Figure 2.2:
System BernoulliEuler: acausal bond graph
The acausal bond graph of system BernoulliEuler is
displayed in Figure 2.2 (on page ) and its label
file is listed in Section 2.1.3 (on page ).
The subsystems are listed in Section 2.1.3 (on page ).
This component represents one lump of a lumped model of a uniform beam
modelled using the the Bernoulli-Euler assumptions:
The shear forces can be neglected.
Rotational inertia can be neglected.
The I component represents the inertial properties of
the lump in the perpendicular direction. In particular the velocity
of the lump is:
(2.1)
where is the lump mass and is the net vertical
force.
The C component represents the angular stiffness of the
lump. In particular the torque acting on the lump is:
(2.2)
where is the lump (angular) stiffness and
is the net angular velocity.
The TF component represents the relation between the
angular domains