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Abstract Flying insects have a robust flight system that allows them to fly even when their forewings are damaged. The insect must adjust wingbeat kinematics to aerodynamically compensate for the loss of wing area. However, the mechanisms that allow insects with asynchronous flight muscle to adapt to wing damage are not well understood. Here, we investigated the phase and amplitude relationships between thorax deformation and flapping angle in tethered flying bumblebees subject to wing clipping and weighting. We used synchronized laser vibrometry and high-speed videography to measure thorax deformation and flapping angle, respectively. We found that changes in wing inertia did not affect thorax deformation amplitude but did influence wingbeat frequency. Increasing wing inertia increased flapping amplitude and caused a phase lag between thorax deformation and flapping angle, whereas decreasing wing inertia did not affect flapping amplitude and caused the flapping angle to lead thorax deformation. Our findings indicate that bumblebees adapt to wing damage by adjusting their wingbeat frequency rather than altering their wing stroke amplitude. Additionally, our results suggest that bumblebees operate near a wing-hinge-dominated resonant frequency, and that moments generated by steering muscles within the wing hinge influence the phase between thorax deformation and wing stroke nontrivially. These insights can inform the design of resilient, insect-inspired flapping-wing micro air vehicles.
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Analysis of passive flexion in propelling a plunging plate using a torsion spring model
We mimic a flapping wing through a fluid–structure interaction (FSI) framework based upon a generalized lumped-torsional flexibility model. The developed fluid and structural solvers together determine the aerodynamic forces, wing deformation and self-propelled motion. A phenomenological solution to the linear single-spring structural dynamics equation is established to help offer insight and validate the computations under the limit of small deformation. The cruising velocity and power requirements are evaluated by varying the flapping Reynolds number ( $$20\leqslant Re_{f}\leqslant 100$$ ), stiffness (represented by frequency ratio, $$1\lesssim \unicode[STIX]{x1D714}^{\ast }\leqslant 10$$ ) and the ratio of aerodynamic to structural inertia forces (represented by a dimensionless parameter $$\unicode[STIX]{x1D713}$$ ( $$0.1\leqslant \unicode[STIX]{x1D713}\leqslant 3$$ )). For structural inertia dominated flows ( $$\unicode[STIX]{x1D713}\ll 1$$ ), pitching and plunging are shown to always remain in phase ( $$\unicode[STIX]{x1D719}\approx 0$$ ) with the maximum wing deformation occurring at the end of the stroke. When aerodynamics dominates ( $$\unicode[STIX]{x1D713}>1$$ ), a large phase difference is induced ( $$\unicode[STIX]{x1D719}\approx \unicode[STIX]{x03C0}/2$$ ) and the maximum deformation occurs at mid-stroke. Lattice Boltzmann simulations show that there is an optimal $$\unicode[STIX]{x1D714}^{\ast }$$ at which cruising velocity is maximized and the location of optimum shifts away from unit frequency ratio ( $$\unicode[STIX]{x1D714}^{\ast }=1$$ ) as $$\unicode[STIX]{x1D713}$$ increases. Furthermore, aerodynamics administered deformations exhibit better performance than those governed by structural inertia, quantified in terms of distance travelled per unit work input. Closer examination reveals that although maximum thrust transpires at unit frequency ratio, it is not transformed into the highest cruising velocity. Rather, the maximum velocity occurs at the condition when the relative tip displacement $${\approx}\,0.3$$ .
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- Award ID(s):
- 1761618
- PAR ID:
- 10321248
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 857
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2018.736
