Difference between revisions of "Template:Equations for the eigenfunctions of a free beam"
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− | We can find | + | We can find eigenfunctions which satisfy |
<center> | <center> | ||
− | <math>\partial_x^4 | + | <math>\partial_x^4 X_n = \lambda_n^4 X_n |
\,\,\, -L \leq x \leq L | \,\,\, -L \leq x \leq L | ||
</math> | </math> | ||
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plus the edge conditions of zero bending moment and shear stress | plus the edge conditions of zero bending moment and shear stress | ||
<center><math>\begin{matrix} | <center><math>\begin{matrix} | ||
− | \partial_x^3 | + | \partial_x^3 X_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 | + | \partial_x^2 X_n = 0 \;\;\; \mbox{ at } z = 0 \;\;\; x = \pm L. |
\end{matrix}</math></center> | \end{matrix}</math></center> |
Latest revision as of 10:40, 8 April 2009
We can find eigenfunctions which satisfy
[math]\displaystyle{ \partial_x^4 X_n = \lambda_n^4 X_n \,\,\, -L \leq x \leq L }[/math]
plus the edge conditions of zero bending moment and shear stress