Control of Lamb Waves by Phononic Crystal...
Transcript of Control of Lamb Waves by Phononic Crystal...
DanielTorrent,YabinJinandBahramDjafari-RouhaniRamónyCajalFellow
UniversitatJaumeI,CastellóndelaPlana(Spain)
ControlofLambWavesbyPhononicCrystalPlates
1. Introduction2. RefractiveDevicesfortheA0Mode
3. ApplicationtotheControloftheS0Mode
4. FullControlofLambWaves
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î Vibration of Phononic Crystal Plates
Propagation:xaxis
u!≈ux x!
u!≈uz z!
u!≈uy y"!
ω ≈
cph
12kA2
ω ≈ cpks
ω ≈ cSHks
SymmetricmodeS
ShearmodeSH
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Anti-symmetricmodeA(Flexuralmode)
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î Vibration of Phononic Crystal Plates
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î Vibration of Phononic Crystal Plates
Torrent,Pennec,Djafari-Rouhani,PRB(2014)
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EffectiveMediumTheoryforFlexrualWaves(A0Mode)
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î Vibration of Phononic Crystal Plates
DanielTorrent
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• LuneburgandMaxwelllensrequirelessdemandingindexvariations
• Thesetwodevicescanbedoneeasily• Highfillingfractionsarerequirednearthe
centerofthelens
Luneburg: Maxwell:
î Vibration of Phononic Crystal Plates
DanielTorrent
DanielTorrent
î Vibration of Phononic Crystal Plates
LuneburgLensforFlexuralWaves
Torrent,Pennec,Djafari-Rouhani,JAP(2014)
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DanielTorrent
î Vibration of Phononic Crystal Plates
MaxwellLensforFlexuralWaves
Torrent,Pennec,Djafari-Rouhani,JAP(2014)
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DanielTorrent
2
,
12
p S
pA
v k
v hk
ω
ω
=
= ( )*
22* 1
bp
b b
EDvvρρ
=−
nS =
vp1
vp2
,nA2 =
vp1
vp2
h1
h2
h 1= h2nS
nA = nS
0
0.05
0.1
0.15
0.2
0.25
ωa/2π
c t
Holes Triangular Ra = 0.3a
0
0.05
0.1
0.15
0.2
0.25
ωa/2π
c t
Lead Triangular Ra = 0.3a
Γ XJ
î Vibration of Phononic Crystal Plates
CanwealsocontroltheS0mode?
Region1 Region2
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RefractivedevicesforboththeS0andA0modes
Jin,Torrent,Pennec,Pan,Djafari-Rouhani,JAP(2015)19/03/18
î Vibration of Phononic Crystal Plates
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î Vibration of Phononic Crystal Plates
CanwealsocontroltheSH0mode?
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1 2 3 4 5nS
2
4
6
8
10
12
nSH
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î Vibration of Phononic Crystal Plates
A0 ,S0 ,SH0
h0 ,Ra ,Rb
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x /a
y/a
S 0 mod e
−30 0 30
−30
0
30
x /a
SH 0 mod e
−30 0 30
−30
0
30
x /a
A 0 mod e
−30 0 30
−30
0
30
x /a
y/a
S 0 M od e
−22 0 22
−22
0
22
x/a
SH 0 M od e
−22 0 22
−22
0
22
x /a
A 0 M od e
−22 0 22
−22
0
22
S0 Mode
-22 0 22 x/a
-22
0
22
y/a
0 1
SH0 Mode
-22 0 22 x/a
-22
0
22
0 1
A0 Mode
-22 0 22 x/a
-22
0
22
0 1
x /a
y/a
S 0 M od e
−22 0 22
−22
0
22
x/a
SH 0 M od e
−22 0 22
−22
0
22
x /a
A 0 M od e
−22 0 22
−22
0
22
î Vibration of Phononic Crystal Plates
GRINLens LuneburgLens
MaxwellLens LN+LN+MX
Jin,Torrent,Pennec,Pan,Djafari-Rouhani,Sci.Rep(2016)
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î Vibration of Phononic Crystal Plates
1. HomogenizationtheoryforFlexuralWaves,PRB(09-2014)
2. RefractivedevicesfortheA0mode,JAP(12-2014)
3. RefractivedevicesfortheA0andtheS0modes,JAP(06-2015)
4. HomogenizationtheoryforBulkElasticWaves,PRB(11-2015)
5. RefractivedevicesfortheA0,S0andtheSH0modes,Sci.Rep.(04-2016)
6. BeamsplittersfortheA0,S0andtheSH0modes,AIPAdvances(12-2016)
7. Invisiblelensforflexuralwaves,JPhysD.(05-2017)
8. Analysisoftherobustnessoftopologicaledgestates,Submitted(2018)
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î Vibration of Phononic Crystal Plates
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