From de7d59f56e4c4bed6042eb74220923bf47db839b Mon Sep 17 00:00:00 2001 From: jbon Date: Tue, 12 Dec 2017 15:21:12 +0100 Subject: [PATCH 01/12] =?UTF-8?q?initial=20scripts=20provided=20by=20J?= =?UTF-8?q?=C3=A9r=C3=B4me?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- acoustics/envelope_detection.m | 36 ++++++++++++++++++++++++++++++++++ acoustics/test_code.m | 28 ++++++++++++++++++++++++++ acoustics/zero_padding.m | 28 ++++++++++++++++++++++++++ 3 files changed, 92 insertions(+) create mode 100644 acoustics/envelope_detection.m create mode 100644 acoustics/test_code.m create mode 100644 acoustics/zero_padding.m diff --git a/acoustics/envelope_detection.m b/acoustics/envelope_detection.m new file mode 100644 index 0000000..daf026c --- /dev/null +++ b/acoustics/envelope_detection.m @@ -0,0 +1,36 @@ +function [envelope] = envelope_detection (signal, fech, fmin, fmax,option) + +%function to determine the envelope of a the data vector named signal +%fech is the sampling frequency of the data vector in MHz +%we add a filtering of the signal between fmin and fmax in MHz +%option refer to the option of the zero padding process: +%sigzp is filled with 0 from N to Nzeropad if option = 0 +%sigzp is filled with the mean of sig from N to Nzeropad if option != 0 +%%%% +%if signal have an offset, the output envelope won't have, but still need to put +%option != 0 if signal have an offset and want a clean envelope + +if fmin<0 + fmin=0; +endif +if fmax>fech/2 + fmax=fech/2; +endif +if fmax Date: Tue, 12 Dec 2017 18:05:55 +0100 Subject: [PATCH 02/12] computing acoustics - probem description --- acoustics/Problem description.pdf | Bin 0 -> 13692 bytes acoustics/Problem description.svg | 387 ++++++++++++++++++++++++++++++ 2 files changed, 387 insertions(+) create mode 100644 acoustics/Problem description.pdf create mode 100644 acoustics/Problem description.svg diff --git a/acoustics/Problem description.pdf b/acoustics/Problem 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HcmV?d00001 diff --git a/acoustics/Problem description.svg b/acoustics/Problem description.svg new file mode 100644 index 0000000..821b5f3 --- /dev/null +++ b/acoustics/Problem description.svg @@ -0,0 +1,387 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + + + + + + + + + A + a + + + B + C + solid elements: - A: transducer - B: copper (high acoustic impedence) - C: diffusing material (low acoustic impedence)signals: - a: produced by the transducer - b: reflected at 45° towards the patient - c: refracted through the cooper/air interface - d: reflected by the copper/composite interface - e: refracted through the copper/air interfaceProblem: determine the angle of vectors b, c, d, e, and f, and the attenuation in dB of the corresponding signals + b + c + d + e + f + + From 741e156aad4a5db6571ca1f6f33911668e3be7dc Mon Sep 17 00:00:00 2001 From: jbon Date: Tue, 12 Dec 2017 18:17:29 +0100 Subject: [PATCH 03/12] update problem description --- 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a/acoustics/Problem description.svg b/acoustics/Problem description.svg index 821b5f3..0cb95e8 100644 --- a/acoustics/Problem description.svg +++ b/acoustics/Problem description.svg @@ -113,8 +113,8 @@ inkscape:pageopacity="0.0" inkscape:pageshadow="2" inkscape:zoom="0.7" - inkscape:cx="124.98284" - inkscape:cy="625.00509" + inkscape:cx="265.19573" + inkscape:cy="409.70799" inkscape:document-units="px" inkscape:current-layer="layer1" showgrid="false" @@ -287,7 +287,7 @@ sodipodi:role="line" x="64.171867" y="726.87408" - id="tspan4788"> - C: diffusing material (low acoustic impedence) - C: resin/glass-fiber composite (low acoustic impedence) - b: reflected at 45° towards the patient - b: refracted at 45° towards the patient - c: refracted through the cooper/air interface - c: transmitted through the cooper/air interface - d: reflected by the copper/composite interface - d: refracted by the copper/composite interface - e: refracted through the copper/air interface - e: transmitted through the copper/air interface - f: transmitted through the copper/composite interfaceProblem: determine the angle of vectors b, c, d, e, and f, and Problem: determine the angle of vectors b, c, d, e, and f, and the attenuation in dB of the corresponding signals Date: Tue, 12 Dec 2017 18:20:52 +0100 Subject: [PATCH 04/12] update problem description --- acoustics/Problem description.pdf | Bin 13716 -> 13704 bytes acoustics/Problem description.svg | 10 +++++----- 2 files changed, 5 insertions(+), 5 deletions(-) diff --git a/acoustics/Problem description.pdf b/acoustics/Problem description.pdf index 8fae2001249c8e9d4da2579287c9d59501fc67fc..605302791a394ba14d04e0d06add4c954b1b67ee 100644 GIT binary patch delta 1559 zcmZXOc{tPw9LAAZjVtHlTAJ~!Bb1rnmMX|$f``13ae|?