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Some docs improvements. Added Zwikker Kosten explicit in bibtex

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Anne de Jong 2022-07-11 12:38:23 +02:00
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44
lrftubes.bib
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@ -275,28 +275,6 @@ The full solution of the problem has been obtained by Kirchhoff (1868) in the fo
file = {Karal - 1953 - The analogous acoustical impedance for discontinui.pdf:/home/anne/.literature/storage/ZSJSCHMS/Karal - 1953 - The analogous acoustical impedance for discontinui.pdf:application/pdf} file = {Karal - 1953 - The analogous acoustical impedance for discontinui.pdf:/home/anne/.literature/storage/ZSJSCHMS/Karal - 1953 - The analogous acoustical impedance for discontinui.pdf:application/pdf}
} }
@article{keefe_acoustical_1984,
title = {Acoustical wave propagation in cylindrical ducts: Transmission line parameter approximations for isothermal and nonisothermal boundary conditions},
volume = {75},
pages = {58--62},
number = {1},
journaltitle = {The Journal of the Acoustical Society of America},
author = {Keefe, Douglas H},
date = {1984},
file = {Keefe - 1984 - Acoustical wave propagation in cylindrical ducts .pdf:/home/anne/.literature/storage/WPM2TBDL/Keefe - 1984 - Acoustical wave propagation in cylindrical ducts .pdf:application/pdf}
}
@article{thompson_analog_2014,
title = {Analog model for thermoviscous propagation in a cylindrical tube},
volume = {135},
pages = {585--590},
number = {2},
journaltitle = {The Journal of the Acoustical Society of America},
author = {Thompson, Stephen C and Gabrielson, Thomas B and Warren, Daniel M},
date = {2014},
file = {Thompson e.a. - 2014 - Analog model for thermoviscous propagation in a cy.pdf:/home/anne/.literature/storage/ZGSV8RWF/Thompson e.a. - 2014 - Analog model for thermoviscous propagation in a cy.pdf:application/pdf}
}
@article{benade_propagation_1968, @article{benade_propagation_1968,
title = {On the propagation of sound waves in a cylindrical conduit}, title = {On the propagation of sound waves in a cylindrical conduit},
volume = {44}, volume = {44},
@ -383,19 +361,11 @@ The full solution of the problem has been obtained by Kirchhoff (1868) in the fo
file = {Kino et al. - 2009 - Investigation of non-acoustical parameters of comp.pdf:/home/anne/.literature/storage/I9P5SZAE/Kino et al. - 2009 - Investigation of non-acoustical parameters of comp.pdf:application/pdf} file = {Kino et al. - 2009 - Investigation of non-acoustical parameters of comp.pdf:/home/anne/.literature/storage/I9P5SZAE/Kino et al. - 2009 - Investigation of non-acoustical parameters of comp.pdf:application/pdf}
} }
@article{leniowska_plate_resonance_1999, @book{zwikker_sound_1949,
title = {Vibrations of circular plate interacting with an ideal compressible fluid}, title = {Sound Absorbing Materials},
volume = {24}, url = {https://books.google.com/books?id=ezUOnQEACAAJ},
url = {https://acoustics.ippt.pan.pl/index.php/aa/article/viewFile/1117/952}, publisher = {Elsevier Publishing Company},
