Template:Added mass damping and force matrices definition - Revision history

Meylan at 12:57, 26 April 2011

2011-04-26T12:57:33Z

← Older revision		Revision as of 12:57, 26 April 2011
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	A_{\mu\nu} = \mathrm{Re} \left\{\rho\iint_{\partial\Omega_{B}}		A_{\mu\nu} = \mathrm{Re} \left\{\rho\iint_{\partial\Omega_{B}}
	\phi_{\nu}^{\mathrm{R}} \mathbf{n}_{\mu}\, dS \right\}		\phi_{\nu}^{\mathrm{R}} \mathbf{n}_{\mu}\, dS \right\}
			</math></center>
	and the damping matrix by		and the damping matrix by
	<center><math>		<center><math>

Meylan at 12:56, 26 April 2011

2011-04-26T12:56:49Z

← Older revision		Revision as of 12:56, 26 April 2011
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	We ~~then~~ define the ~~matrices~~		We define the added mass matrix by
	<center><math>		<center><math>
	A_{\mu\nu} = \mathrm{Re} \left\{ ~~-\frac{\mathrm{i}}{\omega}~~\rho\iint_{\partial\Omega_{B}}		A_{\mu\nu} = \mathrm{Re} \left\{\rho\iint_{\partial\Omega_{B}}
	\phi_{\nu}^{\mathrm{R}} \mathbf{n}_{\mu}\, dS \right\}		\phi_{\nu}^{\mathrm{R}} \mathbf{n}_{\mu}\, dS \right\}
	~~</math></center>~~		and the damping matrix by
	~~which is called~~ the ~~added mass~~ matrix ~~and~~
	~~We then define the matrices~~
	<center><math>		<center><math>
	B_{\mu\nu} = \mathrm{Im} \left\{ \rho\iint_{\partial\Omega_{B}}		B_{\mu\nu} = \mathrm{Im} \left\{ \omega \rho\iint_{\partial\Omega_{B}}
	\phi_{\nu}^{\mathrm{R}} \mathbf{n}_{\mu}\, dS \right\}		\phi_{\nu}^{\mathrm{R}} \mathbf{n}_{\mu}\, dS \right\}
	</math></center>		</math></center>
	~~which is called the damping matrix~~ and the forcing vector is		and the forcing vector by
	<center><math>		<center><math>
	f_{\mu} = \mathrm{i}\omega\rho\iint_{\partial\Omega_{B}}		f_{\mu} = \mathrm{i}\omega\rho\iint_{\partial\Omega_{B}}
	\left(\phi^{\mathrm{I}} + \phi^{\mathrm{D}} \right) \mathbf{n}_{\mu}\, dS		\left(\phi^{\mathrm{I}} + \phi^{\mathrm{D}} \right) \mathbf{n}_{\mu}\, dS
	</math></center>		</math></center>

Meylan at 12:21, 26 April 2011

2011-04-26T12:21:20Z

← Older revision		Revision as of 12:21, 26 April 2011
Line 12:		Line 12:
	which is called the damping matrix and the forcing vector is		which is called the damping matrix and the forcing vector is
	<center><math>		<center><math>
	f_{\mu} = -\mathrm{i}\omega\rho\iint_{\partial\Omega_{B}}		f_{\mu} = \mathrm{i}\omega\rho\iint_{\partial\Omega_{B}}
	\left(\phi^{\mathrm{I}} + \phi^{\mathrm{D}} \right) \mathbf{n}_{\mu}\, dS		\left(\phi^{\mathrm{I}} + \phi^{\mathrm{D}} \right) \mathbf{n}_{\mu}\, dS
	</math></center>		</math></center>