|N_kG{zrFuW|PB0}heZ~!inzmJ!ltJzddj@ry zlKikY990Xcv--)@9(@s6i<}#W5l+Z+wo*(}7w%hkB|eqn?U%iw27z#|Yc|}=VmYQI zv*H400_}~$B>CLPu>OP~%#}QkH2k^Htwb}O+sqi{n-JgR)89g_b%C56A*K0!NhXgw 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id="tspan4800"> - b: refracted at 45° towards the patient - b: reflected at 45° towards the patient - d: refracted by the copper/composite interface - d: reflected by the copper/composite interface Date: Tue, 12 Dec 2017 18:55:04 +0100 Subject: [PATCH 05/12] add readme --- acoustics/readme.md | 19 +++++++++++++++++++ 1 file changed, 19 insertions(+) create mode 100644 acoustics/readme.md diff --git a/acoustics/readme.md b/acoustics/readme.md new file mode 100644 index 0000000..79b05de --- /dev/null +++ b/acoustics/readme.md @@ -0,0 +1,19 @@ +Acoustics of mirrored waves +=========================== + +References: + +- about longitudinal and shear waves + + - https://www.slideshare.net/RakeshSingh125/minor-project-report-28478524 + (p19) + +- speed of sound in different materials: + + - http://www.ondacorp.com/tecref_acoustictable.shtml + + - http://www.rfcafe.com/references/general/velocity-sound-media.htm + + - https://en.wikipedia.org/wiki/Speeds_of_sound_of_the_elements_(data_page) + +- refraction angles From e136ce62293d15bf61adb35e68a8c25332e1a157 Mon Sep 17 00:00:00 2001 From: jbon Date: Sat, 30 Dec 2017 13:52:53 +0100 Subject: [PATCH 06/12] first solution regarding longitudinal wave transmission MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit - 45°>critical angle - no transmission --- acoustics/acousticsOfMirrors.m | 53 +++++++++++++ acoustics/readme.md | 141 ++++++++++++++++++++++++++++++--- 2 files changed, 185 insertions(+), 9 deletions(-) create mode 100644 acoustics/acousticsOfMirrors.m diff --git a/acoustics/acousticsOfMirrors.m b/acoustics/acousticsOfMirrors.m new file mode 100644 index 0000000..7b48da0 --- /dev/null +++ b/acoustics/acousticsOfMirrors.m @@ -0,0 +1,53 @@ +function acousticsOfMirrors + % Speed of longitudinal wave propagation in the considered media. + % we take the mean value of all source we found + vWater = mean([1480,1483,1484,1493,1496]); + vCopper = mean([4660,4760,4760,4660,3560]); + vPCB = mean([4726,3070,2100,2460]); + + % hereafter are computed the angles between the propagation direction and + % the normal vector of the planar boundary between media + % naming convention: angle_a_X is the angle between the propagation vector + % "a" and the planar boundary "X" + angle_a_B = deg2rad(19.388043); + angle_b_B = angle_a_B; + angle_c_B = transmittedAngle(vWater, vCopper, angle_a_B); + angle_c_C = angle_c_B; + angle_d_C = angle_c_C; + angle_d_B = angle_d_C; + angle_e_B = transmittedAngle(vCopper, vWater, angle_d_B); + angle_f_C = transmittedAngle(vCopper, vPCB, angle_c_B); + + disp(strcat("a->B : ",num2str(rad2deg(angle_a_B)))); + disp(strcat(" B->c : ",num2str(rad2deg(angle_c_B)))); + disp(strcat("c->C : ",num2str(rad2deg(angle_c_C)))); + disp(strcat(" C->d : ",num2str(rad2deg(angle_d_C)))); + disp(strcat("d->B : ",num2str(rad2deg(angle_d_B)))); + disp(strcat(" B->e : ",num2str(rad2deg(angle_e_B)))); + disp(strcat(" C->f : ",num2str(rad2deg(angle_f_C)))); + + return; +endfunction + +% Share of the energy which is reflected at the boundary between two +% media of acoustic impedences "z1" and "z2" +function x = reflectionCoeff (z1, z2) + x = ((z2-z1)/(z2+z1))^2; + return; +endfunction + +% Angle of the transmitted wave meeting the boundary between two +% media of longitudinal wave velocities "v1" and "v2" at an incendent +% angle "incident_angle" +function x = transmittedAngle (v1, v2, incident_angle) + x = asin (sin(incident_angle)*v2/v1); + return; +endfunction + +% returns the critical angle for longitudinal wave transmission. Any +% wave meeting the boundary with a greater angle than those returned +% will be totally reflected +function x = criticalAngleOfLongitudinalTransmission(v1, v2) + x = asin (v1/v2) + return; +endfunction \ No newline at end of file diff --git a/acoustics/readme.md b/acoustics/readme.md index 79b05de..7587ac3 100644 --- a/acoustics/readme.md +++ b/acoustics/readme.md @@ -1,19 +1,142 @@ Acoustics of mirrored waves =========================== -References: +Hypotheses +---------- -- about longitudinal and shear waves +**Propagation mode**. There are four modes of acoustic wave propagation: +longitudinal (compression), transverse (shear), surface (Rayleigh), plate (Lamb) +[1]. Transverse, surface