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Requirements for further development of surface wave and plate wave non-contact scanner
The general concept of surface wave non-contact scanners is illustrated in Fig.1.24. The scanner uses an air-coupled emitter which radiates ultrasonic wave into the specimen surface. Part of energy of this wave is reradiated into air, and is then received by air-coupled receiver inclined with the same angle. Our experience shows that the performance of the both scanners is considerably influenced by its operating parameters such as transducers dimensions and shape, transducers inclination, the transducer-sample distance, the excitation signal shape and its bandwidth, positions and number of reception points, etc. Therefore, in order to optimize the parameters of scanner it is necessary to clarify:
– Influence of transducer size and shape;
– Influence of transducer inclination with respect to specimen and the sensitivity to this angle adjustment;
– Influence of the distance between transducers and the tested specimen;
– Influence of used frequency bandwidth, on the recorded surface wave signal and its parameters. However, despite the advances made in air-coupled transducer technology, there is at present a lack of suitable modeling tool for the characterization and evaluation of such scanner. In order to clarify the role of above parameters and to find the recommendations for optimal operation, the computational tool enabling to model the entire system is required.
Several researchers have modeled the non-contact Lamb wave testing devices. Castaings and Cawley (1996) and Castaings et al. (1997) modeled Lamb wave non-contact system using Finite Element Method (FEM). Ke et al. (2009) also used FEM and performed a 3D simulation of the system; in order to avoid modeling the surrounding air domain, two elliptic-shaped zones are employed to simulate the excitation produced by emitter and the detection by receiver, but the wave propagation in air was neglected. Similar work was done by Fan et al. (2015) and Delrue et al. (2010). In Fan’s work the influence of the non-contact wedge angle on the Lamb signal radiation was also presented.
The above works prove FEM to be an effective and promising tool for the understanding and modeling of the air-coupled system. However, FEM is time consuming and additionally the referred works pay more attention to the validation of FEM model itself, and less attention is given to the optimization of the system performance (perhaps because of very poor computational efficiency of FEM methods). In addition, they focus mostly on Lamb waves and not surface waves (although the two kinds of models have similarity). The Distributed Point Source Method proposed by Banerjee and Kundu (2007) could be used for the ultrasonic field prediction in plates immerged in fluid, but it is not yet applied to the air-coupled case. Another approach under the form of “LMAB” toolbox, combining the pulse response approach with analytical solution, enabling to model non-contact Lamb waves setup was developed by Prego-Borges (2010).
Despite the above advances, there is at present a lack of suitable simple and rapid modeling tool of the above mentioned scanner and the goal of this thesis is just the development of such a tool but less time consuming and simpler than used already FEM methods and to use this tool to study the influence of operational parameters in order to optimize the testing performance. The computational tool proposed in this research is based on Rayleigh’s integral and on the spatial impulse response concept which enable rapid time domain prediction of the field radiated by planar or quasi-planar emitters of any shape. Previous research concerning the non-contact systems emphasize the influence of the strong attenuation in air, therefore the particular effort was made in order to adapt this integral to causal modelling of the pulsed field in absorbing medium.
The proposed model will include three steps (Fig.1.24):
(1) Computing ultrasonic field radiated from non-contact transducer into a solid sample;
(2) Modeling the surface wave propagation along the sample surface;
(3) Modeling the field re-radiated from solid to receiver through air and received by the finite aperture receiver.
Rayleigh’s integral in frequency domain for lossless medium II.1.1 General case
Among all kinds of possible solutions for acoustic field modelling, the method based on Rayleigh’s integral is largely used for the reasons of simple expression, easy numerical and analytical development, etc. The Rayleigh’s integral physically models the Huygens’ Principle: every point may be considered as the source of an outgoing spherical wavelet, and the field at an arbitrary point can be constructed from the superposition of these wavelets. The solution is firstly proposed by Rayleigh who studied a baffled planar piston under continuous-constant frequency excitation (Rayleigh 1877).
The problem of wave radiation consists in determining the acoustic field radiated from a vibrating surface S, observed at point M x, y, z which is immerged in homogeneous and isotropic fluid. It is illustrated in Fig.2.1: the fluid is particularly limited by a half-space Ve which is surrounded by surface S S , where represents a baffle, S is an arbitrary surface infinite far, S is the surface vibrating. This case has been extensively studied in both frequency and time domain. The mathematical and historical development about the problem can be found in references (Morse and Ingard 1968, Khalid 1996, Schmerr 1998). Here we just give a brief introduction to the solutions.
