diff --git a/img/quadrupole.pdf b/img/quadrupole.pdf index 03768c1..62e5814 100644 Binary files a/img/quadrupole.pdf and b/img/quadrupole.pdf differ diff --git a/img/quadrupole_mechel.png b/img/quadrupole_mechel.png new file mode 100644 index 0000000..15a07fa Binary files /dev/null and b/img/quadrupole_mechel.png differ diff --git a/img/two_port_probing.pdf b/img/two_port_probing.pdf new file mode 100644 index 0000000..dead063 Binary files /dev/null and b/img/two_port_probing.pdf differ diff --git a/lrftubes.lyx b/lrftubes.lyx index 5c834aa..e80c2dc 100644 --- a/lrftubes.lyx +++ b/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