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Robust Time-Reversal Focusing of Lamb Waves in a Plate
Time reversal focusing is the process of back propagating wavefields to focus their energy in time and space, which has abundant practical applications. In this project, we will investigate, through experiments and simulations, the robustness of time-reversal focusing of waves in a thin plate.
Time reversal (TR) can be understood as the process of backward propagating elastic or acoustic waves to focus their respective energy onto a specific location in time and space. While initially believed impossible to achieve experimentally, the groundbreaking experiments of Derode et al. (1995), showed that it is possible to successfully retro-focus high-order multiply scattered acoustic waves through a forest of steel rods submerged in a water tank back to their source location. Draeger and Fink (1999) turned their attention to closed chaotic cavities and showed that excellent time-reversal can even be achieved using only a single source and receiver as long as the source or receiver can be placed at the desired focusing point. They explain their results using a simple equation, called the cavity equation. Their closed cavity was composed of a thin 2D plate, supporting Lamb wave propagation, and forms the basis for all subsequent work on time-reversal in plates. Recently, Heaton et al. (2017) designed a visual demonstration of time reversal focusing in a thin plate for educational purposes. By focusing the energy at a specific point on the plate they selectively knock over one Lego mini figure, while leaving others around it standing. More serious applications of the time-reversal technique range from underwater acoustics to biomedical ultrasound imaging and therapy, as well as seismology. Another prominent example is non-destructive testing, where flaws, such as defects and cracks in mechanical parts, can be detected through the focused pulses (Young et al., 2019). In this thesis, we will investigate the robustness of time-reversal focusing using Lamb waves in experiments and numerical simulations. This also includes the educational experimental demonstration using Lego figures. All experiments will be conducted using the equipment in the Center for Immersive Wave Experimentation at ETH. In particular the robotized 3D scanning Laser-Doppler Vibrometer (LDV) system to measure and visualize the Lamb waves propagating in a thin aluminium plate.
Time reversal (TR) can be understood as the process of backward propagating elastic or acoustic waves to focus their respective energy onto a specific location in time and space. While initially believed impossible to achieve experimentally, the groundbreaking experiments of Derode et al. (1995), showed that it is possible to successfully retro-focus high-order multiply scattered acoustic waves through a forest of steel rods submerged in a water tank back to their source location. Draeger and Fink (1999) turned their attention to closed chaotic cavities and showed that excellent time-reversal can even be achieved using only a single source and receiver as long as the source or receiver can be placed at the desired focusing point. They explain their results using a simple equation, called the cavity equation. Their closed cavity was composed of a thin 2D plate, supporting Lamb wave propagation, and forms the basis for all subsequent work on time-reversal in plates. Recently, Heaton et al. (2017) designed a visual demonstration of time reversal focusing in a thin plate for educational purposes. By focusing the energy at a specific point on the plate they selectively knock over one Lego mini figure, while leaving others around it standing. More serious applications of the time-reversal technique range from underwater acoustics to biomedical ultrasound imaging and therapy, as well as seismology. Another prominent example is non-destructive testing, where flaws, such as defects and cracks in mechanical parts, can be detected through the focused pulses (Young et al., 2019). In this thesis, we will investigate the robustness of time-reversal focusing using Lamb waves in experiments and numerical simulations. This also includes the educational experimental demonstration using Lego figures. All experiments will be conducted using the equipment in the Center for Immersive Wave Experimentation at ETH. In particular the robotized 3D scanning Laser-Doppler Vibrometer (LDV) system to measure and visualize the Lamb waves propagating in a thin aluminium plate.
The aim of this thesis is to investigate the influence of, e.g., the position, amplitude, and pre-processing of (the data from) the one or two transducers used in the time-reversal process, to see how this affects the resolution of the focal spot. Furthermore, we will also investigate the validity of the cavity equation of Draeger and Fink (1999) for plates with 90 degree bends. Finally, if time allows, we will investigate the generalizations of the cavity equation as this could yield novel interferometric expressions for closed cavities. This work will be carried out as part of ERC Advanced project MATRIX: Machine for Time-Reversal and Immersive eXperimentation.
The aim of this thesis is to investigate the influence of, e.g., the position, amplitude, and pre-processing of (the data from) the one or two transducers used in the time-reversal process, to see how this affects the resolution of the focal spot. Furthermore, we will also investigate the validity of the cavity equation of Draeger and Fink (1999) for plates with 90 degree bends. Finally, if time allows, we will investigate the generalizations of the cavity equation as this could yield novel interferometric expressions for closed cavities. This work will be carried out as part of ERC Advanced project MATRIX: Machine for Time-Reversal and Immersive eXperimentation.
If you are interested in this opportunity, please get in touch with us:
Theodor Becker (theodor.becker@erdw.ethz.ch;
Dirk-Jan van Manen (dirkjan.vanmanen@erdw.ethz.ch);
Henrik Thomsen (henrik.thomsen@erdw.ethz.ch)
If you are interested in this opportunity, please get in touch with us: Theodor Becker (theodor.becker@erdw.ethz.ch; Dirk-Jan van Manen (dirkjan.vanmanen@erdw.ethz.ch); Henrik Thomsen (henrik.thomsen@erdw.ethz.ch)