and plate propagation are either much weaker than the +longitudinal propagation or their occur in specific conditions. Therefore, we +consider here only longitudinal waves. - - https://www.slideshare.net/RakeshSingh125/minor-project-report-28478524 - (p19) +**Material**. All mediums are considered here to be isotropic. That is, the +elastic constant is equal in all directions of the medium. -- speed of sound in different materials: +Variables +--------- - - http://www.ondacorp.com/tecref_acoustictable.shtml +Compressional velocity (speed of longitudinal wave propagation, in m/s): - - http://www.rfcafe.com/references/general/velocity-sound-media.htm +- In copper : - - https://en.wikipedia.org/wiki/Speeds_of_sound_of_the_elements_(data_page) + - 4660 [2] -- refraction angles + - 4760 (annealed) [6] + + - 4760 (annealed) [7] + + - 4660 [10] + + - 3560 [13] + + - In air: + + - 331.45 (dry) [6] + + - 331.2 (dry at 0°C) [8] + + - 331 [13] + + - In composite: + + - 4726 (Glass fiber-reinforced polyester composite) [9] + + - 3070 (graphite/epoxy) [10] + + - 2100 (L385:340 epoxy at 20°C) [11] + + - 2460 to 3170 (depending on thickness and material ratio) [14] + + - In water: + + - 1480 (at 20°C) [10] + + - 1483 (at 20°C) [12] + + - 1484 [8] + + - 1493 [13] + + - 1496 (distilled) [6] + +Acoustic impedence (in Ns/m³): + +- Copper: + + - 41.6e6 [3] + +- Air + + - 413 (at 20°C) [3] + +- Water + + - 1.48e6 [3] + +Formula +------- + +Share of the energy which is reflected at the boundary between two media of +acoustic impedences z1 and z2 [4]: + +$$((z2-z1)/(z2+z1))^2;$$ + +Angle of the transmitted wave meeting the boundary between two media of +longitudinal wave velocities v1 and v2 at an angle alpha, derived from Snell’s +law [5]: + +$$asin (sin(incident_angle)*v2/v1)$$ + +Critical angle of longitudinal wave transmission: + +$$x = asin (v1/v2)$$ + +References +---------- + +[1] https://www.slideshare.net/RakeshSingh125/minor-project-report-28478524, p +9-12 + +[2] https://www.slideshare.net/RakeshSingh125/minor-project-report-28478524, p +15 + +[3] https://www.slideshare.net/RakeshSingh125/minor-project-report-28478524, p +16 + +[4] https://www.slideshare.net/RakeshSingh125/minor-project-report-28478524, p +17 + +[5] https://www.slideshare.net/RakeshSingh125/minor-project-report-28478524, p +18 + +[6] http://www.rfcafe.com/references/general/velocity-sound-media.htm + +[7] https://en.wikipedia.org/wiki/Speeds_of_sound_of_the_elements_(data_page) + +[8] https://en.wikipedia.org/wiki/Speed_of_sound + +[9] https://arxiv.org/ftp/arxiv/papers/1511/1511.04543.pdf + +[10] +https://www.olympus-ims.com/de/ndt-tutorials/thickness-gage/appendices-velocities/ + +[11] +http://www.ndt.net/article/wcndt2004/pdf/materials_characterization/616_mchugh.pdf + +[12] http://www.ondacorp.com/images/Liquids.pdf + +[13] http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/Soundv.html + +[14] +http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.457.3039&rep=rep1&type=pdf + +  + +weitere infos +------------- + +https://de.wikipedia.org/wiki/Snelliussches_Brechungsgesetz -\> Konvertierung +der Druckscwelle zur Scherschwelle + +https://en.wikipedia.org/wiki/Snell%27s_law From f8ff256b8ec8197865170ec14b7be16e620f0e04 Mon Sep 17 00:00:00 2001 From: jbon Date: Tue, 2 Jan 2018 17:11:00 +0100 Subject: [PATCH 07/12] added considerations about shear propagation --- acoustics/Problem description.svg | 628 ++++++++++++++++++++---------- acoustics/Problem_description.png | Bin 0 -> 50256 bytes acoustics/acousticsOfMirrors.m | 65 ++-- acoustics/readme.md | 113 ++++-- 4 files changed, 544 insertions(+), 262 deletions(-) create mode 100644 acoustics/Problem_description.png diff --git a/acoustics/Problem description.svg b/acoustics/Problem description.svg index d998f8a..30bc523 100644 --- a/acoustics/Problem description.svg +++ b/acoustics/Problem description.svg @@ -9,9 +9,9 @@ xmlns="http://www.w3.org/2000/svg" xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd" xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape" - width="210mm" - height="297mm" - viewBox="0 0 744.09448819 1052.3622047" + width="235.0508mm" + height="133.16676mm" + viewBox="0 0 832.85715 471.85073" id="svg2" version="1.1" inkscape:version="0.91 r13725" @@ -19,90 +19,305 @@ + 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transform="matrix(-0.8,0,0,-0.8,-10,0)" + inkscape:connector-curvature="0" /> + d="M 0,0 5,-5 -12.5,0 5,5 0,0 Z" + style="fill:#000000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:1pt;stroke-opacity:1" + transform="matrix(-0.8,0,0,-0.8,-10,0)" + inkscape:connector-curvature="0" /> + d="M 