your own copy.

Transcription

your own copy.

The Dynamics of a Railway
Vehicle on a Disturbed Track
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26
4. Numerics
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27
10
Semi axis b [mm]
Semi axis a [mm]
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8
6
4
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28
4. Numerics
0.15
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8
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5. Results
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Amplitude [mm]
10
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6
4
2
10
8
6
4
2
10
8
6
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10
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50
10
30
50
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10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
30
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10
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50
10
30
50
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5. Results
Amplitude [mm]
10
8
6
4
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10
8
6
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10
8
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10
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50
10
30
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UËWW=¢d{B|:=$g««À~k_a$d=|@$==kÀg=~G
AW£Wk=|Gk£z$G:$M=|=kg!£}|Wk
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«$W"kK
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=|U«G?~=~$[~=k@=~G©$_=|±GÁ£ $G±£d|~?|¦~w@GK
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¦~=W=?~=|?|$="£3k$kk$=|W¢Ã{B|¤k=@?~«=~G
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!k=@?~k=|*k|k~$$W=[£Mk ª%=|*~êéAW=k@*~
=|a$?W~$«~=!g_£}|~#|±=|!Àg
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[k~ÀgGB"%g=
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|k$:="$$«.~=k$W@$?~À
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g=§

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45
6
2
1
0
-1
-2
20
20.1
20.2
20.3
20.4
0
-2
-4
20
20.1
20.2
20.3
20.4
20.5
r~et!%ó ¬ Q
s}Æº s}òoÄxv ³ ÉoºYw&ó ¯ C
Time [s]
Time [s]
6
10
4
2
-6
20.5
-r sKt ó ¬ Á
s}oºs}òoÄxv ³ ÉoºYw~ó ¬ C
2
0
-2
-4
-6
4
20
20.2
20.4
20.6
20.8
r ¸t"ó Qs}oºs}òoÄxv ³ ÉÆºYw&ó ¯ C
Time [s]
5
0
-5
-10
20
20.2
20.4
20.6
20.8
r ºet ó Qs}Æº s}òoÄxv ³ ÉoºYw&ó ¦ c C
Time [s]
[%ìdX®dÑ¶5Â«À[E½\£e½º«¶eºÑ\½Ädgì[
a$#P:M\«Ó¶iBe:·K½¾5Å
\½ Ë ¶ Ð¶e½À Ë ¢ Ð¶5½¼P
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=|~=«$@kk%$}=|E?$~ÀWª=|£}=|g
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=|wa$?W~[$"«~=!~À}~@?k$
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46
5. Results
g=w,~À·?Gü=|Wa_
[=|#~G|KB$E,~À@$W?=ª.=WwÌ~¢²,¢°W¶¢
5%|ì[\Íd«hK·\·ì¾ºÃ¶5£5½ø H\M»ª¶Yº:* \&ü[¶eÓ Â8e£e½ö¢}:\½a¶E:¶ez:& &¶
Ói¶ BeK·K½¾5ÅÄ¶ }Ã:ÒÅªP¶e\·Àe-º»¼·¶d}KÂ8K½Ã
Í3=|k§$M=|~d=k@=~G©W*=g$"E,$¤g=|@éAk@$M|Á,~ÀU~®¿
@GK=~À%G=«.}~=|«g?$W
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}=g$"U,$¤gÌ~¢A²,¢°$°gª=|
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kE¢
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="$*=|gE=| k$=|s$:=|
k[~a'~E==kg
47
8e-07
67600
6e-07
67400
4e-07
67200
Vertical force [N]
Add. penetration [m]
2e-07
0
-2e-07
-4e-07
66800
66600
66400
66200
-6e-07
-8e-07
67000
66000
60
60.5
61
61.5
62
62.5
65800
63
60
Time [s]
60.5
61
61.5
62
62.5
Time [s]
r-sKtkñvºoºYv ³ vx{es(Äò5wYw ³ s ³ vx{%ºYwuò ³·´a
r~5tu¼w ³ v¸s(Äa|{]¸w
0.008
0.006
0.004
0.002
0
-0.002
-0.004
-0.006
-0.008
60
60.5
61
61.5
62
62.5
63
¹r ¸)
t (AvÃ]òÆÄìs(¸wCw ³ {}||{ ³ s}oº ws}
y ´ w wuÄÃw ³ È Ã{6Äxvº s}oººes(Ã ´ wuºÄxvx¤wÃ È wuÃyò[wu¸fË
³ v Kuw Ä *
Time [s]
[%-ì[\d[¿µª,DW}KP Mª¶7B±\½¾ÏÀe-º:}e½\½e¾º,+%ÂW»º\½Ä»¶e¶5Â«:Ã:}º-º\·\·¾ºÈ