Acoustic field modeling in lossy medium
In conformity with previous sections the acoustic field radiated from transducer into homogeneous, non-attenuating medium can be determined in frequency domain by Rayleigh’s integral given in Eqs. (2.6) or (2.8) and in time domain by Eqs. (2.20) or (2.21). However, nearly all media, such as air, tissue etc. are lossy and are characterized by attenuation . For most materials, the power law exponent has values from 0 to 2, with the majority in the 1 2 range. For example, for underwater acoustics, absorption by some sediments has 1 . In medical ultrasound, for tissue absorption, varies from 1 to 1.7. In geophysics, rock layers often have 1 (Szabo 1994). In air, 2 has been proved by experiment (Bass et al. 1990).
The attenuation modifies the field radiated by a transducer. The amplitude are usually scaled down for the reason of energy absorption; while pulse does not retain its initial shape because of velocity dispersion which means that each wave component travels at a velocity depending on frequency.
Table of contents :
Résumé général
General introduction
Chapter I Principle and use of non-contact ultrasonic non-destructive methods
I.1 From contact to non-contact NDTs
I.1.1 Traditional “contact” ultrasonic techniques
I.1.2 “Semi-contact” ultrasonic techniques
I.2 Non-contact ultrasonic techniques
I.2.1 Non-contact ultrasonic wave generation and reception
I.2.2 Examples of non-contact approaches
I.3 Air-coupled ultrasonic surface/Lamb wave scanner developed in host laboratory
I.3.1 “High frequency” scanner and its different applications
I.3.2 “Low frequency” scanner
I.3.3 Requirements for further development of surface wave and plate wave non-contact scanner
Chapter II Time domain methods based on the Rayleigh’s integral for the prediction of the field radiated by ultrasonic transducers
II.1 Rayleigh’s integral in frequency domain for lossless medium
II.1.1 General case
II.1.2 Rayleigh’s integral in frequency domain
II.1.3 Rayleigh’s integral in frequency domain in terms of transfer function
II.2 Rayleigh’s integral in time domain for lossless medium
II.2.1 Spatial impulse response (SIR)
II.2.2 Time domain field for an arbitrary excitation
II.3 Acoustic field modeling in lossy medium
II.3.1 Rayleigh’s integral for lossy medium in frequency domain
II.3.2 Rayleigh’s integral for lossy media in time domain
II.4 Numerical computation of acoustic field in time domain
II.4.1 Principles of Discrete Representation computation approach
II.4.2 General case-computation using arbitrary Green’s function
II.5 Conclusions
Appendix II.A Analytical solution for spatial impulse response of uniformly excited baffled piston
Chapter III A Time domain model and experimental validation of the acoustic field radiated and received by air-coupled transducers
III.1 Theory: time domain model of the EPR system
III.1.1 Radiation and reception: case of lossless medium
III.1.2 Radiation and reception: case of lossy medium
III.1.3 Special case of attenuation in air
III.2 Experiments and prediction error
III.2.1 Experimental setup
III.2.2 Predictions
III.3 Conclusions
Appendix III.A Chirp technique and signal measurements
Appendix III.B Recovery of the electric response of ultrasonic system
III.B.1 Case of a lossless medium
III.B.2 Case of a lossy medium
Appendix III.C Influence of the receiver size
Chapter IV Time domain model and experimental validation of noncontact surface wave scanner
IV.1 Time domain model of the ESR system
IV.1.1 Step 1: Acoustic wave propagation from air-coupled emitter to solid sample
IV.1.2 Step 2: Surface wave propagation along sample
IV.1.3 Step 3: Surface wave re-radiation from structure surface to air-coupled receiver
IV.1.4 Total system response observed on receiver output
IV.2 Experimental system
IV.3 Experimental validation and prediction error
IV.3.1 Prediction
IV.3.2 Prediction errors
IV.3.3 Recommendation for computations
IV.3.4 Sensitivity of medium parameters on the computational accuracy
IV.3.5 Influence of scanner setting on recorded signal
IV.3.6 Computational efficiency
IV.4 Conclusions
Appendix IV.A Measurement for attenuation and velocity in plexiglas
IV.A.1 Attenuation
IV.A.2 Velocity of SW in plexiglas
Appendix IV.B Simplified model of ESR system
Bibliography
