ASCEE
/
lrftubes_doc
4
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Some docs improvements. Added Zwikker Kosten explicit in bibtex

This commit is contained in:
Anne de Jong 2022-07-11 12:38:23 +02:00
parent b00e3e2b57
commit c0e014ae71
2 changed files with 92 additions and 70 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

46
lrftubes.bib
View File

@ -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}
}
@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,
title = {On the propagation of sound waves in a cylindrical conduit},
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}
}
@article{leniowska_plate_resonance_1999,
title = {Vibrations of circular plate interacting with an ideal compressible fluid},
volume = {24},
url = {https://acoustics.ippt.pan.pl/index.php/aa/article/viewFile/1117/952},
pages = {427--441},
number = {4},
journaltitle = {Archives of acoustics},
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}
}
@book{zwikker_sound_1949,
title = {Sound Absorbing Materials},
url = {https://books.google.com/books?id=ezUOnQEACAAJ},
publisher = {Elsevier Publishing Company},
author = {Zwikker, C. and Kosten, C.W.},
date = {1949},
lccn = {50006127}
}

116
lrftubes.lyx
View File

@ -3435,7 +3435,9 @@ status open
\backslash
lrftubes
lrftubes
\backslash
\end_layout
\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_inset Formula
\begin{equation}
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]}
\end{equation}
\begin{align}
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.\\
& \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
@ -5198,7 +5201,7 @@ S_{f}=\exp\left(\alpha x\right)
\begin_inset Note Note
status open
status collapsed
\begin_layout Plain Layout
\begin_inset Formula $\frac{\mathrm{d}^{2}p}{\mathrm{d}x^{2}}+\alpha\frac{\mathrm{d}p}{\mathrm{d}x}+\Gamma^{2}p=0$
@ -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_inset Note Note
status open
status collapsed
\begin_layout Plain Layout
If we assume
@ -7682,7 +7685,8 @@ Both tubes on either side of the discontinuity are cylindrical.
\end_layout
\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
\begin_layout Itemize
@ -8428,9 +8432,16 @@ noprefix "false"
It would be beneficial for computing time to replace the outside world
by a boundary condition on the port.
Here it is approached as a scattering problem.
More information is described in 'Sound absorbing materials' (1949) Zwikker
et al., pp.
132-134.
More information is described in
\begin_inset CommandInset citation
LatexCommand cite
after "p. 132-134"
key "zwikker_sound_1949"
literal "false"
\end_inset
.
The pressure field can be written as:
\end_layout
@ -8454,23 +8465,24 @@ in which
\begin_inset Formula $p_{i}$
\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 $p_{s}$
\end_inset
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
behind it are ignored, the amplitude of the incident plane wave and its
reflection can be described as:
behind it are ignored, the amplitude of the incident plane wave is:
\end_layout
\begin_layout Standard
\begin_inset Formula
\begin{equation}
p_{i}(x,t)=\begin{cases}
P_{i}\cdot\cos(kx) & x<0\\
undefined & x=0\\
p_{i}(x,\omega)=\begin{cases}
P_{i}\cdot\cos(kx) & x<=0\\
0 & x>0
\end{cases}
\end{equation}
@ -8485,8 +8497,8 @@ in which
\begin_inset Formula $P_{i}$
\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
\series medium
\shape up
@ -8520,7 +8532,7 @@ in which
\begin_inset Formula $k$
\end_inset
is the wavenumber and
is the wave number and
\begin_inset Formula $x$
\end_inset
@ -8528,7 +8540,7 @@ in which
There is no scattered pressure field, so this is the total pressure field
right away.
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
\begin_inset Formula $p_{s}$
\end_inset
@ -8539,7 +8551,7 @@ in which
\begin_inset Formula $x<0$
\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,
the scattered field near the boundary (but still outside of the port) is
given by:
@ -8548,7 +8560,7 @@ in which
\begin_layout Standard
\begin_inset Formula
\begin{equation}
p_{s}(x=0^{-})=-Z_{rad}U
p_{s}(x=0^{-})=-Z_{\mathrm{rad}}U
\end{equation}
\end_inset
@ -8558,10 +8570,10 @@ p_{s}(x=0^{-})=-Z_{rad}U
\begin_layout Standard
in which
\begin_inset Formula $Z_{rad}$
\begin_inset Formula $Z_{\mathrm{rad}}$
\end_inset
is the radiation impedance of a baffled piston and
is the radiation impedance of a baffled piston and
\begin_inset Formula $U$
\end_inset
@ -8642,7 +8654,7 @@ velocities
\begin_layout Standard
\begin_inset Formula
\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_inset
@ -8652,10 +8664,10 @@ p_{t}(x=0)=P_{i}-z_{rad}v\label{eq:bc-planewave-port-pressure}
\begin_layout Standard
in which
\begin_inset Formula $z_{rad}$
\begin_inset Formula $z_{\mathrm{rad}}$
\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 $v$
\end_inset
@ -8669,8 +8681,16 @@ boundary condition in COMSOL.
\begin_inset Formula $v$
\end_inset
can be 'measured' by averaging the normal component of the velocity and
adding a minus sign to make it inwards.
can be
\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
\begin_inset Formula $v$
\end_inset
@ -8698,7 +8718,39 @@ in which
\begin_inset Formula $p_{t}(x=0)$
\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
\begin_layout Standard
@ -9294,7 +9346,7 @@ reference "eq:U_vs_V"
a bit:
\begin_inset Note Note
status open
status collapsed
\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{S_{l}}\left(z_{m}+\frac{\left(B\ell\right)^{2}}{Z_{\mathrm{el}}}\right)U_{l}=p_{l}S_{l}-p_{r}S_{r}+\frac{B\ell}{Z_{\mathrm{el}}}V_{\mathrm{in}}$