Template:Equations for a free beam - Revision history

Meylan at 08:33, 7 November 2008

2008-11-07T08:33:32Z

← Older revision		Revision as of 08:33, 7 November 2008
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	<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>
Line 10:		Line 10:
	\end{matrix}</math></center>		\end{matrix}</math></center>
	<center><math>\begin{matrix}		<center><math>\begin{matrix}
	\partial_x^2 w_n = 0 \;\;\; \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>

Meylan at 08:32, 7 November 2008

2008-11-07T08:32:56Z

← Older revision		Revision as of 08:32, 7 November 2008
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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>

Meylan at 08:32, 7 November 2008

2008-11-07T08:32:08Z

← Older revision		Revision as of 08:32, 7 November 2008
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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.
	<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{ for } \;\;\;\; \mbox{ at } z = 0 \;\;\; x = \pm L
	\end{matrix}</math></center>		\end{matrix}</math></center>
	~~Note that other boundary conditions can be applied at the ends of the beam.~~

Meylan at 08:29, 7 November 2008

2008-11-07T08:29:50Z

New page

We can find a the eigenfunction which satisfy
<center>
<math>\partial_x^4 w_n = \lambda_n^4 w_n</math>
</center>
plus the edge conditions.
<center><math>\begin{matrix}
\partial_x^3 w_n= 0 \;\;\;\; \mbox{ at } z = 0 \;\;\; x = \pm l,
\end{matrix}</math></center>
<center><math>\begin{matrix}
\partial_x^2 w_n = 0\mbox{ for } \;\;\;\; \mbox{ at } z = 0 \;\;\; x = \pm l.
\end{matrix}</math></center>
Note that other boundary conditions can be applied at the ends of the beam.