Difference between revisions of "Template:Equations for a free beam"

From WikiWaves
Jump to navigationJump to search
 
(One intermediate revision by the same user not shown)
Line 2: Line 2:
 
<center>
 
<center>
 
<math>\partial_x^4 w_n = \lambda_n^4 w_n
 
<math>\partial_x^4 w_n = \lambda_n^4 w_n
\,\,\_L \leq x \leq L
+
\,\,\, -L \leq x \leq L
 
</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>

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

[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]