1. Elastic immersive experimentation: theory and physical implementation
- Author
-
Thomsen, Henrik Rasmus
- Subjects
- immersive boundary conditions, wave experimentation, elastic wave propagation, Laser Doppler vibrometry, piezoelectric actuators, wavefield separation, FD injection, method of multiple point sources, Earth sciences
- Abstract
Mechanical wave propagation offers one of the most reliable ways to understand and characterize natural and synthetic materials which only offer limited accessibility, or which for other reasons can not be probed directly. Thus, an ever increasing understanding of elastic wave propagation phenomena in such real earth materials and media is essential to drive scientific progress. This thesis introduces the concept of elastic immersive wave experimentation (IWE), a fundamentally new laboratory designed to study wave propagation phenomena at significantly lower frequencies than previously possible. By actively controlling the boundary conditions of a physical experiment: (1) unwanted reflections from said boundaries can be cancelled and (2) the wavefield propagating in the physical domain can seamlessly interact with a chosen virtual domain. Thus, ensuing experiments can be conducted at frequencies between 1-50 kHz, orders of magnitude closer to the seismic frequency band, than, e.g., conventional laboratory modelling conducted at ultrasonic frequencies. First, a theoretical derivation of elastic immersive boundary conditions (IBC’s) is provided, with a particular emphasis on the key components required for a physical implementation. It is shown, that applying the incident traction measured at the free-surface of a solid target completely cancels unwanted boundary reflections in the physical domain. The wavefield at the free-surface of the experimental target is recorded using a laser Doppler vibrometer. A closed loop control system then computes the IBC’s needed to fully immerse the target in a virtual wave propagation state. The IBC’s are applied at the surface through a dense population of three-component piezoelectric shear actuators. A thorough study of the dynamic response of the three-component actuators is vital to their usability in the context of elastic IWE. To this end, the orthogonality of the individual components of the stacked three-component actuators was confirmed. Moreover, an analysis of the actuators frequency response showed that they can be tuned in the desired experimental frequency range. A first experimental realization of elastic IWE follows, successfully cancelling both, broadband longitudinal and flexural waves at one end of an aluminum beam while virtually extending the dimensions of the beam. The ability to isolate the wavefield incident at the free-surface is an important cornerstone of elastic IWE. This thesis introduces a numerical injection based wavefield separation scheme which requires only recordings of the three-component particle velocity at the free-surface and, in its simplest implementation, only knowledge of the material properties near the receivers. It is differentiated between open and closed recording and injection surfaces. When applying the method proposed in this thesis along an open injection surface, the full up- and downgoing wavefield can be retrieved. Land seismic surveys are commonly conducted along horizontal recording arrays at the earth’s surface. Hence, the applicability of the method to further advance multicomponent seismic data processing, is demonstrated with synthetic examples. In the context of elastic IWE the incident wavefield must be characterized across the entire 3D surface of the experimental target, i.e. the recording surface takes on the form of a closed 3D boundary. The proposed wavefield separation scheme is shown to be accurate at handling sharp corners during wavefield injection. It is found that injection along a closed surface leads to the recovery of exactly what is required by IWE: the primary incident wavefield, corresponding to the first-order interactions of the wavefield with the free-surface. The applicability of the method is validated by isolating the primary incident wavefield of experimental particle velocity recordings, acquired along five faces of a cubic granite rock volume. This thesis presents the basis for the physical realization of elastic immersive wave experimentation. Several suggestions are made to fully realizing 3D elastic IWE. For instance, modelling the full 3D elastic immersive experiment would lead to a better understanding of the required sampling of the emitting surface. Furthermore, the three-component actuators can be used to apply the IBC’s on one side of a cubic granite rock. Such experiments would also provide insight into the footprint of the actuators on the free-surface boundary of the target. Finally, long-term applications, such as wavefield focusing and metamaterial research are discussed.
- Published
- 2021