Meylan at 22:26, 28 April 2010

2010-04-28T22:26:33Z

← Older revision		Revision as of 22:26, 28 April 2010
Line 2:		Line 2:
	<center><math>		<center><math>
	A_{\mu\nu} = \mathrm{Re} \left\{ -\frac{\mathrm{i}}{\omega}\rho\iint_{\partial\Omega_{B}}		A_{\mu\nu} = \mathrm{Re} \left\{ -\frac{\mathrm{i}}{\omega}\rho\iint_{\partial\Omega_{B}}
	\phi_{\nu}^{\mathrm{R}} n_{\mu}\, dS \right\}		\phi_{\nu}^{\mathrm{R}} \mathbf{n}_{\mu}\, dS \right\}
	</math></center>		</math></center>
	which is called the added mass matrix and		which is called the added mass matrix and
Line 8:		Line 8:
	<center><math>		<center><math>
	B_{\mu\nu} = \mathrm{Im} \left\{ \rho\iint_{\partial\Omega_{B}}		B_{\mu\nu} = \mathrm{Im} \left\{ \rho\iint_{\partial\Omega_{B}}
	\phi_{\nu}^{\mathrm{R}} n_{\mu}\, dS \right\}		\phi_{\nu}^{\mathrm{R}} \mathbf{n}_{\mu}\, dS \right\}
	</math></center>		</math></center>
	which is called the damping matrix and the forcing vector is		which is called the damping matrix and the forcing vector is
	<center><math>		<center><math>
	f_{\mu} = -\mathrm{i}\omega\rho\iint_{\partial\Omega_{B}}		f_{\mu} = -\mathrm{i}\omega\rho\iint_{\partial\Omega_{B}}
	\left(\phi^{\mathrm{I}} + \phi^{\mathrm{D}} \right) n_{\mu}\, dS		\left(\phi^{\mathrm{I}} + \phi^{\mathrm{D}} \right) \mathbf{n}_{\mu}\, dS
	</math></center>		</math></center>

Meylan: Created page with 'We then define the matrices $A_{\mu\nu} = \mathrm{Re} \left\{ -\frac{\mathrm{i}}{\omega}\rho\iint_{\partial\Omega_{B}} \phi_{\nu}^{\mathrm{R}} n_{\mu}\, dS \right\…'$

2010-04-28T09:35:53Z

Created page with 'We then define the matrices <center><math> A_{\mu\nu} = \mathrm{Re} \left\{ -\frac{\mathrm{i}}{\omega}\rho\iint_{\partial\Omega_{B}} \phi_{\nu}^{\mathrm{R}} n_{\mu}\, dS \right\…'

New page

We then define the matrices
<center><math>
A_{\mu\nu} = \mathrm{Re} \left\{ -\frac{\mathrm{i}}{\omega}\rho\iint_{\partial\Omega_{B}}
\phi_{\nu}^{\mathrm{R}} n_{\mu}\, dS \right\}
</math></center>
which is called the added mass matrix and
We then define the matrices
<center><math>
B_{\mu\nu} = \mathrm{Im} \left\{ \rho\iint_{\partial\Omega_{B}}
\phi_{\nu}^{\mathrm{R}} n_{\mu}\, dS \right\}
</math></center>
which is called the damping matrix and the forcing vector is
<center><math>
f_{\mu} = -\mathrm{i}\omega\rho\iint_{\partial\Omega_{B}}
\left(\phi^{\mathrm{I}} + \phi^{\mathrm{D}} \right) n_{\mu}\, dS
</math></center>

Template:Added mass damping and force matrices definition - Revision history

Meylan at 12:57, 26 April 2011

Meylan at 12:56, 26 April 2011

Meylan at 12:21, 26 April 2011

Meylan at 22:26, 28 April 2010

Meylan: Created page with 'We then define the matrices A_{\mu\nu} = \mathrm{Re} \left\{ -\frac{\mathrm{i}}{\omega}\rho\iint_{\partial\Omega_{B}} \phi_{\nu}^{\mathrm{R}} n_{\mu}\, dS \right\…'

Meylan: Created page with 'We then define the matrices $A_{\mu\nu} = \mathrm{Re} \left\{ -\frac{\mathrm{i}}{\omega}\rho\iint_{\partial\Omega_{B}} \phi_{\nu}^{\mathrm{R}} n_{\mu}\, dS \right\…'$