¶5Ã}ÀM\½`ÅªÑ¶[¢}i BeÙ A5%Kº:MµÒº::\½a5ºÓ:¤ BeK·±:\
ü _Í8SÂ Îº}þ}K½Ã:·ì\½¼¡\Ã7 È
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_Í_ÂÑþ¶e½À? KeÇK\½¾ ¶5Â?»·ì\À[
`ÂMÂ«
63
48
5. Results
0.005
0.004
Distance [m]/[1e-4 m]
0.003
0.002
0.001
0
-0.001
-0.002
-0.003
-0.004
-0.005
60
60.2
60.4
60.6
60.8
61
Time [s]
5%\ìd\ea&µªÑº:e·£À·\½¼Ñ-ºPÅªÑ·¶ez:¶e·ª»ªeº}\£e½Ï ¡ÅªÑÓUª}:·xº:KÜº¢:¶dKz}À8Åª
Àe-º»¼·¶[}KÂ8:½W ¡\PÇ¶e\·&µª«À[¶eº}À ¶5½¼À&À[5z}iÀ ÈÀd¶Yºª}ÀH·ì\½¼KºÑ¶eÇPÅª«¶dÀ[Àe\£e½¶e·
»ª:½¼:¶e£e½ÏÀ[z»¼Å*º:}¶e·}À,¢:
ü ¼Æ¾.- Ke«ÅªM· }¶e½À ¤%?¶5\·xº:*µª«Ó_ª5¹ ¿¤e½z¶e·
À[5z}À ·ì\½¼Kº8¶5/ N¼01ÄÂÑÂ ºeÓº«\_À[+ B¤£¶e£e½Á¢}:Ó}:½+\«ÓUª}:·xº:K ¶e½À \«¶e\·
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$À[$W=©WG
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49
10
Semi axis b [mm]
9
8
7
6
5
4
0.001
0.002
0.003
0.004
0.005
32 54
âLãåä:ædç¶è
0
ê 7éWëìxí5èPð·è+òWä:öí2ïºøKöí½èPðÅôiöèç¶ô7ð õ+èó
76 82
y
þ7ãõîxð·ô÷¯è+ó¿èòMöõCúè+ö Lèè+ò
ô7òxþ
¿ó
ãÙô+ûãõïºøKö6í5è÷ïiòMöô÷öNèð6ð)ã îxõ+è'øï7ç?ð·ôiöèç¯ôið
ó4ê
0.005
0.004
Distance [m]/[1e-4 m]
0.003
0.002
0.001
0
-0.001
-0.002
-0.003
-0.004
-0.005
60
:ê
60.4
60.6
60.8
61
Time [s]
$2 549
âLãåä:ædç¶è
60.2
Më-ìxí5èõï7ð)ãþHð)ã6òeèãõöí½èCð·ô7öè+ç¶ô7ð½î5ïõã6öãïiò
Eí5èèð õ+è+öNõæ5ú+öç¶ô:÷+öèþö6í5è
ïºøö6í5è
þ7ãõîxð·ô÷¯è+ó¿èòMöJïºøPöí½èCç¶ô7ã6ð·êOìeí½è¿þôõ¶í½èþ-ôiòeþOþïiööèþ7üÇþ:ôõ¶í5è¯þHðåã6òxèõCôiç¶èCöí½è4ô:þþiã6öãïiòxô7ð
,:<;>=@?0A
9
î5è+òxè+öç¶ô7öãï7òþ:èîxöíCõ+÷ôið·èþú+ñ
CBD=0EF
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ç¯ôiã6ð í5èò
Oôiòxþ
ü Hó
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ó^õ¶í½ï
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ö6í5èPõîxã è4÷ïió¿èõPã6ò«öí½èî5èòeèöç¶ôiöãïiò
þ:èîxöí½ê
y
ìxí5èöígç¶èèLí5ïiçã·ýïiòMöô7ð
í5èèð õ+è+ö'ôiòeþ
úè+ö Lèè+òHöí½è
ö6í5è
50
5. Results
0.6
0.3
0
-0.3
-0.6
-0.015
-0.01
ê
:ë
0
0.005
0.01
0.015
Lateral deviation [m]
D2 5402 JI
âLãåä7ædç¯è
-0.005
¿í5ôiöNó4ô7ñú¯è
ô÷í½ôïiöã÷õï7ð)ædöãïiòxê
5.3 Lateral sinusoidal gauge irregularities
æ87¯
51
íÏÙGA<?BIÙ>D:L&>AJÑD:Ø,ÙJÀÑÙ-ÀP<ÚD:BIBI<!ÀC2:ÙÒBED}GIDK<?>
Amplitude [mm]
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
30
50
10
30
50
10
30
Wavelength [m]
50
10
30
50
[%ì[\K[Mµ?ºz¶e½À[¶eÇÀÑÀdB¤£¶e£e½, LEE²?¶e[a?\Ç[%·¶5\£Kº¶eÂ8±ÀdK·\·ÇÀ«¶5½¼À
Åª
BeK·¤:\ü_-Lº @¾ÇÀH¶e% ÍhÂ Îº:, %PÓU¾\zÑ¶5½¼À ¢K·¶dÇ }eÇº»e½¼Àeº¡Ã ¼ ¢}K\½¾
¾ ¾¾¾KM¾HÂPþEKº»ª}:6 Be:·ìü[
Æ $$M~?=WGg?~=~kg=M#|g?$@
W?~ËWk:,B«|$
~êéAW=k@$|$B£3k$@¿
k$=| AW£WkÉ=|"£¤?$~ÀW¢"{B|~À!=~[W:
=g=:%$~g:=|"=|
==g=~
=~W$_«.~@==kW¢ºÌ~¢²,¢°kè©=|£}=|
=$g? W,~Àg=~G¹$I
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$"«~=kBg=$W!=|$ ï±"u=|W=~ÀdW#$~k%d~§G
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kWª ¸ £GI4R
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«AG}
E?|$$k~=|G$$$M$=
=|$N
&°kë±[Ê£d|~?|§~*=k$À~
=~g¢!{B|"$~§@G@W? ~da$!$"«~=k
k=w=|$0gAGè§"Eª£}|~#|¦~À:
=~ÀgAÁ$m=|m"a'~"$$£Mk0~==Wg¿
g?~l$¢[Î,$,~Àg=|[==$g?©W,~g=~G $3=|[g
W?$$=~G©$3=|
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W!=|g_=|$«~=d~ÀM$W?U=[$A~±"G
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«.$@$ª%G£3k$kk$=|AkÁ£sæg¶wþG~$*~·$?[g=~GªK$
==~f=|"a$?W~E$«.~=
A?g=|Wg=$AW·$?"$K ~a$?"g=~G
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dG[~$%
52
5. Results
~*g!±£3k$kk$=|©$ö%¢ç²UEªA=|=k@G G
!~*g!gAG°k²UEª$=|
k$
!G"~g=~$~*g!µ$²±Ê$¤GUa$!$«~=kBgAÁ$"²±"E¢
Í}G$~Às£M
W©¹WGg=~$©@g#~$@©AW£WksGk£ $=~Gs$w=|§a=G%
£}|Wk=W*$§g
W?$f$=~G§$=|:=kg*£}|WkÀ
W =W=|:=|?Wg?g
¿
k$3~[Ì~¢²,¢°kè ¬® ¡#¢Í*[@$==k
«AG~«AG=~=~$*@Ágg?~$@*AW£WkU=|
Gk£ $f=|=kg}£}|Wk
WB$Àg
W?$~=«$@kk%3$f=|·=G%B£}|Wk
WW¢
Amplitude [mm]
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
30
50
10
30
50
10
30
Wavelength [m]
50
10
30
50
5%$ìd\9¯YQµ`}e:·¶e£e½ DE ²?¶e[a \Ã[%·¶e\£º,¶e Â8¤À[:·\·}À+¶e½¼À*Åª
BY:·¤K\ü_-Ù
º @¾}À_¶5N _Í_SÂ Îº: %¡ÓU¾\zM¶5½¼ÀH¢K·¶dÇ }eÇº»e½¼ÀeºN¼5þEKº»ª}:6BeK·ü[
¨}Y'3

