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% -*-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.
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.1 1999/10/11 05:08:14 peterg
% %% Initial revision
% %%
% %% Revision 1.1 1999/05/18 04:01:50 peterg
% %% Initial revision
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% -*-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.
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.2 1999/11/24 22:17:26 peterg
% %% Updated to correspond to Reza's beam
% %%
% %% Revision 1.1 1999/10/11 05:08:14 peterg
% %% Initial revision
% %%
% %% Revision 1.1 1999/05/18 04:01:50 peterg
% %% Initial revision
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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The system parameters are also given in Section
\Ref{sec:PinnedBeam_numpar.tex}.
\begin{table}[htbp]
\begin{center}
\begin{tabular}{||l|l|l|l||}
\hline
\hline
Index & Theory & Model & Theory & Model \\
\hline
1 & 19.05 & 19.01 & 29.72 & 31.28\\
2 & 76.24 & 75.57 & 96.50 & 100.80\\
3 & 171.58 & 168.29 & 200.73 & 208.20\\
4 & 304.76 & 294.89 & 344.13 & 350.88\\
5 & 476.34 & 452.25 & 524.98 & 525.23\\
\hline
\hline
\end{tabular}
\caption{Mode frequencies (rad $s^{-1}$)}
\label{tab:freq}
\end{center}
\end{table}
Standard modal analysis give the theoretical system resonant
frequencies (based on the Bernoulli-Euler beam with the same values of
$EI$ and $\rho A$). The system anti-resonances correspond to those of
the \emph{inverse} system with reversed causality, that the driven
pinned end is replaced by a clamped end; again modal analysis of the
inverse system gives the system anti resonances. The model and
theoretical values are compared in Table \ref{tab:freq} for the first
5 modes. (This table was generated using the script MakeFreqTable.m)
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The system parameters are also given in Section
\Ref{sec:PinnedBeam_numpar.tex}.
\begin{table}[htbp]
\begin{center}
\begin{tabular}{||l|l|l|l|l||}
\hline
\hline
Index & $f_r$ (theory) & $f_r$ (model)& $f_a$ (theory) & $f_a$ (model) \\
\hline
1 & 19.05 & 19.01 & 29.72 & 31.28\\
2 & 76.24 & 75.57 & 96.50 & 100.80\\
3 & 171.58 & 168.29 & 200.73 & 208.20\\
4 & 304.76 & 294.89 & 344.13 & 350.88\\
5 & 476.34 & 452.25 & 524.98 & 525.23\\
\hline
\hline
\end{tabular}
\caption{Resonant and anti-resonant frequencies (Hz)}
\label{tab:freq}
\end{center}
\end{table}
Standard modal analysis give the theoretical system resonant
frequencies $f_r$ (based on the Bernoulli-Euler beam with the same values of
$EI$ and $\rho A$). The system anti-resonances $f_a$ correspond to those of
the \emph{inverse} system with reversed causality, that the driven
pinned end is replaced by a clamped end; again modal analysis of the
inverse system gives the system anti resonances. The model and
theoretical values are compared in Table \ref{tab:freq} for the first
5 modes. (This table was generated using the script MakeFreqTable.m)
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