Collaborative Research: Experiment, Theory, and Simulation of Aeroelastic Limit Cycle Oscillations for Energy Harvesting Applications

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Given the emphasis on carbon-free energy, power system minimization, and decentralized power generation, the development of vibration-based energy harvesting technologies has become a topic of great interest over the past 20 years. A typical aeroelastic energy harvesting scheme involves immersing a thin, elastic structure in a fluid (water or air) flow. Under certain conditions, the presence of the flow brings about a structural self-excited vibration, known as flutter, resulting in periodic oscillations. It has been recently shown that, via affixed piezo-electric materials, electrical energy can be harvested from these structural oscillations. This sort of energy holds promise as an alternative energy source, but also brings about mathematical modeling and experimental implementation challenges. Slender cantilever plates in an axial flow are particularly prone to the flutter instability, even at low flow speeds. To effectively and efficiently harvest energy from this system, one must understand the qualitative features of the resulting limit cycle oscillation. This is done by formulating appropriate partial differential equation models, analyzing their mathematical properties, simulating dynamics through scientific computation, and comparing these results against experimental data. This project will provide opportunities and support for the training of undergraduate and graduate students. From a technical point of view, the analysis described above requires understanding large cantilever deflections driven by a flow. The models studied must capture the de-stabilizing effects of the flow as coupled to nonlinear cantilever dynamics. Unlike traditional large deflection elasticity (based on the structure's ability to stretch), a cantilever's inextensibility gives rise to the primary nonlinear effects of interest: nonlocal inertia and nonlinear stiffness. This project derives and analyzes PDE models for the post-flutter behavior of cantilevered structures in an axial flow of fluid. Specifically, it: (i) improves cantilever modeling and makes predictions that will lead to better energy harvesting devices; (ii) develops a rigorous theory of PDE solutions for a novel elasticity model; (iii) addresses a gap in the mathematical literature concerning unstable nonlinear cantilevers; (iv) refines spectral and finite element computational methods for nonlinear cantilevers; (v) creates a synergy of modeling, theory, computation, and wind-tunnel experimentation; (vi) provides a clearly formulated, challenging mathematical problem with a direct and realizable connection to engineering applications.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.