W«U~À,$,~Àwg=|*@$?=kg=~G±

?@=?$ª,|W?}£d=|$À=kk:AW
£}|W==|wgg?~$@w~ÀB
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Amplitude [mm]
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
30
50
10
30
50
10
30
Wavelength [m]
50
10
30
50
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9
4
2
0
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20
20.1 20.2 20.3 20.4 20.5 20.6 20.7 20.8 20.9
r-sKtBñAòoÄxv ³ ÉoºYw ® C
Time [s]
6
3
0
-3
-6
-9
20
20.1 20.2 20.3 20.4 20.5 20.6 20.7 20.8 20.9
r~5tBñAòoÄxv ³ ÉoºYw © C
Time [s]
[%dì[\®dûµ:Â?»e¶5·¢}}ª¶iB¤£e+ `\Ñ }Çe½MÓUª}:·xº:K_¶5½¼À\Ä·£ }«¶5\·W%½¼ÀdK
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56
5. Results
10
10
5
0
-5
-10
20
5
0
-5
-10
20.1 20.2 20.3 20.4 20.5 20.6 20.7 20.8
r-sKtQPÑsKwuÄxwY ³·´ ó
20
Time [s]
20.6
20.8
21
r~5tQPÑsKwuÄxwY ³a´ ó 9
21.2
8
4
20.4
Time [s]
6
2
0
-2
-4
-6
20.2
20
20.2 20.4 20.6 20.8
21
21.2 21.4 21.6 21.8
r ¸t<PÑsKwuÄxwY ³a´ ó ¦ c
Time [s]
4
0
-4
-8
20
20.5
21
21.5
r ºet"PÑsKwuÄxwY ³·´ ó ¦ ¬
22
Time [s]
5%Iìd_Íd`µ:Â?»eÇ¶e·E¢}Ç¶iB¤£e_ Ñ\C }5½ÜÓUª}:·xº:K¶5½¼À ÅªM· }C¶5\·A%½À[:P\þ
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57
6
Displacement [mm]/[1e-3 rad]
8
4
0
-4
-8
20
20.5
21
21.5
r-sKtQPÑsKwuÄxwY ³·´ ó ¦
22
4
2
0
-2
-4
-6
22.5
20
Time [s]
2
22
r~5t<PMsKwuÄxw¤ ³a´ ó ¦ 9
22.5
23
0
-2
-4
20
20.5
21
21.5
22
22.5
r¹¸t"PÑsKwuÄxwY ³·´ ó ¬ c
23
4
2
0
-2
-4
-6
23.5
Time [s]
20
20.5
21
21.5
22
22.5
23
r¹º5t<PMsKwuÄxw¤ ³a´ ó ¬ ¬
23.5
24
Time [s]
6
6
21.5
6
4
4
2
0
-2
-4
-6
21
Time [s]
6
-6
20.5
20
20.5
21
21.5
22
22.5
23
23.5
rwt"PÑsKwuÄxwY ³·´ ó ¬
Time [s]
24
24.5
4
2
0
-2
-4
-6
20 20.5 21 21.5 22 22.5 23 23.5 24 24.5
r|ztQPÑsKwuÄxwY ³·´ ó ¬ 9
Time [s]
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58
5. Results
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5.4 Effect of the velocity
59
Amplitude [mm]
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
30
50
10
30
50
10
30
Wavelength [m]
50
10
30
50
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?$=~k%±$m°W¶$¶ m£$¤Wkk ~s=|k