0,0 5,-5 -12.5,0 5,5 0,0 Z" + style="fill:#000000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:1pt;stroke-opacity:1" + transform="matrix(-0.8,0,0,-0.8,-10,0)" + inkscape:connector-curvature="0" /> + + + + + + + + + + + + + + + + inkscape:window-maximized="1" + fit-margin-top="0" + fit-margin-left="0" + fit-margin-right="0" + fit-margin-bottom="0" + showguides="false" /> @@ -138,87 +358,58 @@ + id="layer1" + transform="translate(96.53006,-56.119756)"> + style="fill:#ffd97d;fill-opacity:1;fill-rule:evenodd;stroke:none;stroke-width:1.25;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1" + id="rect5551" + width="832.85718" + height="138.57141" + x="-96.53006" + y="251.41711" /> - + style="fill:#08d97d;fill-opacity:1;fill-rule:evenodd;stroke:none;stroke-width:1.25;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1" + id="rect5551-1" + width="832.68384" + height="138.57141" + x="-96.393211" + y="389.39908" /> - A - a + inkscape:connector-curvature="0" + sodipodi:nodetypes="cc" /> B + x="617.00574" + y="255.82253">boundary A C + x="610.4093" + y="405.85992">boundary B solid elements: - A: transducer - B: copper (high acoustic impedence) - C: resin/glass-fiber composite (low acoustic impedence)signals: - a: produced by the transducer - b: reflected at 45° towards the patient - c: transmitted through the cooper/air interface - d: reflected by the copper/composite interface - e: transmitted through the copper/air interface - f: transmitted through the copper/composite interfaceProblem: determine the angle of vectors b, c, d, e, and f, and + + + + + + the attenuation in dB of the corresponding signals + id="tspan11457" + x="632.84247" + y="323.42316">copper b + id="tspan11461" + x="622.69965" + y="465.56931">composite c + id="tspan11457-4" + x="645.37207" + y="136.56424">water + useful reflected wave + incident wave d + id="tspan11748" + x="172.19635" + y="130.85626" + style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:13.75px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Italic'">echo 1 e + id="tspan11752" + x="305.00812" + y="-258.50623" + style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:13.75px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Italic'">direct shear reflection f + id="tspan11752-1" + x="192.47485" + y="40.373837" + 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zh`mNYSaSp6AY3V$65OlA@k)gh_;WFTu}aQ8532LXbiM=^gzoS&$jZl89!Jw(o?D~F z{(6Dn-%K6ok23cIq5^Hf^q`U6Q~zf5CHFi={cL3kk!E~z{4Up(cs`zAL(;Rz;* qFs-LQmvB~!K6;N0$OV%Q`q~#a%Q^5bwJsoF1lf;Dpz;s;f&T}d@hH#$ literal 0 HcmV?d00001 diff --git a/acoustics/acousticsOfMirrors.m b/acoustics/acousticsOfMirrors.m index 7b48da0..d57c106 100644 --- a/acoustics/acousticsOfMirrors.m +++ b/acoustics/acousticsOfMirrors.m @@ -1,30 +1,49 @@ function acousticsOfMirrors % Speed of longitudinal wave propagation in the considered media. % we take the mean value of all source we found - vWater = mean([1480,1483,1484,1493,1496]); - vCopper = mean([4660,4760,4760,4660,3560]); - vPCB = mean([4726,3070,2100,2460]); + vlWater = mean([1480,1483,1484,1493,1496]); + vlCopper = mean([4660,4760,4760,4660,3560]); + vlPCB = mean([4726,3070,2100,2460]); + % Speed of shear wave propagation in the considered media. + % we take the mean value of all source we found + vsWater = vlWater / 2; + vsCopper = mean([2330,2325,2325]); + vsPCB = vlPCB / 2; + + % critical angles: + disp (strcat("critical angle of longitudinal transmission Water->Copper : ", num2str(rad2deg(criticalAngleOfTransmission(vlWater, vlCopper))))); + disp (strcat("critical angle of shear transmission Water->Copper : ", num2str(rad2deg(criticalAngleOfTransmission(vlWater, vsCopper))))); + % hereafter are computed the angles between the propagation direction and % the normal vector of the planar boundary between media - % naming convention: angle_a_X is the angle between the propagation vector - % "a" and the planar boundary "X" - angle_a_B = deg2rad(19.388043); - angle_b_B = angle_a_B; - angle_c_B = transmittedAngle(vWater, vCopper, angle_a_B); - angle_c_C = angle_c_B; - angle_d_C = angle_c_C; - angle_d_B = angle_d_C; - angle_e_B = transmittedAngle(vCopper, vWater, angle_d_B); - angle_f_C = transmittedAngle(vCopper, vPCB, angle_c_B); - - disp(strcat("a->B : ",num2str(rad2deg(angle_a_B)))); - disp(strcat(" B->c : ",num2str(rad2deg(angle_c_B)))); - disp(strcat("c->C : ",num2str(rad2deg(angle_c_C)))); - disp(strcat(" C->d : ",num2str(rad2deg(angle_d_C)))); - disp(strcat("d->B : ",num2str(rad2deg(angle_d_B)))); - disp(strcat(" B->e : ",num2str(rad2deg(angle_e_B)))); - disp(strcat(" C->f : ",num2str(rad2deg(angle_f_C)))); + % naming convention: ("P"|"S") "_" ("R"|"T") "_" is the angle between the normal vector + % of the boundary X and the propagation vector + % of the pressure (P) or shear (S) wave reflected (R) or transmitted (T) by the boundary X for the Nth time + % example: P_R_A_2 is the pressure wave reflected by the boundary A for the second time + + incident = deg2rad(45); + + % Pressure waves + P_T_A_1 = transmittedAngle(vlWater, vlCopper, incident); + P_T_A_2 = transmittedAngle(vlCopper, vlWater, P_T_A_1); + P_T_B_1 = transmittedAngle(vlCopper, vlPCB, P_T_A_1); + + % Shear waves + S_R_A_1 = transmittedAngle(vlWater, vsWater, incident); + S_T_A_1 = transmittedAngle(vsWater, vsCopper, incident); + S_T_A_2 = transmittedAngle(vsCopper, vsWater, S_T_A_1); + S_T_B_1 = transmittedAngle(vsCopper, vsPCB, S_T_A_1); + + % display in octave console + disp(strcat("incident : ",num2str(rad2deg(incident)))); + disp(strcat("P_T_A_1 : ",num2str(rad2deg(P_T_A_1)))); + disp(strcat("P_T_A_2 : ",num2str(rad2deg(P_T_A_2)))); + disp(strcat("P_T_B_1 : ",num2str(rad2deg(P_T_B_1)))); + disp(strcat("S_R_A_1 : ",num2str(rad2deg(S_R_A_1)))); + disp(strcat("S_T_A_1 : ",num2str(rad2deg(S_T_A_1)))); + disp(strcat("S_T_A_2 : ",num2str(rad2deg(S_T_A_2)))); + disp(strcat("S_T_B_1 : ",num2str(rad2deg(S_T_B_1)))); return; endfunction @@ -47,7 +66,7 @@ % returns the critical angle for longitudinal wave transmission. Any % wave meeting the boundary with a greater angle than those returned % will be totally reflected -function x = criticalAngleOfLongitudinalTransmission(v1, v2) - x = asin (v1/v2) +function x = criticalAngleOfTransmission(v1, v2) + x = asin (v1/v2); return; endfunction \ No newline at end of file diff --git a/acoustics/readme.md b/acoustics/readme.md index 7587ac3..83b48a8 100644 --- a/acoustics/readme.md +++ b/acoustics/readme.md @@ -1,17 +1,58 @@ Acoustics of mirrored waves =========================== +Problem description +------------------- + +[./Problem_Description.jpg](./Problem_Description.jpg) + +- Problem 1: define the angles of all reflected and transmitted longitudinal + (black vectors) and shear (red vectors) waves. + +- Problem 2: situate the echos, that is, the distance between the useful + reflected wave and the echos + +- Problem 3: determine the magnitude of all vectors + +Results +------- + +- Critical angle of longitudinal transmission Water-\>Copper : 19.4° + +- Critical angle of shear transmission Water-\>Copper : 39.7° + +- The incident angle (45°) is greater than the critical angles of longitudinal + and shear transmission, therefore, there is no transmission of the incident + wave into the copper layer, therefore no echo. + +- There is a direct shear reflection of 20.7° + +(to reproduce the results, execute in Octave the script “acousticsOfMirrors.m”) + +Open questions +-------------- + +- Is the incident wave only longitudinal or also bears a shear component? + +- Information missing about the shear velocity of water and composite + material. For water, I considered it to be equal to the longitudinal + velocity. For composite material, I considered it to be the half of + longitudinal velocity, as an analogy to copper. + Hypotheses ---------- **Propagation mode**. There are four modes of acoustic wave propagation: longitudinal (compression), transverse (shear), surface (Rayleigh), plate (Lamb) -[1]. Transverse, surface and plate propagation are either much weaker than the -longitudinal propagation or their occur in specific conditions. Therefore, we -consider here only longitudinal waves. +[1]. Surface and plate propagation occur in specific conditions and are note +considered here only longitudinal waves. -**Material**. All mediums are considered here to be isotropic. That is, the -elastic constant is equal in all directions of the medium. +**Material**. All mediums are considered here to be homogeneous and isotropic. +That is, the elastic constant is equal in all directions and at any point of the +medium. + +**Incident angle**. The incident wave meets the first boundary water/copper with +an angle of 45°. Variables --------- @@ -22,43 +63,59 @@ Compressional velocity (speed of longitudinal wave propagation, in m/s): - 4660 [2] - - 4760 (annealed) [6] + - 4760 (annealed) [6] + + - 4760 (annealed) [7] + + - 4660 [10] + + - 3560 [13] + +- In air: + + - 331.45 (dry) [6] + + - 331.2 (dry at 0°C) [8] + + - 331 [13] + +- In composite: - - 4760 (annealed) [7] + - 4726 (Glass fiber-reinforced polyester composite) [9] - - 4660 [10] + - 3070 (graphite/epoxy) [10] - - 3560 [13] + - 2100 (L385:340 epoxy at 20°C) [11] - - In air: + - 2460 to 3170 (depending on thickness and material ratio) [14] - - 331.45 (dry) [6] +- In water: - - 331.2 (dry at 0°C) [8] + - 1480 (at 20°C) [10] - - 331 [13] + - 1483 (at 20°C) [12] - - In composite: + - 1484 [8] - - 4726 (Glass fiber-reinforced polyester composite) [9] + - 1493 [13] - - 3070 (graphite/epoxy) [10] + - 1496 (distilled) [6] - - 2100 (L385:340 epoxy at 20°C) [11] +Shear velocity (speed of shear wave propagation, in m/s): - - 2460 to 3170 (depending on thickness and material ratio) [14] +- In copper: - - In water: + - 2330 [2] - - 1480 (at 20°C) [10] + - 2325 [6] - - 1483 (at 20°C) [12] + - 2325 [7] - - 1484 [8] +- In composite: - - 1493 [13] + - unknown - - 1496 (distilled) [6] +- I water and air: no shear wave propagation Acoustic impedence (in Ns/m³): @@ -80,17 +137,17 @@ Formula Share of the energy which is reflected at the boundary between two media of acoustic impedences z1 and z2 [4]: -$$((z2-z1)/(z2+z1))^2;$$ +`((z2-z1)/(z2+z1))^2;` Angle of the transmitted wave meeting the boundary between two media of longitudinal wave velocities v1 and v2 at an angle alpha, derived from Snell’s law [5]: -$$asin (sin(incident_angle)*v2/v1)$$ +`asin (sin(incident_angle)*v2/v1)` -Critical angle of longitudinal wave transmission: +Critical angle of wave transmission: -$$x = asin (v1/v2)$$ +`x = asin (v1/v2)` References ---------- From 9c35504de1c87e21e1121bd0f701a8e1251ff59f Mon Sep 17 00:00:00 2001 From: jbon Date: Tue, 2 Jan 2018 17:13:56 +0100 Subject: [PATCH 08/12] corrected typing error --- acoustics/readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/acoustics/readme.md b/acoustics/readme.md index 83b48a8..d26f7f6 100644 --- a/acoustics/readme.md +++ b/acoustics/readme.md @@ -4,7 +4,7 @@ Acoustics of mirrored waves Problem description ------------------- -[./Problem_Description.jpg](./Problem_Description.jpg) +[./Problem_description.png](./Problem_description.png) - Problem 1: define the angles of all reflected and transmitted longitudinal (black vectors) and shear (red vectors) waves. From f64b5fa60fdc9a8809f9f2579a1f0421e6e41a9b Mon Sep 17 00:00:00 2001 From: jbon Date: Tue, 2 Jan 2018 17:16:05 +0100 Subject: [PATCH 09/12] corrected typing error 2 --- acoustics/readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/acoustics/readme.md b/acoustics/readme.md index d26f7f6..6ac62ba 100644 --- a/acoustics/readme.md +++ b/acoustics/readme.md @@ -4,7 +4,7 @@ Acoustics of mirrored waves Problem description ------------------- -[./Problem_description.png](./Problem_description.png) +![./Problem_description.png](./Problem_description.png) - Problem 1: define the angles of all reflected and transmitted longitudinal (black vectors) and shear (red vectors) waves. From 1752942bf7628af33196b8d35b9795c00a4a821f Mon Sep 17 00:00:00 2001 From: jbon Date: Thu, 11 Jan 2018 16:03:45 +0100 Subject: [PATCH 10/12] update data acoustic velocities --- acoustics/readme.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/acoustics/readme.md b/acoustics/readme.md index 6ac62ba..0345911 100644 --- a/acoustics/readme.md +++ b/acoustics/readme.md @@ -113,9 +113,9 @@ Shear velocity (speed of shear wave propagation, in m/s): - In composite: - - unknown + - No data found. As default value we take compression velocity / sqrt(2) -- I water and air: no shear wave propagation +- In water and air: no shear wave propagation Acoustic impedence (in Ns/m³): From 196a6e1bb05a70ca8d0fb5effae614269e6cca98 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?J=C3=A9r=C3=A9my=20Bonvoisin?= Date: Tue, 17 Apr 2018 16:00:58 +0100 Subject: [PATCH 11/12] restructure acoustics readme --- acoustics/readme.md | 202 ++++++++++++-------------------------------- 1 file changed, 53 insertions(+), 149 deletions(-) diff --git a/acoustics/readme.md b/acoustics/readme.md index 0345911..9493879 100644 --- a/acoustics/readme.md +++ b/acoustics/readme.md @@ -1,199 +1,103 @@ -Acoustics of mirrored waves -=========================== +# Acoustic implications of using a mirror +[TOC] -Problem description -------------------- +## Problem description -![./Problem_description.png](./Problem_description.png) - -- Problem 1: define the angles of all reflected and transmitted longitudinal - (black vectors) and shear (red vectors) waves. - -- Problem 2: situate the echos, that is, the distance between the useful - reflected wave and the echos - -- Problem 3: determine the magnitude of all vectors - -Results -------- - -- Critical angle of longitudinal transmission Water-\>Copper : 19.4° - -- Critical angle of shear transmission