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Acoustic Signature Optimisation for Bioinspired Flapping-Wing Micro Aerial Vehicles

Yi Lun Duh, Krispin C. V. Broers, Sophie F. Armanini

arXiv:2610.37190v1cs.RO

TL;DR

Existing measurements show engineered flapping wings can be louder than the animals they imitate, despite quietness being cited as an advantage. The paper combines venation optimisation and trailing-edge fringes to target reversal clicks and swoosh. In testing, the optimised venation reduced the reversal click by 7.8 dB against the same-day baseline wing.

  • Problem

    Few studies measure FWMAV noise, and engineered flapping wings have been measured as 15–30 dB louder than the animals they imitate.

    Source: §I · p. 1

  • Method

    The paper proposes an integrated wing-design framework combining a venation-layout optimisation model with experimentally optimised trailing-edge fringes.

    Source: §I · p. 2

  • Results

    M1 reduced the click by 7.8 dB at the 90° position against the same-day B0 frame.

    Source: B. Wing Venation Testing · p. 7

  • Takeaways & Limitations

    The framework targets the reversal click and trailing-edge swoosh through two distinct geometric design variables: venation layout and fringe pattern.

    Source: §I · p. 2, B. Bioinspired Trailing-Edge Fringes · p. 3, C. Wing Venation · p. 3

Abstract

from arXiv · show

Flapping-wing micro air vehicles are prized for quiet flight, yet the few existing measurements show engineered wings to be 15-30 dB louder than the animals they imitate. This paper investigates two passive geometric approaches to reduce the acoustic signature of a flapping membrane wing, and applies these to an exemplary wing. A significant sound source in flapping wings is the impulsive click radiated at stroke reversal, when a slack membrane snaps between two curvatures. Our first noise-reduction approach optimises the wing's venation layout, based on an analytical model of the reversal click as a dynamic snap-through of the membrane. The optimised venation pattern was manufactured and resulted in a reduction of up to 8 dB during the reversal snap in experiments. During testing, the venation was found to be sensitive to orientation rather than thickness. Secondly, an additive trailing-edge fringe inspired by hummingbird feathers was shown to further reduce the broadband swoosh by 3-4 dB at no lift cost, matching a cut serration wing without removing lifting area.

I. INTRODUCTION

Existing measurements challenge the assumption that flapping-wing vehicles are quiet, while the literature has rarely measured their acoustic signatures. The paper targets two sources—reversal clicks and trailing-edge swoosh—with geometric design strategies.

I. INTRODUCTION

  • Engineered flapping wings have been measured as 15–30 dB louder than the animals they imitate, and only a handful of studies measure FWMAV noise.A reversal click occurs twice per cycle, yet prior designs had not set out to suppress it.Source: §I · p. 1
  • A slack membrane can snap through at stroke reversal to produce an atonal click, while vortical flow shed near the trailing edge produces broadband swoosh.The click depends on membrane bending stiffness and its distribution; the swoosh is controlled by trailing-edge shape or serration.Source: §I · p. 1
  • Prior work had not used either venation layout or edge geometry to reduce flapping-membrane noise, despite studying these features for other purposes.The paper identifies flexible-wing serrations and acoustic optimisation of venation as unstudied design opportunities.Source: §I · pp. 1–2
  • The proposed framework combines venation-layout optimisation with an experimentally optimised trailing-edge fringe to address both main noise sources.The stated contributions include a venation optimisation model, bioinspired fringes, and an integrated manufacturing approach.Source: §I · p. 2

II. WING DESIGN FRAMEWORK

The framework uses an integrated manufacturing process to produce repeatable wing designs with configurable venation. Its baseline wing combines a passive-pitch mounting with a defined frame, membrane, and planform.

A. Design and Manufacturing

  • A CNC waterjet-cut, single-piece carbon-fibre frame with integrated venation is bonded to a foam-sheet membrane, enabling precise, repeatable designs.This replaces separately cut rods and connecting structures that constrain design and complicate manufacturing.Source: A. Design and Manufacturing · p. 2
  • The baseline wing attaches at the root-chord/leading-edge intersection and passively pitches around the leading-edge axis, with a limiter setting maximum pitch and permitting frictionless reversal.A stiff tip chord supports greater wing area at shorter span and produces passive wing twist during translation.Source: A. Design and Manufacturing · pp. 2–3
  • The baseline has a straight, unvenated trailing edge, a 135 mm span, 45 mm root chord, 15 mm tip chord, and a 0.7 mm EPE membrane.Its carbon-fibre frame is 1 mm thick; the membrane is bonded to one face of the frame.Source: A. Design and Manufacturing · p. 3

B. Bioinspired Trailing-Edge Fringes

The section describes trailing-edge fringes as a geometric approach to broadband swoosh and introduces optimised venation placement as a way to reduce reversal clicks. It relates the two strategies to distinct acoustic mechanisms.

