Elastic Immersive Wave Experimentation: Theory And Physical Implementation

We present a proof of concept of elastic immersive wave experimentation. A physical experiment of finite volume is connected with a numerical domain via the novel theory of immersive boundary conditions. We show that by applying the incident traction measured at the free surface of a solid target, we can completely cancel unwanted boundary reflections in the physical domain. The propagating waves can then seamlessly interact with a virtual, numerical domain while we fully account for long-range interactions between the two domains. Utilizing a laser Doppler vibrometer, we can accurately record the three-component particle motion of the wave field at the surface of a thin aluminum beam. The recordings are used to iteratively construct the immersive boundary conditions which are applied to the lateral ends of the beam by three-component piezoelectric actuators. Our one-dimensional experimental results show that we can actively cancel the waves reflected at the free-surface end of the aluminum beam for individually excited, broadband longitudinal and flexural wave modes, as well as for the simultaneous excitation of the two. Finally, we introduce interactions between the physical and a desired numerical domain, thereby virtually extending the physical aluminum beam.