W$=k~w
,$ÉgAG$0|G:
~%
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m=|U
?$=~k%#¡#¢ ¸ |k$E#|G
k

=|£ =|=WU$B=|mW$
k£}|W=U0°W¶$¶:
?$=~kK£$~%
W$?g
k
W
Ì~¢²,¢çµ ó ¡#¢ºÌ~¢²,¢çµ ó K¡#ª_£d|W=m=|E£3k$kk$=|¾~² $¹=|Ea$?W~
$"«~=}~3æ:[Eª,?|Á£}£}|g3=Wk"
A!w«AW?~,Uë¼X ó
,@=G~Ëkg=~Gª
.M~
«Ak@=~::«|$=d«A$=
?$~MG!W$E
W!=|g3=|!
G=~G±|$3$3$W
@G%$W=$k¾@G«W
k[ Z ¸ Ìf~¢²,¢çµ ó a¡=|Ea$?W~$"«~=U|$"Wk
~À@=k$
k¦
²§"y$0|W=m¤«AW?~,¦öX ó ~
Wk¢Ì~$$ªfÌ~¢'²,¢çµ ó Á¡
?|Á£}M=|!W$
!£}|k±=|*£Á$kk$=|E~*°kµ,¢ç² $[=|*a$?W~$«~=
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=~'²¤"Eª5~~k$=~§
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G=~GÉ|$$@GK$W=$k¦

«AW?~,~À}
G=~Gªg}k$
_=|«AW?~±~_G$WB=|gB=|wæg¶«AW?~$5=|
a$?W~?|Á£}¤~m=|_$G=$¢
¨dY'}WBB=W£}|g}|g««Ak3~5G$$w~==WGg?~=~k3g=:,kkU£}~=|
60
5. Results
Amplitude [mm]
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
30
50
10
30
50
10
30
Wavelength [m]
50
10
30
50
5%ì[W
dMµ¼ Ç5:·¶e£e½& LE¶I:½z:·ì\½¼W\Ã5%·¶e\£ºW¶eÇ?Â8±ÀdK·\·ÇÀM¶e½ÀÒÅª
BY:·¤K\ü_-Ù
º @¾}À_¶5Í_ÂSÎº:%¡ÓU¾\zM¶5½¼ÀH¢K·¶dÇ }eÇº»e½¼ÀeºN¼5þEKº»ª}:6BeK·ü[
$kW~E$èg¶U*)W¢BÌ~¢A²,¢çµ$²[=|Á£}d=|:==$g?W,~Àg=~G¤~¤=|gdW$=$¢
¸ ?|G§A@G«g=k £d~=| Ì~¢²,¢°kèE$
=~Àf·W
kG =|k|k~$
·$$"«~=kfk==|$"è!"8 $"$"«~=M$Aè"÷=k==~?|$G~À
=|G$$O
&°kµ["ü£}|~À?|~}"$W=g?$wW~g=~G.¡#¢3Í}G$~À£w
Ww=|=W
$kª=|Wg=£}~W5$f?W$k%wd $@
$'$£$'@G|k$3AWk
Y',«Ak@
k¢ ¸ a$@'G=|_=|~#w$|$5$?Á£}"#|£}~Wk¢f{B|3?|$$
~=|"l£M@$==kg=~GÉ

?@=?k~=|"?$$ª5~"«~U=|gw$G==|
=$_
k«A$?$k|k~$=|GÀ:A_Y'«Ak@
k¢B {B|B@$==kÀg=~G"~"g$kg=
Á$k¤
"=|wg««k~-'Aª,Ì~¢Ì¢çµ$Ì~¢Ì¢çæ,¢ ¡
]3~§$?W
?|k= ~M~d=k$À~*=|=$"=|=W$*W!%$§g

GdY'$«.k$=|}
k«A$?$Ak|Á,~$Á¢Ì~¢,²,¢çµ$è:?|Á£}M
GdY'$«.k
$=|
k«A$?$GAk|Á,~$5£}|kw=|a$?W~*$«~=~²,¢ç²d[E¢ ¸ U K¡£

W!=|g£}|k±=|d£3k$kk$=|E$=|*a$?W~~3ö%¢ç² =|*=k==~:Àg
W?$
G=W~Àg=~G ~w#|É~$=|"«AW?~©µ¼X°[
G=~G©
Wk¦~ =|±æg¶*)wW$=
61
4
2
0
-2
-4
100
100.5
101
101.5
102
102.5
101.5
102
102.5
rsKt"PÑsKwÄxwY ³·´ ó s}oºs}òoÄxv ³ ÉÆºYw&ó ® C
Time [s]
6
4
2
0
-2
-4
-6
100
100.5
101
r~5t<PÑsKwuÄxwY ³·´ ó Ás}oº s}òoÄxv ³ ÉoºYwó C
Time [s]
12
8
4
0
-4
-8
-12
100
100.5
101
101.5
102
102.5
103
103.5
104
104.5
105
r ¸t<PÑsKwuÄxwY ³a´ ó ¦ ¬ Ás}Æº s}òoÄxv ³ ÉoºYw&ó C
105.5
106
106.5
Time [s]
[%Eìd7¼eÂ8P}¶eºKKº ÓI\\Ä¶4BY:·¤K\ü 3Í8ÂSÎº¡¶e½À_}K½Ã:·ì\½¼¡\Ã5%·¶e\£º:
K½&}¶dÇ }¶Yº:Ò¶ÑÇ¶e½ªº£:½E ÍÍÑº?-ºW\½zÃ5¶5Ã}ÀdMµª·\½¼ÒÀ[E½\£5½ªº¶5Åªº:¶eÂ8
¶eºÒ\½&d~ì[_Íd
h
62
5. Results
Amplitude [mm]
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
30
50
10
30
50
10
30
Wavelength [m]
50
10
30
50
5%ì[ì[«µªWºÃ¶5½¼À[¶5ÀMÀ[+B±£¶5£5½, LE%²?¶5[d\Ã[%·¶e\£º¶5WÂ«¤À[:·\·}À«¶e½¼À
\
Be:·±:\ü-Ùº @¾}À¶5N _Í_SÂ Îº:, %PÓU¾\z«¶e½À¢:·¶[}&}eKº»ª5½¼ÀYº¡zD
¼VW ¢}:\½a
¾X ¾¾¾0M0\HÂÑþEº»}K6 BY:·ìü[
Ì~¢²,¢çµg¶aA¡
¡#¢MÌ$3=|!Y'M£3k$kk$=|3=|*k|k~$M~$
@G«g#g