pages = {427--441}, author = {Zwikker, C. and Kosten, C.W.},
number = {4}, date = {1949},
journaltitle = {Archives of acoustics}, lccn = {50006127}
author = {Leniowska, L.},
date = {1999}
}
@misc{calcdevice,
title = {Natural frequency calculators (web page)},
url = {https://calcdevice.com/natural-frequency-of-circular-plate-id224.html},
urldate = {2022-05-25}
} }

114
lrftubes.lyx
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@ -3436,6 +3436,8 @@ status open
\backslash \backslash
lrftubes lrftubes
\backslash
\end_layout \end_layout
\end_inset \end_inset
@ -4509,9 +4511,10 @@ C_{2} & =\frac{J_{0}\left(\alpha_{0}\right)-J_{0}\left(\alpha_{1}\right)}{J_{0}\
\begin_layout Standard \begin_layout Standard
\begin_inset Formula \begin_inset Formula
\begin{equation} \begin{align}
f_{i}=\delta_{i}\left(1+i\right)\frac{\left\{ H_{0}^{(1)}\left(\alpha_{0}\right)-H_{0}^{(1)}\left(\alpha_{1}\right)\right\} \left[r_{0}H_{-1}^{(2)}\left(\alpha_{0}\right)-r_{1}H_{-1}^{(2)}\left(\alpha_{1}\right)\right]+\left\{ H_{0}^{(2)}\left(\alpha_{0}\right)-H_{0}^{(2)}\left(\alpha_{1}\right)\right\} \left[r_{1}H_{-1}^{(1)}\left(\alpha_{1}\right)-r_{0}H_{-1}^{(1)}\left(\alpha_{0}\right)\right]}{\left(r_{1}^{2}-r_{0}^{2}\right)\left[H_{0}^{(1)}\left(\alpha_{0}\right)H_{0}^{(2)}\left(\alpha_{1}\right)-H_{0}^{(1)}\left(\alpha_{1}\right)H_{0}^{(2)}\left(\alpha_{0}\right)\right]} f_{i} & =\delta_{i}\left(1+i\right)\left[\frac{\left\{ H_{0}^{(1)}\left(\alpha_{0}\right)-H_{0}^{(1)}\left(\alpha_{1}\right)\right\} \left[r_{0}H_{-1}^{(2)}\left(\alpha_{0}\right)-r_{1}H_{-1}^{(2)}\left(\alpha_{1}\right)\right]}{\left(r_{1}^{2}-r_{0}^{2}\right)\left[H_{0}^{(1)}\left(\alpha_{0}\right)H_{0}^{(2)}\left(\alpha_{1}\right)-H_{0}^{(1)}\left(\alpha_{1}\right)H_{0}^{(2)}\left(\alpha_{0}\right)\right]}+\right.\\
\end{equation} & \qquad\qquad\qquad\left.\frac{\left\{ H_{0}^{(2)}\left(\alpha_{0}\right)-H_{0}^{(2)}\left(\alpha_{1}\right)\right\} \left[r_{1}H_{-1}^{(1)}\left(\alpha_{1}\right)-r_{0}H_{-1}^{(1)}\left(\alpha_{0}\right)\right]}{\left(r_{1}^{2}-r_{0}^{2}\right)\left[H_{0}^{(1)}\left(\alpha_{0}\right)H_{0}^{(2)}\left(\alpha_{1}\right)-H_{0}^{(1)}\left(\alpha_{1}\right)H_{0}^{(2)}\left(\alpha_{0}\right)\right]}\right]
\end{align}
\end_inset \end_inset
@ -5198,7 +5201,7 @@ S_{f}=\exp\left(\alpha x\right)
\begin_inset Note Note \begin_inset Note Note
status open status collapsed
\begin_layout Plain Layout \begin_layout Plain Layout
\begin_inset Formula $\frac{\mathrm{d}^{2}p}{\mathrm{d}x^{2}}+\alpha\frac{\mathrm{d}p}{\mathrm{d}x}+\Gamma^{2}p=0$ \begin_inset Formula $\frac{\mathrm{d}^{2}p}{\mathrm{d}x^{2}}+\alpha\frac{\mathrm{d}p}{\mathrm{d}x}+\Gamma^{2}p=0$
@ -5559,7 +5562,7 @@ p=\frac{C_{1}\exp\left(-i\Gamma x\right)+C_{1}\exp\left(-i\Gamma x\right)}{r_{0}
\begin_layout Standard \begin_layout Standard
\begin_inset Note Note \begin_inset Note Note
status open status collapsed
\begin_layout Plain Layout \begin_layout Plain Layout
If we assume If we assume
@ -7682,7 +7685,8 @@ Both tubes on either side of the discontinuity are cylindrical.
