Difference between revisions of "Template:Equations for a free beam"
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We can find a the eigenfunction which satisfy | We can find a the eigenfunction which satisfy | ||
<center> | <center> | ||
| − | <math>\partial_x^4 w_n = \lambda_n^4 w_n</math> | + | <math>\partial_x^4 w_n = \lambda_n^4 w_n |
| + | \,\,\, -L \leq x \leq L | ||
| + | </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 | + | \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 | + | \partial_x^2 w_n = 0 \;\;\; \mbox{ at } z = 0 \;\;\; x = \pm L. |
\end{matrix}</math></center> | \end{matrix}</math></center> | ||
| − | |||
Latest revision as of 08:33, 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
