BernoulliEuler

Figure 1.2: 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:

1. The shear forces can be neglected.
2. 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 $v$ is:

  $$\dot v = \frac{\Delta f}{\Delta m}$$ (1.1)

  
  
  where $\Delta m$ is the lump mass and $\Delta f$ is the net vertical force.
• The C component represents the angular stiffness of the lump. In particular the torque acting on the lump is:

  $$\dot \tau = \Delta k \Delta \Omega$$ (1.2)

  
  
  where $\Delta k$ is the lump (angular) stiffness and $\Delta \Omega$ is the net angular velocity.
• The TF component represents the relation between the angular domains

  $$\begin{align}\tau &= \Delta x \Delta f \\ \Delta v &= \Delta x \Omega \end{align}$$