Difference between revisions of "Eigenfunctions for a Uniform Free Beam"

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\end{matrix}</math></center>
 
\end{matrix}</math></center>
 
This solution is discussed further in [[Eigenfunctions for a Free Beam]].
 
This solution is discussed further in [[Eigenfunctions for a Free Beam]].
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<center><math>
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\frac{1}{2}
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xx
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Revision as of 21:31, 6 November 2008

We can find a the eigenfunction which satisfy

[math]\displaystyle{ \partial_x^4 w_n = \lambda_n^4 w_n }[/math]

plus the edge conditions.

[math]\displaystyle{ \begin{matrix} \frac{\partial^3}{\partial x^3} \frac{\partial\phi}{\partial z}= 0 \;\;\;\; \mbox{ at } z = 0 \;\;\; x = \pm L, \end{matrix} }[/math]
[math]\displaystyle{ \begin{matrix} \frac{\partial^2}{\partial x^2} \frac{\partial\phi}{\partial z} = 0\mbox{ for } \;\;\;\; \mbox{ at } z = 0 \;\;\; x = \pm L. \end{matrix} }[/math]

This solution is discussed further in Eigenfunctions for a Free Beam.


[math]\displaystyle{ \frac{1}{2} xx }[/math]