B. Bioinspired Trailing-Edge Fringes

  • Trailing-edge fringes target broadband swoosh from vortical flow near the trailing edge, assessed in the 300–1000 Hz band.The passage attributes that band to Wu et al. and notes that Ji et al. report a reduction over the same band.Source: B. Bioinspired Trailing-Edge Fringes · p. 3
  • An additive triangular fringe preserves the baseline planform and removes no load-bearing membrane, unlike a cut serration.Fringe designs vary by tooth height and pitch; five fringe designs and one serrated version were manufactured for testing.Source: B. Bioinspired Trailing-Edge Fringes · p. 3

C. Wing Venation

  • Venation placement is proposed to minimise reversal noise because the click is an inertia-driven dynamic snap-through governed by the distribution of local bending rigidity.A stiffener spanning the emerging curl can suppress inversion, while misplaced stiffness may shift the instability to a less favourable location.Source: C. Wing Venation · p. 3

III. ACOUSTIC OPTIMISATION MODEL

The optimisation model searches for a quiet venation layout by simulating wing deflection through stroke reversal and scoring the resulting click. Its inputs include wing properties, prescribed kinematics and a stiffening-material mass budget; the output is a frame and venation layout.

III. ACOUSTIC OPTIMISATION MODEL

  • The model takes planform, material properties, prescribed kinematics and a mass budget as inputs, and returns the frame widths and venation layout of the quietest wing found.It iterates from a candidate geometry through a time-dependent plate solution and click-strength objective, then uses a Gaussian process to select the next layout.Source: §III · p. 3
  • The optimisation loop converts each candidate layout into a wing geometry, solves its deflection through stroke reversal, scores click strength and selects the next layout.Fig. 3 overviews this iterative process.Source: §III · p. 3, Figure 3 · p. 4
  • The prescribed pitch is represented by a saturating sinusoid that concentrates nearly all pitch angular acceleration into the flip just after stroke reversal.Users supply the amplitudes, frequency and stop angle; the example wing uses Φ = 95°, f = 10 Hz and Θ = 40°.Source: §III · p. 4

A. Structural model

The structural model follows the membrane wing dynamically through reversal, where inertia can trigger snap-through. It represents the wing as a nonlinear plate with spatially varying stiffness from the venation.

A. Structural model

  • The model represents the wing as a near-membrane whose transverse resistance comes largely from tension acting through curvature, with venation determining the local stiffness distribution.The venation layout changes the plate stiffness over the wing; the bare sheet's bending rigidity is small relative to its tension-mediated response.Source: A. Structural model · pp. 4–5
  • The von Kármán plate model includes geometric stiffness, which can lose positive definiteness as the sheet bends and thereby permit reversal snap-through.The model is considered valid while the deflection-to-thickness ratio remains moderate, w/hm ≲ 5–10.Source: A. Structural model · p. 4
  • The discretised plate is integrated through time with inertia, damping and nonlinear internal forces to capture the reversal event.The implicit generalised-α method and Newton iterations solve the response at each time step.Source: A. Structural model · p. 4
  • A static load-deflection check found no snap, supporting the conclusion that the reversal inversion requires inertia from the moving wing.The check used arc-length continuation to follow the response under a slowly increasing static force.Source: A. Structural model · p. 4
  • The transverse load is the wing's inertial reaction to prescribed rigid-body rotations, with local mass and position relative to the pitch axis entering the load.The model retains entrained-air mass as inertia but omits aerodynamic pressure and the small in-plane centrifugal tension.Source: A. Structural model · pp. 4–5

B. The loading-rate surrogate, design space and optimisation

The optimisation ranks manufacturable venation layouts using a loading-rate surrogate for reversal-click strength. Its lowest-cost design uses one diagonal rib, while the model supports relative comparisons rather than absolute noise predictions.

