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On the design of an electromagnetic aeroelastic energy harvester from nonlinear flutter

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Abstract

A new energy harvester by coupling the electromagnetic induction and the pitch vibration of a rigid wing is built up in this paper. It is aimed: (1) to harvest energy from the pitch limit cycle oscillation (LCO) of the wing due to the preloaded free-play nonlinearity; (2) to introduce a theoretical analysis scheme based on the equivalent linearized method into the design of this harvester. With the equivalent linearized method, the domains of the single stable LCO and double stable LCOs are respectively obtained. Combining the analytical and numerical solutions, the single stable LCO along with the stable limit cycle amplitude greater than its corresponding unstable one is recognized as the better mode for harvesting, since the larger limit cycle domain is induced and the more energy are yielded. Based on such chosen mode, analyses of varying parameters are conducted with respect to the plunge stiffness, pitch stiffness, distance of elastic axis from center of gravity, distance of geometric center from elastic axis, load resistance and magnetic flux density. Meanwhile, three indicators are applied to reveal their effects on the harvesting performances: (1) the size of limit cycle domain, (2) the onset velocity of LCO, and (3) the energy output.

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Notes

  1. The equation of motion of the rigid wing/airfoil is not formulated at length here since a vast amount of work has been done around it in the area of aeroelasticity. Interested readers are referred to the textbook Introduction to Structural Dynamics and Aeroelasticity (2nd Edition) by Dewey H. Hodges and G. Alvin Pierce.

  2. Even though the more energy may be harvested at the larger amplitude in terms of the tendency of output voltage shown in Figs. 9 and 11, the stall of the wing may be induced if a larger angle is considered, which will reduce the airloads and is unfavorable for the energy harvesting.

  3. Some disparities are observed between these boundary lines and the initial condition \({\alpha _0}\) used to compute the LCOs, and \(\left| {{\alpha _0}} \right| > 0.3\) rad is often required for the computation of the large amplitude LCOs. These may be attributed to the other zero variables in the initial condition because a LCO can be efficiently solved through specifying the initial condition as the convergent values of the last LCO.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No: 11772273) and the Applied and Basic Research Plans of Sichuan Province, China (Grant No: 2015JY0083). The authors are grateful to the anonymous reviewers whose work greatly improved this paper.

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  1. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, 610031, People’s Republic of China

    Sheng Liu, Peng Li & Yiren Yang

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  1. Sheng Liu
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Correspondence to Peng Li.

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Liu, S., Li, P. & Yang, Y. On the design of an electromagnetic aeroelastic energy harvester from nonlinear flutter. Meccanica 53, 2807–2831 (2018). https://doi.org/10.1007/s11012-018-0875-6

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