Eigenfunction Matching for a Vertical Fixed Plate - Revision history

Meylan at 01:23, 7 April 2010

2010-04-07T01:23:26Z

2010-04-07T01:22:10Z

Matlab Code

← Older revision		Revision as of 01:22, 7 April 2010
Line 203:		Line 203:
	== Matlab Code ==		== Matlab Code ==

	~~A program to calculate the coefficients for the semi-infinite dock problems can be found here~~
	{{vertical fixed plate code}}		{{vertical fixed plate code}}

2010-04-07T01:18:31Z

Matlab Code

← Older revision		Revision as of 01:18, 7 April 2010
Line 204:		Line 204:

	A program to calculate the coefficients for the semi-infinite dock problems can be found here		A program to calculate the coefficients for the semi-infinite dock problems can be found here
	{{~~semiinfinite_dock~~ code}}		{{vertical fixed plate code}}

	=== Additional code ===		=== Additional code ===

2010-04-07T01:17:53Z

Solution using Symmetry

← Older revision		Revision as of 01:17, 7 April 2010
Line 51:		Line 51:

	{{incident potential for two dimensions}}		{{incident potential for two dimensions}}

			== Expansion of the Potential ==

			Therefore the potential can
			be expanded as
			<center>
			<math>
			\phi(x,z)=e^{-{k}_0x}\phi_0(z)+\sum_{m=0}^{\infty}a_{m}e^{{k}_{m}x}\phi_{m}(z), \;\;x<0
			</math>
			</center>
			and
			<center>
			<math>
			\phi(x,z)=\sum_{m=0}^{\infty}b_{m}
			e^{-{k}_{m}x}\phi_{m}(z), \;\;x>0
			</math>
			</center>

	== Solution using Symmetry ==		== Solution using Symmetry ==

2010-04-07T01:15:38Z

Solution with Waves Incident at an Angle

← Older revision		Revision as of 01:15, 7 April 2010
Line 176:		Line 176:
	<math>		<math>
	\phi(x,z)=\sum_{m=0}^{\infty}b_{m}		\phi(x,z)=\sum_{m=0}^{\infty}b_{m}
	e^{-\hat{~~\kappa~~}_{m}x}\~~psi_~~{m}(z), \;\;x>0		e^{-\hat{k}_{m}x}\phi_{m}(z), \;\;x>0
	</math>		</math>
	</center>		</center>
Line 183:		Line 183:

	The equations are derived almost identically to those above and we obtain		The equations are derived almost identically to those above and we obtain
	~~<center>~~
	~~<math>~~
	~~A_{0}\delta_{0l}+a_{l}A_{l}~~
	~~=\sum_{n=0}^{\infty}b_{m}B_{ml}~~
	~~</math>~~
	~~</center>~~
	~~and~~
	~~<center>~~
	~~<math>~~
	~~-\hat{k_{0}}A_{0}\delta_{0l}+a_{l}\hat{k}_{l}A_l~~
	~~=-\sum_{m=0}^{\infty}b_{m}\hat{\kappa}_{m}B_{ml}~~
	~~</math>~~
	~~</center>~~
	~~and these are solved exactly as before.~~

	== Matlab Code ==		== Matlab Code ==

2010-04-06T23:01:28Z

Anti-symmetric solution

2010-04-06T22:47:57Z

Anti-symmetric solution

@@ Line 99: / Line 99: @@
 \right\}
 dz = 0
 </math>
 </center>

2010-04-06T22:34:01Z

Solution to the original problem

← Older revision		Revision as of 22:34, 6 April 2010
Line 132:		Line 132:
	<math>		<math>
	\phi(x,z)=\sum_{m=0}^{\infty}\frac{1}{2}\left(a_{m}^{s} - a_{m}^{a}\right)		\phi(x,z)=\sum_{m=0}^{\infty}\frac{1}{2}\left(a_{m}^{s} - a_{m}^{a}\right)
	e^{-~~\kappa_~~{m}x}\phi_{m}(z), \;\;x>0		e^{-k_{m}x}\phi_{m}(z), \;\;x>0
	</math>		</math>
	</center>		</center>



	== Solution with Waves Incident at an Angle ==		== Solution with Waves Incident at an Angle ==

2010-04-06T22:33:35Z

2010-04-06T22:29:55Z

Solution to the original problem

← Older revision		Revision as of 22:29, 6 April 2010
Line 110:		Line 110:
	</math>		</math>
	</center>		</center>
	and in the ~~dock-covered~~ region ~~we now consider a potential written as~~		and in the right open water region is just
	<center>		<center>
	<math>		<math>
	~~\phi(x,z)=b_0 \psi_~~{0}~~(z) + \sum_{m~~=~~1}^{\infty}b_{m}~~		a_{m} = \frac{1}{2}\left(a_{m}^{s} - a_{m}^{a}\right)
	\frac{~~\cos\kappa_{m} x~~}{~~\cos \kappa_m L~~}\~~psi_{m}~~(z)
	~~-c_0 \frac{x}{L} \psi_{0}(z) + \sum_~~{m=1}^{~~\infty~~}c_{m}
	~~\frac~~{~~\sin\kappa_{m~~} ~~x}{-\sin~~ \~~kappa_m L} \psi_{m}(z~~)
	~~, \;\;-L<x<L~~
	</math>		</math>
	</center>		</center>
	~~and we obtain~~
	~~<center>~~
	~~<math>~~
	~~b_{m}=\frac{1}{2}\left(b_{m}^{s}+b_{m}^{a}\right)~~
	~~</math>.~~
	~~</center>~~


	=== Expansion of the potential ===		=== Expansion of the potential ===