Template:Free surface submerged plate relations - Revision history

Mike smith at 23:36, 8 August 2009

2009-08-08T23:36:46Z

← Older revision		Revision as of 23:36, 8 August 2009
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	</math>		</math>
	</center>		</center>
			depending on whether the root <math>\mu_n</math> is above or below.

Adi Kurniawan: /* Inner product between free surface and submerged plate modes */

2008-12-23T05:36:37Z

Inner product between free surface and submerged plate modes

← Older revision		Revision as of 05:36, 23 December 2008
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	<center>		<center>
	<math>		<math>
	\int\nolimits_{-d}^{0}\phi_{n}^h(z)\chi_{m}^d(z) d z=B_{mn}		\int\nolimits_{-d}^{0}\phi_{n}^h(z)\chi_{m}^d(z) \mathrm{d} z=B_{mn}
	</math>		</math>
	</center>		</center>
Line 10:		Line 10:
	<center>		<center>
	<math>		<math>
	\int\nolimits_{-d}^{0}\phi_{n}^h(z)\phi_{m}^d(z) d z		\int\nolimits_{-d}^{0}\phi_{n}^h(z)\phi_{m}^d(z) \mathrm{d} z
	</math>		</math>
	</center>		</center>
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	<center>		<center>
	<math>		<math>
	\int\nolimits_{-h}^{-d}\phi_{n}^h(z)\psi_{m}(z) d z		\int\nolimits_{-h}^{-d}\phi_{n}^h(z)\psi_{m}(z) \mathrm{d} z
	</math>		</math>
	</center>		</center>

Meylan: /* Inner product between free surface and submerged plate modes */

2008-09-07T11:16:04Z

Inner product between free surface and submerged plate modes

← Older revision		Revision as of 11:16, 7 September 2008
Line 10:		Line 10:
	<center>		<center>
	<math>		<math>
	\int\nolimits_{-d}^{0}\phi_{n}^h(z)\phi_{m}^d(z) d z~~=B_{mn}~~		\int\nolimits_{-d}^{0}\phi_{n}^h(z)\phi_{m}^d(z) d z
	</math>		</math>
	</center>		</center>
Line 16:		Line 16:
	<center>		<center>
	<math>		<math>
	\int\nolimits_{-h}^{-d}\phi_{n}^h(z)\psi_{m}(z) d z~~=B_{mn}~~		\int\nolimits_{-h}^{-d}\phi_{n}^h(z)\psi_{m}(z) d z
	</math>		</math>
	</center>		</center>

Meylan at 11:14, 7 September 2008

2008-09-07T11:14:09Z

New page

== Inner product between free surface and submerged plate modes ==

We define
<center>
<math>
\int\nolimits_{-d}^{0}\phi_{n}^h(z)\chi_{m}^d(z) d z=B_{mn}
</math>
</center>
where <math>B_{mn}</math> is either
<center>
<math>
\int\nolimits_{-d}^{0}\phi_{n}^h(z)\phi_{m}^d(z) d z=B_{mn}
</math>
</center>
or
<center>
<math>
\int\nolimits_{-h}^{-d}\phi_{n}^h(z)\psi_{m}(z) d z=B_{mn}
</math>
</center>