W::
,~«É%=~'£[$W
=|mµg¶ £Á$kk$=| a¡#ª=|~w«AW?~ °¾X°

G=~G
Wk"
¤AWl£MWk¦=|°Áö%¢ç²Å$ =|Uµg¶Å£3k$kk$=|ÉA@¿
|k~$M·$M=|*æg¶:*)MW$=$¢?¨}$
*=|g=|}a$?W~w~À=|k
!èg¶w*)W$
k~
²,¢ç²" £}|W=k$3~M£$B²:" ~±=|!æg¶*)3W$
kkª=|~~MGd
A!g

w
W}"$=B$=|B=|~#:.$$~~À'Á$kU~
=B«%£3g?ªG$[·$#W~
$«~=3$²"zG~$kMGG}«$£}~=|"?~G~\$W$%$«.~=3G=W~À¿
=~GW¢,~««~À}=|dY','Gg«±$*=«~}
w£3k$kk$=|"$æg¶ #~G
!
E=|«AW?~ µ¼Xçæm$
E$=W=$k©~§=|[æg¶¸)W$
Ì~¢5²,¢çµ°Ga¡$
a#¡
¡3=|GG|=|£3k$kk$=||W=w~B±~
=G$Wk¢Âs|k¤=|£3k$kk$=|
~"~@=k$
k ==|W[
0æ$µ,¢ç²© .¡$¾æ$²© a¡" «AW?~ºµ¼Xç²©
GÀ=~G
g««Akg?Wª,=|?|$$·=G =|µ¼XçæW$
~À=|g_=|*g?$*Y'W??~Gm|$$$
$©Y'
?
£d~¢[Ì~¢5²,¢çµ$èa#¡w=|£}E«.|$
"«A$=
?$~$M=|Uæ$µ,¢ç²¤ÅW$=
.¡#ª|W=!=|Y'
?
£d~~k$=~U
WkE$B="$À%$«3kg_=|"~~
63
6
8
4
0
-4
-8
20
20.1
20.2
20.3
20.4
20.5
r-sKt<PÑsKwuÄxwY ³a´ ó 9
20.6
4
2
0
-2
-4
-6
20.7
20
20.2 20.4 20.6 20.8
6
4
2
0
-2
-4
20
20.5
21
21.5
r¹¸t"PÑsKwuÄxwY ·³ ´ ó ® c
22
4
2
0
-2
-4
-6
22.5
20
20.5
21.5
22
22.5
23
Time [s]
6
0.1
0.075
4
21
r¹º5t<PMsKwuÄxw¤ a³ ´ ó ®¬
Time [s]
2
0
-2
-4
-6
21.2 21.4 21.6 21.8
Time [s]
6
-6
21
r~et"PÑsKwuÄxwY ³·´ ó ¬ c
Time [s]
0.05
0.025
0
-0.025
-0.05
-0.075
20
20.5
21
21.5
22
rwt"PÑsKwuÄxwY ³·´ ó ®
Time [s]
22.5
23
-0.1
-0.003 -0.002 -0.001
0
0.001 0.002 0.003
r|Ãt<] ´ (s Ãw~ò5{ ³ s}v ³ {}|r¹º5t
[%\ì[^5P5Â««}¶Yº:Kº¡ÓI\\¸¶OBY:·¤K\ü ÍÂSÎº«¶e½¼ÀMa¶e[aM\Ã5%·¶5\£Kº:?h½
}¶dÇÇ¶eº:H¶P Ke:\½a¸¶eÂW»¼·ì\À[
ì[ ì,ÂMÂ - º8¾º:}À[Áµ¼H·ì\½¼HÀ[E½\£e½º¶e\
º:¶5Â«Ñ¶YºÒ\½ d~ ì[_ Íeþ¯ @a}z»¼ Ë . Ð«ºª5ÓI\½a ¶ª» ¶Yº:C»ª5¶5\¼ K5Ò\¡·¶ezK¶5·Â8e£e½
\ }Çe½ÓUª}:·xº:Kz
64
5. Results
$"a'~üg
W?$~
«À$WkKW¢
æ«76æ
«
¸<?@GùJPO F,R&ÙÒ>U<
, " g}£w|Á$:~%$k
=~Gg
k«=@k%
W?~Àw$EG$$:~=?WGg?~=~kWª
£}|g}|g««Ak_~f£M:
=E""~-'==ð ¸ |k$?|G=k$¤Y'$«.£}|W?=|
«|$
[$=|[?~G|%?$~À~¶¢°±£Á$kk$=|0g·
W=|UW·w?$~ ¢UÌf~?
wW:
=|~ gAG£}|g£MU£}~À'Y',«Ak@Wª£m=|GÉY',«Ak@
GW=|~À$
,
~êéAW=k%}a=G=|:@k%
W?~~?=WGg?~EW$
$ªAG§=|:$=|W!|$¤£g=
k£3g=$=| $@!=|g!=|·$?W~ÀU~ÀdmG$W
"W
#~gªA£}|~#|=|G
G~$w$
"W
#~
G=~GW¢
Amplitude [mm]
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
30
50
10
30
50
10
30
Wavelength [m]
50
10
30
50
5%Nì[`¯¤_µª¡ºÃ¶5½¼À[¶5À_ÀdB¤£¶e£e½Æ E Ì »ª¶Yº:ÑÀ5 DW:K½}Ñ Íd\8Ó¶7BY:·:½a[\
¢}KÓ}K½\_· }¡¶e½À`Y¾ ¶5\·-º_Â8±ÀdK·\·}ÀÆ¶e½À`ÅªBeK·¤:\ü*-º@¾ÇÀ*¶e?
Í*ÂSÎº:
%PÓU¾\zÑ¶5½¼ÀH¢K·¶dÇ }eÇº»e½¼Àeº¡Ã ¼ ¢Ç:\½a
¾ ¾¼7¾K_ÂÑþKº»}K6 BeK·ìü[
Î,$,~À¦gm=|
=$g#¾W~g=~G÷
W Ì~¢B²,¢çµGö$¡[£M
W¹"g
?~-'º$
5.5 Effect of phase
~À"g$k3%$~:?|m~$d£}|g£M!=k£ £d~=|"«=d@k%
W?~*~?=WGg?~=~k
Ì~¢K²,¢ç²G¡#¢{}|W=_~="$~éW=k@3~À:=|BW?$~"kK$~$
|g««k
£d~=| ¦£Á$kk$=|s$wµ,¢ç²0Eª_±$¼$«~=$wï¦" ~À±Wkk¾

