Quest for Mechanical Rogue Waves in One-dimensional Discrete Lattices

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The research objective of this award is to provide the needed knowledge for the formation of rogue waves in mechanical structures. Rogue waves are abnormally large-amplitude waves that appear abruptly and disappear without the trace. Rogue waves in the ocean, often referred to as the ?wall of the water,? have been witnessed by seafarers. However, the existence of such waves that swallow big ships in the ocean has been mythical for a long time. It is only a couple of decades ago that their existence has been verified scientifically. Since then, rogue waves have been a subject of intense research in different media. Nonetheless, the realization of mechanical rogue waves in solids and structures remains elusive to date. The quest for such mechanical rogue waves in engineered lattices constitutes the core of this project. The successful formation of mechanical rogue waves will enable scientists and engineers to focus mechanical energy in an efficient and controllable manner. Thus, the findings from this project can open a new avenue to guiding high-amplitude mechanical wave packets, harvesting ambient mechanical energy, and developing novel sensing/actuation systems. From an engineering standpoint, this new mechanism of mechanical energy control can be applied to aerospace, mechanical, and civil industries, thereby benefiting society. From an educational standpoint, this project will help train young minds, including several underrepresented students, in the field of science and engineering.The manipulation of mechanical energy flow (i.e., mechanical waves) is challenging. Particularly, the controllable localization of mechanical energy demands new technical approaches beyond the utilization of conventional linear elastic wave principles. This project will introduce the concept of rogue wave generation, the focusing mechanism of waves mostly observed in fluidic or optical media, to the mechanical realm. As an analytical guideline, the celebrated nonlinear Schr?dinger equation will be applied to one-dimensional mechanical lattices (i.e., nonlinear spring mass systems like Fermi-Pasta-Ulam-Tsingou lattices). Based on this analysis, computational models of dynamic lattices will be established in a form that facilitate the formation of mechanical rogue waves. Lastly, a prototypical system will be fabricated using 1D discrete lattices. The formation of mechanical rogue waves will be verified by conducting full-field measurements of the prototype?s wave dynamics using action camera-based stereo vision techniques. All components of these analytical, computational, and experimental studies will be integrated into the education and training of participating undergraduate and graduate students.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.