\end_layout \end_layout
\begin_layout Itemize \begin_layout Itemize
The wavelength is larger than transverse characteristic length scale. The wavelength is larger than transverse characteristic length scale (no
propagating modes expect for the plane waves).
\end_layout \end_layout
\begin_layout Itemize \begin_layout Itemize
@ -8428,9 +8432,16 @@ noprefix "false"
It would be beneficial for computing time to replace the outside world It would be beneficial for computing time to replace the outside world
by a boundary condition on the port. by a boundary condition on the port.
Here it is approached as a scattering problem. Here it is approached as a scattering problem.
More information is described in 'Sound absorbing materials' (1949) Zwikker More information is described in
et al., pp. \begin_inset CommandInset citation
132-134. LatexCommand cite
after "p. 132-134"
key "zwikker_sound_1949"
literal "false"
\end_inset
.
The pressure field can be written as: The pressure field can be written as:
\end_layout \end_layout
@ -8454,23 +8465,24 @@ in which
\begin_inset Formula $p_{i}$ \begin_inset Formula $p_{i}$
\end_inset \end_inset
the incident pressure field and the incident pressure field (the field as if there were only an infinite
wall) and
\begin_inset Formula $p_{s}$ \begin_inset Formula $p_{s}$
\end_inset \end_inset
the scattered pressure field. the scattered pressure field.
All depend on both position and time. The combination of the incident and scattered field combined result in
the total pressure field.
All depend on both position and time (or frequency).
If only the infinite wall is taken into account and the port and system If only the infinite wall is taken into account and the port and system
behind it are ignored, the amplitude of the incident plane wave and its behind it are ignored, the amplitude of the incident plane wave is:
reflection can be described as:
\end_layout \end_layout
\begin_layout Standard \begin_layout Standard
\begin_inset Formula \begin_inset Formula
\begin{equation} \begin{equation}
p_{i}(x,t)=\begin{cases} p_{i}(x,\omega)=\begin{cases}
P_{i}\cdot\cos(kx) & x<0\\ P_{i}\cdot\cos(kx) & x<=0\\
undefined & x=0\\
0 & x>0 0 & x>0
\end{cases} \end{cases}
\end{equation} \end{equation}
@ -8485,8 +8497,8 @@ in which
\begin_inset Formula $P_{i}$ \begin_inset Formula $P_{i}$
\end_inset \end_inset
is half the amplitude of the incident plane wave (resulting in sound pressure is the amplitude of the incident plane wave at the wall (resulting in sound
pressure
\family roman \family roman
\series medium \series medium
\shape up \shape up
@ -8520,7 +8532,7 @@ in which
\begin_inset Formula $k$ \begin_inset Formula $k$
\end_inset \end_inset
is the wavenumber and is the wave number and
\begin_inset Formula $x$ \begin_inset Formula $x$
\end_inset \end_inset
@ -8528,7 +8540,7 @@ in which
There is no scattered pressure field, so this is the total pressure field There is no scattered pressure field, so this is the total pressure field
right away. right away.
When the port and system behind it are added, the total pressure field When the port and system behind it are added, the total pressure field
no longer is equal to the incident pressure field: a correction must be is no longer equal to the incident pressure field: a correction must be
added, which is captured in added, which is captured in
\begin_inset Formula $p_{s}$ \begin_inset Formula $p_{s}$
\end_inset \end_inset
@ -8539,7 +8551,7 @@ in which
\begin_inset Formula $x<0$ \begin_inset Formula $x<0$
\end_inset \end_inset
, this has the same effect als a baffled piston. , this has the same effect as a baffled piston.
