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					Two methods of mode selection
 using transducers mounted on
    the section of an elastic
           waveguide
 by   Karim Jezzine and Alain Lhémery

      French Atomic Energy Commission
      CEA - Saclay


                                        1
• Context : guided wave (GW) testing
  and mode selection

• Simulation of GW generation by a
  transducer mounted on the section

• Mode selection principle and
  simulation results


                                      2
               GUIDED WAVE TESTING (1/2)

        Resonance between interfaces               Modal propagation

                       L waves
                       S waves



 Advantage: propagation over long distances with limited energy losses
    No extensive transducer scanning required,
    Inspection of zones remote from the source.


 Examples of guided wave inspections
    Pipelines
    Aircraft parts
    Concrete reinforcing tendons
                                                          Control of a pipe
                                                   from « Guided Ultrasonics ltd. »

                                                                                  3
                GUIDED WAVE TESTING (2/2)
                         Characteristics of GW : dispersive and multi-modal
                                                                      1
                                z=500 mm
                                                               Uz
                                                                    0.5



d=20mm                                                                0
                                                           z
                                                                    -0.5


               Emitter          Steel cylinder
               szz=1                                                 -1
                                                                           0   50   100       150    200
                                                                                             time (µs)
                                                                                                           250   300

               srz=0
                                                                                          temps (µs)




                              Importance of understanding and monitoring the
                                       generation of a single mode



   time (µs)      frequency
                    (MHz)



                                                                                                           4
          HOW TO SELECT A MODE? (1/2)
       (i) Which mode       High penetration power
     should be selected?
                            High sensitivity to a given defect geometry or
      Possible criteria :   location
                            Low dispersion in the excitation frequency range
                            enabling a narrow pulse in the time domain.

      (ii) Once chosen, how to generate the mode?

                   Multiple-element                                   Wedge
                   encircling probe


    Immersion                                                    Guiding surface
    transducer

Guide
section
                                                  Interdigital
                                                  transducer

                                                                              5
               HOW TO SELECT A MODE? (2/2)
        Usually: excitation from or through the guiding surface.


   Mode
 selection
principle is
well known:




              Sometimes it can be more convenient to radiate from the section
                 - if the guiding surface is not accessible
                 - if one wants to generate a mode whose energy is
                    concentrated at the center of the section

                                       How to select a single mode
                                          in this configuration?
                                                                            6
• Context : guided wave (GW) testing
  and mode selection

• Simulation of GW generation by a
  transducer mounted on the section

• Mode selection principle and
  simulation results


                                      7
    SIMULATION TOOLS FOR GW
Modes are obtained thanks to the semi-analytical finite
                 element method
 Meshing of only the section by finite elements:
        Elements:      1D (plate/axisym.)   2D (arbitrary section)




     • can deal with guides of arbitrary section
     • easy to account for anisotropy, viscoelasticity,
       multi-layered structures

 Resolution of a quadratic eigensystem (3Mx3M with M
    number of nodes)
             (K 1  jk K 2  k 2 K 3 )d   2 Md  0
                 Wavenumbers            Modal displacement
                                                                     8
               TRANSDUCER MODELLING
      Source mounted on the guide section at z = 0:
          - One selects modes 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
                                   (piezo transducer with viscous fluid coupling)
                                                                        3M
                                            σ zz (source)( xi , yi ,0)   An σ zz(n) ( xi , yi )
                                                                              ~
                                                                        n 1
                               i = 1,…, M            3M                                3M
                                               0   An σ xz(n)( xi , yi )
                                                        ~                         0   An σ yz(n)( xi , yi )
                                                                                           ~
                                                     n 1                               n 1



    Most efficient resolution by using variational principle
                         => Mode amplitudes An
[ It is possible to study the scattering of GW by a normal crack in a similar way.]

      Time-domain solutions obtained by Fourier synthesis

                                                                                                            9
• Context : guided wave (GW) testing
  and mode selection

• Simulation of GW generation by a
  transducer mounted on the section

• Mode selection principle and
  simulation results


                                   10
                              MODE SELECTION
  Aim : to generate a chosen mode whose stress profile is known                          σ xz(m)( x, y )
                                                                                         σ yz(m)( x, y )
                                                                                         σ zz(m) ( x, y )
          SOURCE OF
           NORMAL
           STRESS                                                   z

                               Theoretical observation :
If both the normal and tangential stress of the selected mode could be imposed on
                  the section, only this mode would be generated.
                                         In practice:
  The transducer is modelled as a source of normal stress with zero tangential
          stress imposed (piezo transducer with viscous fluid coupling)

                               Simulation results:
                If one takes σ zz (source)  σ zz(m) , σ xz(source)  σ yz(source)  0
                        generally mode m is not dominant.