~~m
$=$ ?k$~
=~=|g¤~E£}~!|g««Ak ~s=|©=k$£$?¢8ÍdG$~
=|@$==kg=~G =
?@==~ÀÁ$k
=|g««Ak~-'0$"Ì~¢Ì¢ ó ¢ Ì=G
Ì~¢BÌ¢ç²,ª=|©@$?=kg=~G AWl£MWk =|©£}|Wk=W=E$ =| ?$~ÀWª}£©
W
$ÀG
B=|:=$:$}·$d=|«=@kK
W#~~?=WGg?~=~k3Y'@W«}a$d
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?k=B$'=|~}~}=|g}£Á£÷
W[=~G~\$W$%}~êéAW=k@AWl£MWk§=|W·
$"?~G|%£}|Wk ª%@G«.g=dÌ~¢,ÌM¢ç² ¬¤¦ $[Ì~¢,Ì¢ç² ¬¬ ¢'»}W=d£M*
W*=|g=|
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«AG~=[$AWGg=~$w@$=?kg=~Gm£}~=|m=|$=|WB?$~ ªW?

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$3m£Á$kk$=|É$3ö%¢ç²E $
a$?W~!$"«~=M$µ,¢ç²"8a=|}=~G$?W:«~\',k~=|BÁ£WWa@$?W
$3Ì~¢Ì¢ç² ¦¦ ¡#ª£$
W?$[E«AW?~§µ¼Xçµ
G=~G£d|W==|£}|Wk
W=~=
G¤=|wWa_?$~·$BGw«AW?~U$f=|·$#W~[$=|k¤~m=|wY'B«AW?~
~!"Á$k
E=|?~G|%!$$=gG$~¢{B|~À}Ak|Á,~$~k*G£}|k=|
a$?W~:$«À~=}~ÀM~@=k$
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W=$kª$=~À@*=|gM=|!«|$
*~êéW?k@}AW£Wk
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W?$$=~G$=|£}|Wk=W!~À|$m£3k$kk$=|¢ ¸
A$=|§W$
k=|$«À~=k}$=|g
W?$$=~G§g?#g=|W="$ ªAkÁ£
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k·?G ö%¢ç²÷
"°W¶÷=|_
G=~G
#|$$kM%~
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W#$$=~G$A=|}£}|Wk
W
~À"g=G¼²©" ~ =|~À[W$

°W¶d¨~I4R=k=A~ÀB?|$$~À!=|«|$=kAW£Wkw=|~êéAW=k%$=~GWª
.=|3$
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M?k=
k~}«|$
?|~aWª
!=|gf=|Gk£º$=~G~À5~
«.|$
3£}~=|=|_?$~À,~==WGg#~w$=|Bg
W?$$=~G$.=|_£}|Wk
W'~'
,g=
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W=|_?$~ ¢{B|~£3$'Y'«Ak@
k"a=Gþ~=«k@=~À
Ì~¢5ÌM¢ç² ¦¦ £}|W=[=|¤°kµ,¢ç² W$
U=|Á£dwg««?5'~"g
k§ËWW=@$?=kg=~G
~ÀE@GK
?$=}
"=|@$?=kg=~GE$ I °=Wka$}=|$=
W}£Á$kk$=|W¢
Âs|kU,$,~wgM=|*@k%
W?~}~==WGg?~=~kg

