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% Verbal description for system BernoulliEuler (BernoulliEuler_desc.tex)
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The acausal bond graph of system \textbf{BernoulliEuler} is
displayed in Figure \Ref{fig:BernoulliEuler_abg.ps} and its label
file is listed in Section \Ref{sec:BernoulliEuler_lbl}.
The subsystems are listed in Section \Ref{sec:BernoulliEuler_sub}.
This component represents one lump of a lumped model of a uniform beam
modelled using the the Bernoulli-Euler assumptions:
\begin{enumerate}
\item The shear forces can be neglected.
\item Rotational inertia can be neglected.
\end{enumerate}
\begin{itemize}
\item The \textbf{I} component represents the inertial properties of
the lump in the perpendicular direction. In particular the velocity
of the lump $v$ is:
\begin{equation}
\dot v = \frac{\Delta f}{\Delta m}
\end{equation}
where $\Delta m$ is the lump mass and $\Delta f$ is the net vertical
force.
\item The \textbf{C} component represents the angular stiffness of the
lump. In particular the torque acting on the lump is:
\begin{equation}
\dot \tau = \Delta k \Delta \Omega
\end{equation}
where $\Delta k$ is the lump (angular) stiffness and $\Delta \Omega$
is the net angular velocity.
\item The \textbf{TF} component represents the relation between the
angular domains
\begin{equation}
\begin{align}
\tau &= \Delta x \Delta f \\
\Delta v &= \Delta x \Omega
\end{align}
\end{equation}
\end{itemize}