Differences From Artifact [0cbac28189]:

To Artifact [81085b5b72]:


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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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