Diffraction Effects on Ultrasonic Waves Diffraction Effects on Ultrasonic Waves Radiated by a Transducer Mounted on the Radiated by a Transducer Mounted on the Section of a Guide of Arbitrary Geometry Section of a Guide of Arbitrary Geometry by by Karim Jezzine Karim Jezzine and and Alain Lhémery Alain Lhémery French Atomic Energy Commission CEA - Saclay
by Karim Jezzine and Alain Lhémery French Atomic Energy Commission CEA - Saclay. Diffraction Effects on Ultrasonic Waves Radiated by a Transducer Mounted on the Section of a Guide of Arbitrary Geometry. Context of development Theory brief review - PowerPoint PPT Presentation
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Diffraction Effects on Ultrasonic WavesDiffraction Effects on Ultrasonic Waves
Radiated by a Transducer Mounted on the Radiated by a Transducer Mounted on the
Section of a Guide of Arbitrary GeometrySection of a Guide of Arbitrary Geometry
byby Karim JezzineKarim Jezzine and and Alain LhémeryAlain Lhémery
French Atomic Energy CommissionCEA - Saclay
• Context of developmentContext of development
• TheoryTheory• brief reviewbrief review• adaptation of Semi-Analytic F.E. methodadaptation of Semi-Analytic F.E. method
• Validation in the axisymmetric caseValidation in the axisymmetric case
• Transducer diffraction effectsTransducer diffraction effects• influence influence of aof apertureperture // bandwith bandwith in the in the a axisymmetric casexisymmetric case• 2D case2D case: : rectangular cross sectionrectangular cross section
• Summary – Summary – WWorkork in progress in progress
Context of developmentContext of development• industrial needs for simulation tools dealing with guided waves in CIVA (software platform for NDE simulation developed at CEA)
- prediction of transducer diffraction effects to optimise testing configuration (mode selection etc.)
- simulation of radiation, propagation, scattering by a defect and reception• aims: guides of arbitrary section
computer efficiency => 3D computational methods hopeless• 1st application: unusual configuration of testing where the transducer (emitter/receiver) is mounted on the guide section
z
transducer
waveguide
guide axis
S
guide section
• Context of developmentContext of development
• TheoryTheory• brief reviewbrief review• adaptation of Semi-Analytic F.E. methodadaptation of Semi-Analytic F.E. method
• Validation in the axisymmetric caseValidation in the axisymmetric case
• Transducer diffraction effectsTransducer diffraction effects• influence influence of aof apertureperture // bandwith bandwith in the in the a axisymmetric casexisymmetric case• 2D case2D case: : rectangular cross sectionrectangular cross section
• Summary – Summary – WWorkork in progress in progress
Theory: Theory: brief reviewbrief review
• basic idea: benefit of the symmetry of translation to restrict computations to the guide section modal decomposition
n nnn
n nnn
tzkj
tzkj
n
n
eyxAzyxAzyx
eyxAzyxAzyx
)(
)(
),(~),,(),,(
),(~),,(),,(
nn
nn
σσσ
uuu propagation along z
mixed: either ux, uy,zz , or, xz,yz,uz at z=0
pure: either ux,uy,uz , or xz,yz,zz (e.g.: piezo transducer in direct contact) at z=0
modal decomposition : un , n
imposed end conditions: mixed or pure• find An knowing :
• direct projection of the source terms on the mode basis impossible for pure end conditions
- existing: on the guiding surface source modelled as an external force
Liu & Achenbach, J. Appl. Mech. (1995), Zhuang et al., J. Appl. Mech. (1999),Hayashi et al., J. Acoust. Soc. Am. (2003)
- here: on the section
problem closely related to that of the scattering from the free end of a semi-infinite guide:
SAFE: - Rattanawangcharoen et al., J. Appl. Mech. (1994), - Taweel et al., Int. J. Solids Struct. (2000), - Galan & Abascal, Int. J. Numer. Meth. Engng. (2002)
Le Clézio, PhD thesis Bordeaux 1 University (2001)
=> source modelled as a vertical boundary condition
Theory: Theory: adaptation of SAFE… adaptation of SAFE… (contd.)(contd.)
Theory: Theory: adaptation of SAFE… adaptation of SAFE… (contd.)(contd.)
• source mounted on the guide section at z = 0:
- one selects modes (obtained from System #1) that make sense for z > 0: 3M - stress tensor deduced from eigenvector displacement at the M nodes (xi , yi )
- piston-source modelled as source of normal stress
M
niiyz(n)n
M
niixz(n)n
M
niizz(n)nii(source)zz
yxσAyxσA
yxσAyxσ
3
1
3
1
3
1
),(~0),(~0
),(~)0,,(i = 1,…, M (system #2)
• time-domain solutions obtained by Fourier synthesisin system#1, the various matrices are frequency-independent, not the overall system
• Context of developmentContext of development
• TheoryTheory• brief reviewbrief review• adaptation of Semi-Analytic F.E. methodadaptation of Semi-Analytic F.E. method
• Validation in the axisymmetric caseValidation in the axisymmetric case
• Transducer diffraction effectsTransducer diffraction effects• influence influence of aof apertureperture // bandwith bandwith in the in the a axisymmetric casexisymmetric case• 2D case2D case: : rectangular cross sectionrectangular cross section
• Summary – Summary – WWorkork in progress in progress
Validation in the axisymmetric caseValidation in the axisymmetric case
d
transducer E cylindrical guide transducer R
receiver output
2/
0),()(
d
z drrtrvtO
• Simulation of a transducer in reception
d
• (System #1) + (System #2) + IFFT:
d
transducer cylindrical guide
zfield points
field prediction
Validation in the axisymmetric caseValidation in the axisymmetric case
2/
0),(
)(d
z drrtrv
tO
• (very recent) example from Puckett & Peterson (Ultrasonics 43(3), 2005)
configuration:- d = 25 mm- z = 250 mm- fused quartz- piston-like transd.- Gaussian pulses: 1107 kHz – 6.7 % of relative bandwidth
• TheoryTheory• brief reviewbrief review• adaptation of Semi-Analytic F.E. methodadaptation of Semi-Analytic F.E. method
• Validation in the axisymmetric caseValidation in the axisymmetric case
• Transducer diffraction effectsTransducer diffraction effects• influence influence of aof apertureperture // bandwith bandwith in the in the a axisymmetric casexisymmetric case• 2D case2D case: : rectangular cross sectionrectangular cross section
• Summary – Summary – WWorkork in progress in progress
Summary – Work in progressSummary – Work in progress
• Summary:
- SAFE method extended to case of transducer mounted on guide section:- can deal with arbitrary guide (geometry, anisotropy) with symmetry of translation- very efficient numerically (computation in the sole section, i.e. 2D or even 1D)- validated by comparison with existing results for cylinder (theo. – exp.)
- importance of transducer diffraction effects:- requires a proper simulation tool to be predicted- easily studied using SAFE computations- as strong here as in the case of radiation from the guiding surface
• Work in progress: - implementation in CIVA
- scattering by a crack normal to the guide axis computed by SAFE- experimental validation of our own
• axisymmetry: still a 1D computation in the present case• no more real-valued wavenumbers, imaginary parts standing for the leakage of energy in the cement of propagative modes in the steel core.