Updated status Anne

lrftubes.lyx

@@ -124,6 +124,12 @@ LRFTubes documentation - v1.1
 Dr.ir.
  J.A.
  de Jong
+\begin_inset Newline newline
+\end_inset
+
+Ir.
+ C.
+ Jansen
 \end_layout
 
 \begin_layout Standard
@@ -8735,7 +8741,7 @@ where
 \begin_layout Standard
 After some algebraic manipulations we find:
 \begin_inset Note Note
-status open
+status collapsed
 
 \begin_layout Plain Layout
 \begin_inset Formula $z_{m}u=\left(p_{l}-p_{r}\right)S+B\ell I$
@@ -8832,7 +8838,7 @@ To transfer matrix notation:
 
 \begin_inset Formula 
 \begin{align}
-\frac{1}{S_{l}}\left(z_{m}+\frac{\left(B\ell\right)^{2}}{Z_{\mathrm{el}}}\right)U_{l} & =p_{l}S_{l}-p_{r}S_{r}+\frac{B\ell}{Z_{\mathrm{el}}}V_{\mathrm{in}},\\
+\frac{1}{S_{l}}\left(z_{m}+\frac{\left(B\ell\right)^{2}}{Z_{\mathrm{el}}}\right)U_{l} & =p_{l}S_{l}-p_{r}S_{r}+\frac{B\ell}{Z_{\mathrm{el}}}V_{\mathrm{in}},\label{eq:U_vs_V}\\
 U_{r}-U_{l} & =0,
 \end{align}
 
@@ -8869,6 +8875,147 @@ where
 
 \end_layout
 
+\begin_layout Subsection
+Computing the voltage input for given velocity
+\end_layout
+
+\begin_layout Standard
+Suppose we know the membrane velocity, and we want to know the corresponding
+ driving voltage.
+ For that we can rearrange Eq.
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:U_vs_V"
+
+\end_inset
+
+ a bit:
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+\begin_inset Formula $\frac{1}{S_{l}}\left(z_{m}+\frac{\left(B\ell\right)^{2}}{Z_{\mathrm{el}}}\right)U_{l}=p_{l}S_{l}-p_{r}S_{r}+\frac{B\ell}{Z_{\mathrm{el}}}V_{\mathrm{in}}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+Filling in 
+\begin_inset Formula $S_{l}$
+\end_inset
+
+ is 
+\begin_inset Formula $S_{r}$
+\end_inset
+
+ = 
+\begin_inset Formula $S_{d}$
+\end_inset
+
+ and 
+\begin_inset Formula $\frac{p_{r}-p_{l}}{U}=Z_{\mathrm{ac}}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Formula $\left(z_{m}+\frac{\left(B\ell\right)^{2}}{Z_{\mathrm{el}}}+Z_{\mathrm{ac}}S\right)U=\frac{S_{d}B\ell}{Z_{\mathrm{el}}}V_{\mathrm{in}}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+Or:
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Formula $\left(\frac{B\ell}{S_{d}}+\frac{Z_{\mathrm{el}}\left(Z_{\mathrm{ac}}+z_{m}/S_{d}\right)}{B\ell}\right)U=V_{\mathrm{in}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\begin{equation}
+V_{\mathrm{in}}=\left(\frac{B\ell}{S_{d}}+\frac{Z_{\mathrm{el}}\left(Z_{\mathrm{ac}}+z_{m}/S_{d}\right)}{B\ell}\right)U,
+\end{equation}
+
+\end_inset
+
+or equivalently in terms of the mechanical velocity:
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+\begin_inset Formula $\frac{B\ell^{2}+Z_{\mathrm{el}}\left(Z_{\mathrm{ac}}S_{d}+z_{m}\right)}{B\ell}u=V_{\mathrm{in}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula 
+\begin{equation}
+V_{\mathrm{in}}=\frac{B\ell^{2}+Z_{\mathrm{el}}\left(Z_{\mathrm{ac}}S_{d}+z_{m}\right)}{B\ell}u
+\end{equation}
+
+\end_inset
+
+For a COMSOL implementation, in terms of the computed acoustic pressure
+ and derivatives thereof (to create a linear system of equations):
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+\begin_inset Formula $V_{\mathrm{in}}=\frac{B\ell^{2}u+Z_{\mathrm{el}}\left(p+z_{m}u\right)}{B\ell}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Formula $V_{\mathrm{in}}=\left(B\ell+\frac{Z_{\mathrm{el}}z_{m}}{B\ell}\right)u+\frac{Z_{\mathrm{el}}}{B\ell}p$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula 
+\begin{equation}
+V_{\mathrm{in}}=\left(B\ell+\frac{Z_{\mathrm{el}}z_{m}}{B\ell}\right)u+\frac{Z_{\mathrm{el}}}{B\ell}F_{\mathrm{spk}},
+\end{equation}
+
+\end_inset
+
+where 
+\begin_inset Formula $F_{\mathrm{spk}}$
+\end_inset
+
+ is the net force the speaker exerts 
+\emph on
+on the fluid
+\emph default
+.
+\end_layout
+
 \begin_layout Section
 As antireciprocal segment
 \end_layout
@@ -10918,6 +11065,10 @@ Slit orifice
 Lookup model
 \end_layout
 
