motion. Herein, the effort history is
integrated to generate flow thus I-element
receives effort (cause) and generates flow
(effect).
3. R-element (Figure 1(a3)): R-element mod-
els energy dissipation components, such as,
dampers, dashpots, electrical resistors and
valves or losses in fluid lines. For a linear

= e f ,

1 1 2 2

5. GY-element (Figure 1(a5)): The gyrator
establishes the relationship between flow to
effort and effort to flow, gain keeping the
power on the ports the same. The simplest
gyrator is a mechanical gyroscope or an ideal
DC motor. Gyrators are used when power

which leads to f

= or e

rf = ( / ) 1 r e .

2 1

2