% -*-latex-*- Put EMACS into LaTeX-mode
% Verbal description for system PinnedBeam (PinnedBeam_desc.tex)
% Generated by MTT on Mon Apr 19 07:04:54 BST 1999.

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% %% Revision 1.1  1999/05/18 04:01:50  peterg
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The acausal bond graph of system \textbf{PinnedBeam} is displayed in
Figure \Ref{fig:PinnedBeam_abg.ps} and its label file is listed in
Section \Ref{sec:PinnedBeam_lbl}.  The subsystems are listed in Section
\Ref{sec:PinnedBeam_sub}.
   
This example represents the dynamics of a uniform beam with two pinned
ends. The left-hand end is driven by a torque input and the
corresponding collocated angular velocity is measured.  The beam is
approximated by 20 equal lumps using the Bernoulli-Euler approximation
with damping. 

Because the two end lumps have different causality to the rest of the
beam lumps, they are represented seperately.

The system parameters are given in Section
\Ref{sec:PinnedBeam_numpar.tex}. 

 The system has 20 states (10
modes of vibration), 1 inputs and 1 outputs.

The first 5 vibration frequencies are given in Table \ref{tab:freq}
togtherr with the theoretical (based on the Bernoulli-Euler beam with
the same values of $EI$ and $\rho A$. 
\begin{table}[htbp]
  \begin{center}
    \begin{tabular}{||l|l|l||}
      \hline
      \hline
      Mode & Frequency & Theoretical frequency\\
      \hline
      1 & 119.44 & 119.69\\
      2 & 474.83 & 479.02\\
      3 &1057.41 &1078.09\\
      4 &1852.85 &1914.86\\
      5 &2841.54 &2992.95\\
      \hline
      \hline
    \end{tabular}
    \caption{Mode frequencies (rad $s^{-1}$)}
    \label{tab:freq}
  \end{center}
\end{table}

%% Label file for system PinnedBeam (PinnedBeam_lbl.txt)
%SUMMARY PinnedBeam
%DESCRIPTION <Detailed description here>

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% Port aliases

% Argument aliases

%% Each line should be of one of the following forms:
%	     a comment (ie starting with %)
%	     component-name	cr_name	arg1,arg2,..argn
%	     blank

% ---- Component labels ----

% Component type BernoulliEuler
	Lump
	LumpL
	LumpR

% Component type SS
	ssL	SS		external,external
	ssR	SS		0,internal

% Component type Sf
	zeroL	 none		0
	zeroR	 none		0

## -*-octave-*- Put Emacs into octave-mode
## Outline report file for system PinnedBeam (PinnedBeam_rep.txt)
## Generated by MTT on" Mon Apr 19 06:43:08 BST 1999.

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## $Id$
## $Log$
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mtt PinnedBeam abg tex			# The system description
## mtt PinnedBeam cbg ps 		        # The causal bond graph
## Uncomment the following lines or add others
mtt PinnedBeam struc tex	        # The system structure
## mtt PinnedBeam dae tex	        # The system dae
## mtt PinnedBeam ode tex	        # The system ode 
## mtt PinnedBeam sspar tex		# Steady-state parameters
## mtt PinnedBeam ss tex 		# Steady state
## mtt PinnedBeam dm tex		# Descriptor matrices (of linearised system)
## mtt PinnedBeam sm tex		# State matrices (of linearised system)
## mtt PinnedBeam tf tex		# Transfer function (of linearised system)
mtt PinnedBeam simpar tex		# Simulation parameters
mtt PinnedBeam numpar tex		# Numerical simulation parameters
## mtt PinnedBeam input tex		# Simulation input
## mtt PinnedBeam odeso ps		# Simulation output
mtt PinnedBeam lmfr ps		# log modulus of frequency response (of linearised system)