Water-\>Copper : 39.7° - -- The incident angle (45°) is greater than the critical angles of longitudinal - and shear transmission, therefore, there is no transmission of the incident - wave into the copper layer, therefore no echo. - -- There is a direct shear reflection of 20.7° - -(to reproduce the results, execute in Octave the script “acousticsOfMirrors.m”) +* Problem 1 (solved): define the angles of all reflected and transmitted longitudinal (black vectors) and shear (red vectors) waves. +* Problem 2 (solved): situate the echos, that is, the distance between the useful reflected wave and the echos +* Problem 3 (in progress): determine the magnitude of all vectors -Open questions --------------- - -- Is the incident wave only longitudinal or also bears a shear component? - -- Information missing about the shear velocity of water and composite - material. For water, I considered it to be equal to the longitudinal - velocity. For composite material, I considered it to be the half of - longitudinal velocity, as an analogy to copper. - -Hypotheses ----------- - -**Propagation mode**. There are four modes of acoustic wave propagation: -longitudinal (compression), transverse (shear), surface (Rayleigh), plate (Lamb) -[1]. Surface and plate propagation occur in specific conditions and are note -considered here only longitudinal waves. - -**Material**. All mediums are considered here to be homogeneous and isotropic. -That is, the elastic constant is equal in all directions and at any point of the -medium. - -**Incident angle**. The incident wave meets the first boundary water/copper with -an angle of 45°. +![./Problem_description.png](./Problem_description.png) -Variables ---------- +## Results + +* Critical angle of longitudinal transmission from water to copper : 19.4°. +* Critical angle of shear transmission from water to copper : 39.7° +* The incident angle (45°) is greater than the critical angles of longitudinal and shear transmission, therefore, there is no transmission of the incident wave into the copper layer, therefore neither longitudinal nor shear echo ([total internal reflection](https://en.wikipedia.org/wiki/Total_internal_reflection)). +* There is a direct shear reflection of 20.7° + +*(To reproduce the results, execute in Octave the script “acousticsOfMirrors.m”)* + +## Method + +* The angles of the longitudinal and shear waves transmitted and reflected in the case of a longitudinal wave hitting a boundary between two media A and B are given by [Snell's law](https://de.wikipedia.org/wiki/Snelliussches_Brechungsgesetz#Akustik): +``` +sin(a)/vLA = sin(aRS)/vSA = sin(aRL)/vLA = sin(aTS)/vSB = sin(aTL)/vLB +Where + * a is the incident angle + * vLA is the velocity of longidudinal waves in the medium A + * aRS is the angle of the reflected shear wave in medium A + * vSA is velocity of shear waves in the medium A + * aRL is the angle og the reflected longitudinal wave in medium A + * vLA is the velocity of longitudinal waves in the medium A + * aTS is the angle of the transmitted shear wave in medium B + * vSB is the velocity of shear waves in the mediom B + * aTL is the transmitted longitudinal wave in medium B + * vLB is the velocity of longitudinal waves in the B +``` + +* The critical angle of wave transmission is the angle above which an incindent wave is totally reflected. It is [derived from Snell's law](https://en.wikipedia.org/wiki/Snell%27s_law#Total_internal_reflection_and_critical_angle): +``` +alpha = asin (vA/vB) +Where + * alpha is the critical angle + * vA is the velocity of longitudinal waves in medium A + * vB is the velocity of longitudinal waves in medium B +``` + +## Variables Compressional velocity (speed of longitudinal wave propagation, in m/s): - - In copper : - - 4660 [2] - - 4760 (annealed) [6] - - 4760 (annealed) [7] - - 4660 [10] - - 3560 [13] - - In air: - - 331.45 (dry) [6] - - 331.2 (dry at 0°C) [8] - - 331 [13] - - In composite: - - 4726 (Glass fiber-reinforced polyester composite) [9] - - 3070 (graphite/epoxy) [10] - - 2100 (L385:340 epoxy at 20°C) [11] - - 2460 to 3170 (depending on thickness and material ratio) [14] - - In water: - - 1480 (at 20°C) [10] - - 1483 (at 20°C) [12] - - 1484 [8] - - 1493 [13] - - 1496 (distilled) [6] - Shear velocity (speed of shear wave propagation, in m/s): - - In copper: - - 2330 [2] - - 2325 [6] - - 2325 [7] - - In composite: - - No data found. As default value we take compression velocity / sqrt(2) - - In water and air: no shear wave propagation - Acoustic impedence (in Ns/m³): - - Copper: - - 41.6e6 [3] - - Air - - 413 (at 20°C) [3] - - Water - - 1.48e6 [3] -Formula -------- - -Share of the energy which is reflected at the boundary between two media of -acoustic impedences z1 and z2 [4]: - -`((z2-z1)/(z2+z1))^2;` - -Angle of the transmitted wave meeting the boundary between two media of -longitudinal wave velocities v1 and v2 at an angle alpha, derived from Snell’s -law [5]: - -`asin (sin(incident_angle)*v2/v1)` - -Critical angle of wave transmission: - -`x = asin (v1/v2)` - -References ----------- - -[1] https://www.slideshare.net/RakeshSingh125/minor-project-report-28478524, p -9-12 - -[2] https://www.slideshare.net/RakeshSingh125/minor-project-report-28478524, p -15 - -[3] https://www.slideshare.net/RakeshSingh125/minor-project-report-28478524, p -16 - -[4] https://www.slideshare.net/RakeshSingh125/minor-project-report-28478524, p -17 - -[5] https://www.slideshare.net/RakeshSingh125/minor-project-report-28478524, p -18 +## References +[1] https://www.slideshare.net/RakeshSingh125/minor-project-report-28478524, p 9-12 +[2] https://www.slideshare.net/RakeshSingh125/minor-project-report-28478524, p 15 +[3] https://www.slideshare.net/RakeshSingh125/minor-project-report-28478524, p 16 +[4] https://www.slideshare.net/RakeshSingh125/minor-project-report-28478524, p 17 +[5] https://www.slideshare.net/RakeshSingh125/minor-project-report-28478524, p 18 [6] http://www.rfcafe.com/references/general/velocity-sound-media.htm - [7] https://en.wikipedia.org/wiki/Speeds_of_sound_of_the_elements_(data_page) - [8] https://en.wikipedia.org/wiki/Speed_of_sound - [9] https://arxiv.org/ftp/arxiv/papers/1511/1511.04543.pdf - -[10] -https://www.olympus-ims.com/de/ndt-tutorials/thickness-gage/appendices-velocities/ - -[11] -http://www.ndt.net/article/wcndt2004/pdf/materials_characterization/616_mchugh.pdf - +[10] https://www.olympus-ims.com/de/ndt-tutorials/thickness-gage/appendices-velocities/ +[11] http://www.ndt.net/article/wcndt2004/pdf/materials_characterization/616_mchugh.pdf [12] http://www.ondacorp.com/images/Liquids.pdf - [13] http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/Soundv.html - -[14] -http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.457.3039&rep=rep1&type=pdf - -  - -weitere infos -------------- - -https://de.wikipedia.org/wiki/Snelliussches_Brechungsgesetz -\> Konvertierung -der Druckscwelle zur Scherschwelle - -https://en.wikipedia.org/wiki/Snell%27s_law +[14] http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.457.3039&rep=rep1&type=pdf From 41d25698a9080fdbfbeef56c466f2b700d635e42 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?J=C3=A9r=C3=A9my=20Bonvoisin?= Date: Tue, 17 Apr 2018 16:40:38 +0100 Subject: [PATCH 12/12] corrections suite aux commentaires de jerome --- acoustics/acousticsOfMirrors.m | 4 ++-- acoustics/readme.md | 5 ++++- 2 files changed, 6 insertions(+), 3 deletions(-) diff --git a/acoustics/acousticsOfMirrors.m b/acoustics/acousticsOfMirrors.m index d57c106..0eb2578 100644 --- a/acoustics/acousticsOfMirrors.m +++ b/acoustics/acousticsOfMirrors.m @@ -7,9 +7,9 @@ % Speed of shear wave propagation in the considered media. % we take the mean value of all source we found - vsWater = vlWater / 2; + vsWater = vlWater; vsCopper = mean([2330,2325,2325]); - vsPCB = vlPCB / 2; + vsPCB = vlPCB / 2; % hypothese % critical angles: disp (strcat("critical angle of longitudinal transmission Water->Copper : ", num2str(rad2deg(criticalAngleOfTransmission(vlWater, vlCopper))))); diff --git a/acoustics/readme.md b/acoustics/readme.md index 9493879..67eaad9 100644 --- a/acoustics/readme.md +++ b/acoustics/readme.md @@ -14,7 +14,6 @@ * Critical angle of longitudinal transmission from water to copper : 19.4°. * Critical angle of shear transmission from water to copper : 39.7° * The incident angle (45°) is greater than the critical angles of longitudinal and shear transmission, therefore, there is no transmission of the incident wave into the copper layer, therefore neither longitudinal nor shear echo ([total internal reflection](https://en.wikipedia.org/wiki/Total_internal_reflection)). -* There is a direct shear reflection of 20.7° *(To reproduce the results, execute in Octave the script “acousticsOfMirrors.m”)* @@ -101,3 +100,7 @@ Acoustic impedence (in Ns/m³): [12] http://www.ondacorp.com/images/Liquids.pdf [13] http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/Soundv.html [14] http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.457.3039&rep=rep1&type=pdf + +## Furher messy notes +https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/modeconversion.htm +https://acoustics.byu.edu/content/mode-conversion \ No newline at end of file