kK=~GU£3$«$~"
£3k$@¿
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WÌ~¢A²,¢çæG¡dÌf~¢²,¢çµ$ï
65
5. Results
3
3
2
2
66
1
0
-1
-2
-3
25
25.2
25.4
25.6
25.8
26
26.2
0
-1
-2
-3
26.4
rsKt<ó 9 s}Æºs}òoÄxv ³ ÉoºYwtó ¬ C
4
6
Amplitude [m]/[1e-3 rad]
9
0
-2
-4
-6
25
25.2 25.4 25.6 25.8
26
26.2 26.4 26.6 26.8
¹r ¸Çt ó ¦ c Q
s}oºs}òoÄxv ³ ÉÆºYw&ó ® C
Time [s]
25.2
25.4
25.6
25.8
26
26.2
26.4
Time [s]
6
2
25
r~5t"ó 9 Á
s}oº s}òoÄxv ³ ÉÆºYw&ó ®
Time [s]
1
3
0
-3
-6
-9
25
25.5
26
26.5
27
r ºet ó ¦¬ Q
s}Æº }s òoÄxv ³ ÉoºYw&ó ® C
Time [s]
5%$ìd¡a*eÂ8`}¶Yº:KºÓI\ÅQ¶«Be:·±:\ü+ O
_Í¸ÂhÎº ¶e½À+¶_»ªª¶eº:ÄÀe DK:½¼}, Í[\ Ó7¶ BY:·:½a[\Æ¢}:Ó}:½*ÅªM· }W¶e½ÀH\M¤%C¶e\!
· >C¶[} U[%Pºª5Óº«e½8Çe£}
Ói¶ Be:·K½¾5Å Ë% Ð«¶5½¼ÀC K5K\½¾¶5Â?»·ì\Àd±µP·\½¼PÀd ½\£e½ºÒ¶5 Åª º:¶5Â«Ñ¶Yº\½
d& ìd_ Í
=|£}B=|:
k«A$?$Ak|Á,~$}a$}=|=$:#|G~@kd$$«~=kW¢ ¸ ¤=|
W$
$3m·$?W~ÀU$"«~=:$*°" =|G§?|$$"~ÀE="$=|~·!~
«|$
$ª3
©=|g"=|£}|Wk
WaGÁ£d=|¤k$¾~
«.$@kk%$!=|¤£
?$~k¢]3}$§~@=k$=$=|:$«.~=!
ó "Ê?|$$kd=|Ak|Á,~Gkª
k
«AkW~$=|*GÁ£¨$=~Gm~3© ?|$$kª=|!Gk£¨$G|$3?"$.«G?~=~$
$À$ª,g««=5'~"g
k² ¦W°W¶ § ?$ª%=|=G® G|GMG
$=|*«AW?~ªG=|kU~
"g$k±a$
!?|$$Á£}§
I µ ¦%°Wx¶ § ?$¤AWa$=
£}~G~À"$?
m=|
«AG=~=~$$G$¢Â¼|k=|"$«~=:~À~@=k$
k§
©°W¶[ $ ~K
W?k
®¿
~mAk|k~$~w
Wk Ì~¢5²,¢çµ$ï Á¡
¡#¢m{EY'«$~À=|Ak|k~Gl£M¤"$=
$G=kwg=[~WÀkªÌ~¢5²,¢çµ$ï .¡=|£}=|"l£M?$~!
$$W=|W:£}~=|=|
g
W?$~
«$@k"kK$[Ìf~¢%²,¢çæg¶w~'$±~