                                                                                               11
         MODE SELECTION PRINCIPLE
      (1) Find modes showing frequencies at which the tangential stress
          is zero or negligible with respect to normal stress.
      (2) Use a multiple-element ultrasonic transducer to reproduce the
          normal stress profile of the mode at these frequencies.

 Waveguide geometries investigated :
       • cylindrical (rod, tube) : Pochhammer modes
       • plate : Lamb modes
       • rectangular

 Two frequencies have been identified as favourable to mode selection
       (1) So-called ‘universal frequency’: strictly zero tangential stress
                 Lamé modes in a plate (Lamb 1917)
                 Axisymmetric modes in a cylinder or tube (Hudson 1943)
                 Identified for several modes in a rectangular waveguide

       (2) Frequency close to a maximum of group velocity: negligible tangential stress
                 Symmetric and antisymmetric modes in a plate
                 Axisymmetric modes in a cylinder or tube
                 Identified for several modes in a rectangular waveguide


                                                                                    12
              UNIVERSAL FREQUENCIES IN A CYLINDER

                 Identification of universal frequencies for axisymmetric modes in a steel
                                          cylinder of radius 10 mm



     (km/s)     Phase velocity Vj=/bn                (km/s)   Group velocity Vg=d/dbn
      15                                                6




      10                                               4




       5                                                2


Vj  VT 2


                         1                  2 (MHz)                       1                  2 (MHz)




                                                                                              13
            DISCRETISATION OF THE SOURCE

                        Mode chosen : L(0,5)
                           fu5=1.09 MHz
                                                                                     z
Distribution of normal stress
       szz(r) [L(0,5)]
discretised with 5 elements




                                                                Imposed normal
                                                                  stress (zero
                                                              crossings respected)
                                                                        :

                                          Multiple-elements
                                             transducer
                                                                                         (mm)


                                                                                 14
                        SIMULATION RESULTS
                                                     z

                Excitation:
               Toneburst
            centered on fu5 d=20 mm
           with 10% relative
               bandwidth          Emitter   Cylindrical guide   Receiver




  Imposed
normal stress
   at z=0




                                                                                (µs)

                                                                           15
    FREQUENCY OF MAX GROUP VELOCITY
              Identification of the maxima of group velocity for axisymmetric modes in a
                                     steel cylinder of radius 10 mm


                              Minimisation of tangential stress


         Group velocity Vg=d/dbn                                 Mode L(0,5)

(km/s)
     6



    4



    2




                     1               2   (MHz)                                             (mm)



                                                                                             16
               DISCRETISATION OF THE SOURCE

                           Mode chosen : L(0,5)
                            fMaxVg5=0.77 MHz
                                                                                     z
Distribution of normal stress szz(r) [L(0,5)]
        discretised with 6 elements




                                                  Multiple-element transducer


                                                                                17
                        SIMULATION RESULTS
                                                   z

                Excitation:
               Toneburst
              centered on d=20 mm
            fMaxVg5 with 10%
                 relative       Emitter   Cylindrical guide   Receiver
               bandwidth




  Imposed
normal stress
   at z=0




                                                                         (µs)

                                                                         18
ACCOUNT OF A NORMAL CRACK
            Axisymmetric
            normal crack




                            19
      SUMMARY – PRESENT WORK


•    Summary:
    - Two methods of mode selection using multiple-element transducers
     mounted on the section of an elastic waveguide have been
     proposed.

    - Their performances have been assessed thanks to simulations
     based on the semi-analytical finite element method.


•     Present work:
    - Industrial transfer
    - Manufacturing of the transducer
    - Experimental validation


                                                               20
21
COMPARISON OF BOTH METHODS


   Universal frequency or frequency of Vg Max ?


                       Frequency of Vg Max    Universal frequency

 With uniform normal   Slightly selective     Not selective at all
 stress
 Selectivity degree    <100 % at fVg Max      100% at fu
 with ‘ideal’ normal
 stress
 Discretisation of     No zero crossings to   Zero crossings have
 normal stress         be respected           to be respected




                                                                     22
                                       (km/s)   Phase velocity Vf=/bn
                                        15
   EMAT, Comb probe, interdigital
transducer, rings of transducers for
         pipe inspection:
                                        10
    Constant wavelength imposed


                                         5
   Variable angle beam probe :
  Constant phase velocity imposed


                                                        1                2
                                                                             (MHz)



                                                                         23
                          z = 250mm   z = 500mm


0                   d/2
    Standard Exc.




0                   d/2


    Ideal Exc.




0                   d/2
     5 rings
                          z= 250 mm   z= 500 mm



0                   d/2

    Standard Exc.




0                   d/2

     Ideal Exc




0                   d/2

      6 rings
                          (A) fc=700 kHz              (B) fc=771 kHz              (C) fc=771 kHz


                      0                    +d/2   0                    +d/2   0                    +d/2




(a) Full crack




(b) Partial crack 1




(c) Partial crack 2
E/R

                 p   r


                         z

      z= 0.5 m

				
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