On the condition that the wavelength is much larger than the port size, On the condition that the wavelength is much larger than the port size,
the scattered field near the boundary (but still outside of the port) is the scattered field near the boundary (but still outside of the port) is
given by: given by:
@ -8548,7 +8560,7 @@ in which
\begin_layout Standard \begin_layout Standard
\begin_inset Formula \begin_inset Formula
\begin{equation} \begin{equation}
p_{s}(x=0^{-})=-Z_{rad}U p_{s}(x=0^{-})=-Z_{\mathrm{rad}}U
\end{equation} \end{equation}
\end_inset \end_inset
@ -8558,10 +8570,10 @@ p_{s}(x=0^{-})=-Z_{rad}U
\begin_layout Standard \begin_layout Standard
in which in which
\begin_inset Formula $Z_{rad}$ \begin_inset Formula $Z_{\mathrm{rad}}$
\end_inset \end_inset
is the radiation impedance of a baffled piston and is the radiation impedance of a baffled piston and
\begin_inset Formula $U$ \begin_inset Formula $U$
\end_inset \end_inset
@ -8642,7 +8654,7 @@ velocities
\begin_layout Standard \begin_layout Standard
\begin_inset Formula \begin_inset Formula
\begin{equation} \begin{equation}
p_{t}(x=0)=P_{i}-z_{rad}v\label{eq:bc-planewave-port-pressure} p_{t}(x=0)=P_{i}-z_{\mathrm{rad}}v\label{eq:bc-planewave-port-pressure}
\end{equation} \end{equation}
\end_inset \end_inset
@ -8652,10 +8664,10 @@ p_{t}(x=0)=P_{i}-z_{rad}v\label{eq:bc-planewave-port-pressure}
\begin_layout Standard \begin_layout Standard
in which in which
\begin_inset Formula $z_{rad}$ \begin_inset Formula $z_{\mathrm{rad}}$
\end_inset \end_inset
is the specific radiation impedance of a baffled piston and is the specific radiation impedance of a baffled piston and
\begin_inset Formula $v$ \begin_inset Formula $v$
\end_inset \end_inset
@ -8669,8 +8681,16 @@ boundary condition in COMSOL.
\begin_inset Formula $v$ \begin_inset Formula $v$
\end_inset \end_inset
can be 'measured' by averaging the normal component of the velocity and can be
adding a minus sign to make it inwards. \begin_inset Quotes eld
\end_inset
measured
\begin_inset Quotes erd
\end_inset
by averaging the normal component of the velocity and adding a minus sign
to make it inwards.
Alternatively, the equation can be solved for Alternatively, the equation can be solved for
\begin_inset Formula $v$ \begin_inset Formula $v$
\end_inset \end_inset
@ -8698,7 +8718,39 @@ in which
\begin_inset Formula $p_{t}(x=0)$ \begin_inset Formula $p_{t}(x=0)$
\end_inset \end_inset
can be 'measured' by averaging it over the port's boundary. can be
\begin_inset Quotes eld
\end_inset
measured
\begin_inset Quotes erd
\end_inset
by averaging it over the port's boundary.
The LRFTubes implementation of this
\emph on
mixed
\emph default
boundary condition is for a left wall:
\begin_inset Formula
\begin{equation}
p_{L}+Z_{\mathrm{rad}}U_{L}=P_{i},
\end{equation}
\end_inset
and the same on a right wall:
\end_layout
\begin_layout Standard
\begin_inset Formula
\begin{equation}
p_{R}-Z_{\mathrm{rad}}U_{R}=P_{i}
\end{equation}
\end_inset
\end_layout \end_layout
\begin_layout Standard \begin_layout Standard
@ -9294,7 +9346,7 @@ reference "eq:U_vs_V"
a bit: a bit:
\begin_inset Note Note \begin_inset Note Note
status open status collapsed
\begin_layout Plain Layout \begin_layout Plain Layout
\begin_inset Formula $\frac{1}{S_{l}}\left(z_{m}+\frac{\left(B\ell\right)^{2}}{Z_{\mathrm{el}}}\right)U_{l}=p_{l}S_{l}-p_{r}S_{r}+\frac{B\ell}{Z_{\mathrm{el}}}V_{\mathrm{in}}$ \begin_inset Formula $\frac{1}{S_{l}}\left(z_{m}+\frac{\left(B\ell\right)^{2}}{Z_{\mathrm{el}}}\right)U_{l}=p_{l}S_{l}-p_{r}S_{r}+\frac{B\ell}{Z_{\mathrm{el}}}V_{\mathrm{in}}$