?g=~G:$A£}|g|g««kf
¿
67
3
6
2
4
5.5 Effect of phase
1
0
-1
-2
-3
2
0
-2
-4
-6
25 25.5 26 26.5 27 27.5 28 28.5 29 29.5 30
rsKtñUòoÄxv ³ ÉÆºYw ¦ C
25 25.5 26 26.5 27 27.5 28 28.5 29 29.5 30
r~5tBñAòoÄxv ³ ÉoºYw © C
Time [s]
16
16
12
12
8
8
Amplitude [mm]
Time [s]
4
0
-4
-8
-12
-16
4
0
-4
-8
-12
25 25.5 26 26.5 27 27.5 28 28.5 29 29.5 30
r¹¸tñUòoÄxv ³ ÉÆºYw ¦ c C
Time [s]
-16
25
26
r 5º t=Añ òoÄxv ³ ÉoºYw
¸ÄÉÆºYwuº
27
28
29
30
¦ c C È yUv ³·´ vx ´=³ Ãs}vÄYvxÆË
Time [s]
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5. Results
0.12
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Height [mm]
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©}²
74
6. Discussion
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©}ª
76
7. Conclusion
Appendix
6
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20
15
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-60
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3
784
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âÞDæ7â=ç7â=æaáaèaÝ7äÜ7ÝßçÞDÝaàaàaàaãaÝaçÍâÞDéaÝßCæaáaàaÝæÞ&â=éaèaæaéaÝaæÊÜ7çÞDæaáaçaéaÝaãaã7äÜ7ÝaçMß9Þ5ßCé7â=èaãaÝaÝ7äÜ7Ý7â
Ü7ÝÞDÝßCáaèaèÍáÞDáaáaÝ7âaâNßCæ7äaå=Ý7âÊâÞDãaáaàaæaàaÝaç7äÜ7ÝaæÊáÞDçaç7â=çaéaÝ7äÜ7ÝaãËãÞDçaæaÝ7â=ãaÝ7äÜ7ÝaãËàÞDàaçßCàßCèaçaç7äÜ7Ýß
âÞDæ7â=ç7â=æaèaçaÝ7äÜ7ÝßçÞDÝaàaáaè7â=ãaÝÍâÞDéaÝaÝaæ7â=ãaãæÞ&â=éaéaæaéaéaàÊÜ7çÞDæaáaæaã7â=ãaè7äÜ7ÝaçMß9Þ5ßCé7â=èaæaÝaÝ7äÜ7Ý7â
Ü7ÝÞDÝßCáaèaéÍáÞDáaáaÝ7â=ãaèaé7äaå=Ý7âÊâÞDãaáaàaà7â=ãaá7äÜ7ÝaæÊáÞDçaç7â=ÝaàaÝ7äÜ7ÝaãËãÞDçaæßCàßCÝ7äÜ7ÝaãËàÞDàaçßCáaçaèßCà7äÜ7Ýß
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Appendix
ê
§
§
F
784
H
<
:;>
F
Amplitude [mm]
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
30
50
10
30
50
10
30
Wavelength [m]
50
10
30
50
ë]ìí9îïZðëòñ9óRôõð¹ö¼÷;ïaïZðøùú5ì÷ûM÷Cüòýñ²ð=ûúðïaø ìDûðìDïaïZðí;îø.ùïaìDú5ìðaþùïZð2ÿR÷9ðøDøð¥ùûÃúDõ8ð
þ "ð ¥ù#
ú M¥
ÿ þ=
ñ òîï¼
ð kõìDúðÃù
û øù9ö Ëö7÷ïaïZð=þ ÷;
û Nþuï¼ðaþ 8ð¼öú5ì ðø 9ñ
ðø÷öìDú ¥ì&%
ÿ,
94
F. Additional figures
Amplitude [mm]
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
30
50
10
30
50
10
30
Wavelength [m]
50
10
30
50
ë]ìí;îïZðËëòñówôõ8ð+ö7÷;ïaïZð=ø.ùú5ì÷ûd÷CüRýñùî9íðÈìDïaïZðí9îøùïaìDú5ìð=þ(ù;ïZðÈÿ¢÷9ðøDøð ù;ûú õð
þ "ð 2ù;ì
ú o
ÿ þ
ñ òîïZ
ð kõ"ìDúðù
û øù9ö Eö7÷;ïaïZðaþ 8÷
û Nþ PïZð=!þ 8ð7ö=ú5ì ð=ø9ñ mñ#"
ðø÷ö=ìDú 2ì&{
o

Í

ö
$
$
95
Amplitude [mm]
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
30
50
10
30
50
10
30
Wavelength [m]
50
10
30
50
ë]ìí9îïZð¢ëòñ&%óUôõ8ðÈö7÷ïaïZðøùú5ì÷û'7ðú!]ð7ðû£ýù;û)(+ñ'ùî9íðËìDïaïZðí;îøù;ïaìDú4ìð=þËù;ïZðËÿR÷+*
ðøDøð Ëù
û ú õð ðø÷ö=ìDú ¥ì&
þ ð Íù#
ú M
ÿ þ=
ñ òîïZ,
ð kõ"ìDúðÃù;
û )=ø.ù9ö Íö7÷;ïaïZðaþ 8÷
û Nþ-
ï¼ðaþ 8ð¼öú5ì ðø 9ñ
96
Amplitude [mm]
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
30
50
10
30
50
10
30
Wavelength [m]
50
10
30
50
ë]ìí;îïZðëòñ .ó¢ôõðRö7÷ïaïZðøù;ú4ì÷;û£÷*üýñ®/õùþð0;ì 1ðïZð=ûö7ð¹÷Cü¸9ñ2]ù ð=øðûí9ú õ37ðú!]ð7ðû
úDõ8ð¤øð4ü7ú¡ù
û Ãïaìíõú ïZùìDøì&þ$ÿ¢÷ 9ðøDøð ¥ù
û Eú õð ðø÷ö=ìDú ¹ì&ì
þ "ð ¹ù;
ú %C¹ÿ8þñ
òîïZð4kõìDúð
ù
û 2øù9ö Ëö¼÷;ïaïZð=!þ 8÷
û Nþ4uï¼ðaþ 8ð¼öú5ì ðø 9ñ Pñ %CÍö $5$
97
Amplitude [mm]
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
30
50
10
30
50
10
30
Wavelength [m]
50
10
30
50
ë]ìí9îïZð2ëòñ#"9óÍôõ8ðÃö7÷;ïaïZð=ø.ùú5ì÷û67ð=ú]ð7ð=ûÊýùû,(£ñ7õùþð8ì 1ðïZðûö7ð¢÷*ü²ñ]ù ð9*
ø.ð=û"í;ú :
õ 7ð!ú ]ð7ðûú õð+øð4ü7ú¥ù
û ïaìíNõ"ú¢ïZù;ìDøì&þ(ÿ¢5÷ ð=øDøð )ù;
û úDõ8ð ðø÷öìDú ì&²
þ "ð ù;ú
%U¢
ÿ 8þ
ñ òîïZ,
ð kõ"ìDúð¹ù;
û )=ø.ù9ö ö7÷ïaï¼ðaþ 8÷
û þ4 ïZð=þ ð7öú4ì ð=;ø 9ñ Pñ %CËö $ï
98
Appendix
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114
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118
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