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Optimized flapping wing dynamics via DMOC approach

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Abstract

Outstanding aerial capabilities that insects present in nature inspire researchers to undertake a challenge to develop a flapping aerial vehicle with performances unmatched by any manmade object. However, the complex aerodynamic phenomena crucial for the insect flight are not easily understood, let alone modeled and utilized for flight. The researchers managed to develop a quasi-steady aerodynamic model capable of capturing the most important aspects of a fruit fly-like insect flight, while still being efficient enough to allow for the usage in the flapping mechanism optimization loop. This experimentally justified quasi-steady model is used in the paper as a building block for creating a novel optimization algorithm, based on the discrete mechanics and optimal control framework. When compared to the conventional approaches to design optimization, this framework includes the natural description of the energy cost function, while incorporating the physical laws in the form of a discrete Lagrange–d’ Alembert equations inherently in optimization constraints. This leads to the discrete description of the inherently continuous problem, allowing the algorithm to search for the optimal solutions in the whole domain. In other words, in contrast to the conventional approaches involving the assumption on the function family and subsequent optimization on the parameters of that function type, this approach is not constrained by the user input and is capable of yielding any solution that respects the physical laws. As presented by the numerical test cases, optimizing the flapping patterns of a fruit fly-like aerial vehicle in standstill hovering leads to both effective and robust optimization tool.

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Notes

  1. The terms translation and rotation in the names of the first two phenomena are a bit misleading; however, in order to achieve a clear linguistic distinction between these substantially different phenomena, such terms have also been used in this paper. Translational circulation is due to stroke rotation, while rotational circulation is due to pitch rotation.

  2. Although the illustrative terms horseshoe-shaped vortex and doughnut-shaped vortex ring can be found in [1], or vortex ring and dumbbell-shaped vortex structure in [41], we have nevertheless opted for a new term, because we believe that its form is somewhat more practical. A similar approach can be found in [21].

  3. With the aim of minimizing the impact of inertial forces. [33]

  4. There is a misprint in the cited paper. The pitching acceleration is given instead of pitching speed, for comparison see [32] and [33].

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Authors and Affiliations

  1. Department of Aeronautical Engineering, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia

    Zdravko Terze, Viktor Pandža, Marko Kasalo & Dario Zlatar

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Correspondence to Viktor Pandža.

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This work has been fully supported by Croatian Science Foundation under the Project IP-2016-06-6696.

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Terze, Z., Pandža, V., Kasalo, M. et al. Optimized flapping wing dynamics via DMOC approach. Nonlinear Dyn 103, 399–417 (2021). https://doi.org/10.1007/s11071-020-06119-y

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