+\begin_layout Section
+COMSOL model
+\end_layout
+
 \begin_layout Standard
 \align left
 LRFTubes allows importing transfer matrix data from externally computed
@@ -11013,6 +11164,124 @@ LookupModel
 .
 \end_layout
 
+\begin_layout Subsection
+SPICE model
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\noindent
+\align center
+\begin_inset Graphics
+	filename img/two_port_probing.pdf
+	width 90text%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Two-port model, probing the transfer matrix by computing the simulation
+ output.
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:2-port-probing"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+A SPICE model can be created from a COMSOL model, by performing a circuit
+ analysis of the system in two cases, one is the situation providing a voltage
+ source on one side, and measuring the current going in, and the current
+ going out on the other side, while the element is short-circuited.
+ The other is similar, only in this case the segment is 
+\emph on
+open
+\emph default
+ on the other side.
+ Fig.
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:2-port-probing"
+
+\end_inset
+
+ shows the schematic of the two cases that need to be computed.
+ If we assume:
+\begin_inset Formula 
+\begin{equation}
+\left\{ \begin{array}{c}
+p\\
+U
+\end{array}\right\} _{R}=\left[\begin{array}{cc}
+A & B\\
+C & D
+\end{array}\right]\left\{ \begin{array}{c}
+p\\
+U
+\end{array}\right\} _{L},
+\end{equation}
+
+\end_inset
+
+for the components of the transfer matrix, we can set the following equations:
+\begin_inset Formula 
+\begin{align}
+U_{R}^{(1)} & =C+DU_{L}^{(1)},\\
+0 & =A+BU_{L}^{(1)},\\
+0 & =C+DU_{L}^{(2)},\\
+p_{R}^{(2)} & =A+BU_{L}^{(2)},
+\end{align}
+
+\end_inset
+
+which gives four equations, for the four unknown transfer matrix coefficients.
+ We can directly perform this computation using the method 
+\family typewriter
+LookupModel.from_pU
+\family default
+ in 
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+lrftubes
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
 \begin_layout Chapter
 Measuring the transmission matrix using the four microphone method
 \end_layout
@@ -12708,6 +12977,17 @@ acpr.delta/acpr.rho_c
 Or we could write this with a custom density and speed of sound <— TODO!
 \end_layout
 
+\begin_layout Standard
+2D Axisymmetric:
+\end_layout
+
+\begin_layout Standard
+
+\family typewriter
+(hnu*(test(pr)*pr+pz*test(pz))+test(p)*p*acpr.ik^2*(1-gamma)*hkappa)*acpr.delta/ac
+pr.rho_c
+\end_layout
+
 \begin_layout Standard
 \begin_inset CommandInset bibtex
 LatexCommand bibtex