Template:Equations for a free beam: Difference between revisions

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</math>
</math>
</center>
</center>
plus the edge conditions.
plus the edge conditions of zero bending moment and shear stress
<center><math>\begin{matrix}
<center><math>\begin{matrix}
\partial_x^3 w_n= 0 \;\;\;\; \mbox{ at } z = 0 \;\;\; x = \pm L,
\partial_x^3 w_n= 0 \;\;\;\; \mbox{ at } z = 0 \;\;\; x = \pm L,
\end{matrix}</math></center>
\end{matrix}</math></center>
<center><math>\begin{matrix}
<center><math>\begin{matrix}
\partial_x^2 w_n = 0\mbox{ for } \;\;\;\; \mbox{ at } z = 0 \;\;\; x = \pm L
\partial_x^2 w_n = 0 \;\;\; \mbox{ at } z = 0 \;\;\; x = \pm L
\end{matrix}</math></center>
\end{matrix}</math></center>

Revision as of 08:32, 7 November 2008

We can find a the eigenfunction which satisfy

[math]\displaystyle{ \partial_x^4 w_n = \lambda_n^4 w_n \,\,\_L \leq x \leq L }[/math]

plus the edge conditions of zero bending moment and shear stress

[math]\displaystyle{ \begin{matrix} \partial_x^3 w_n= 0 \;\;\;\; \mbox{ at } z = 0 \;\;\; x = \pm L, \end{matrix} }[/math]
[math]\displaystyle{ \begin{matrix} \partial_x^2 w_n = 0 \;\;\; \mbox{ at } z = 0 \;\;\; x = \pm L \end{matrix} }[/math]
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