B. The loading-rate surrogate, design space and optimisation

  • The search minimises a high-passed rate of force change as a computationally cheap surrogate for the click, rather than simulating acoustic propagation.The point-dipole relation applies below about 400 Hz for this wing, covering the 80–300 Hz reversal-click range.Source: B. The loading-rate surrogate, design… · p. 5
  • Each layout uses 47 parameters and is converted to a buildable, connected wing; mass is the only hard constraint, with a 400 mg carbon-fibre budget.The search also evaluated designs up to 490 mg to examine the objective trend, but only designs within budget were eligible for manufacture.Source: B. The loading-rate surrogate, design… · p. 5
  • The objective ranking stayed unchanged when the selected damping coefficient was doubled or halved, but the model cannot establish absolute noise levels for individual designs.The physical effect of damping on the click cannot be quantified because the coefficient was selected rather than measured.Source: B. The loading-rate surrogate, design… · p. 5
  • Across 180 designs, J spans 1.89–10.30, carbon-fibre mass spans 123–490 mg, and peak deflection-to-thickness spans 3.4–7.9.All model evaluations converged.Source: B. The loading-rate surrogate, design… · p. 5
  • The objective rises as the venation centroid moves outboard, and the lowest-cost designs place it within 20 mm of the root.All twenty best designs use ribs angled more than 15° from the chord; the authors suggest diagonal ribs better stiffen a wing that twists during reversal.Source: B. The loading-rate surrogate, design… · pp. 5–6
  • J = 1.89 for M1, whose single rib is at 48.8°; the best bare frame has J = 4.77, while the adverse 43.9° orientation has J = 5.50.M1 uses 52 mg more carbon fibre than the best bare frame.Source: B. The loading-rate surrogate, design… · p. 6

IV. EXPERIMENTAL EVALUATION

The experiments assess whether the model's predicted design ranking holds up acoustically. Selected venation designs and trailing-edge fringes are tested against the same baseline wing at the same operating point.

IV. EXPERIMENTAL EVALUATION

  • The experiments test whether the model's predicted ranking of designs is accurate.The model ranks designs using a surrogate, so the experiments assess their acoustic output.Source: §IV · p. 6
  • Selected venation designs and wings with trailing-edge fringes are manufactured for acoustic testing.Both mitigation strategies are included in the evaluation.Source: §IV · p. 6
  • The acoustic output of each selected design is compared with the same baseline wing at the same operating point.Source: §IV · p. 6

A. Experimental Setup

The tests compared manufactured venation and trailing-edge treatments with a same-day baseline at a fixed 10 Hz flapping frequency. Sound was evaluated from band-limited reversal envelopes, alongside cycle-averaged lift.

A. Experimental Setup

  • All wings were tested at 10 Hz, with motor current adjusted for geometry-dependent inertia to maintain the same frequency.The passive pitch mechanism was used for every test.Source: A. Experimental Setup · p. 6
  • The manufactured sets included two model-selected venation layouts and five additive fringes plus a cut serration, compared with baseline B0.All wings shared the same manufacturing process and the models are shown in Fig. 4.Source: A. Experimental Setup · p. 6, Figure 4 · p. 6
  • Recordings used three microphone positions at 500 mm, with each wing recorded twice and compared against a same-day baseline at matched frequency.The microphone could not measure absolute sound-pressure levels, so the setup supports relative comparisons under matched conditions.Source: A. Experimental Setup · p. 6
  • Reversal sound was evaluated from smoothed Hilbert-transform envelopes after bandpass filtering: 80–1000 Hz for venation and 300–1000 Hz for fringes.The upper cutoff avoids mechanism noise, while the narrower fringe band targets trailing-edge vortex shedding.Source: A. Experimental Setup · p. 6
  • For each wing, the reported reversal amplitude was the median of the largest envelope peaks in 300–400 reversal windows; lift was cycle-averaged from force-sensor recordings.The amplitude reduction compares each wing’s median peak with the same-day B0 baseline; negative ΔL denotes reduced acoustic output.Source: A. Experimental Setup · pp. 6–7

B. Wing Venation Testing

The optimized venation M1 reduced the stroke-reversal snap relative to baseline, while the small change in rib orientation produced a markedly different result. The reduction was localized to the snap band and did not materially change overall A-weighted level or lift.

B. Wing Venation Testing

  • M1 produced 0.112 N cycle-mean lift, compared with 0.102 N for baseline B0.The paper describes this as comparable lift.Source: B. Wing Venation Testing · p. 7
  • The overall A-weighted level remained within 0.8 dB of the frame because the low-frequency snap reduction did not offset noise above 1 kHz.The tested improvement was large within the 80–1000 Hz snap band.Source: B. Wing Venation Testing · p. 7
  • 7.8 dB: M1 reduced the snap band at 90° versus baseline B0, while M1-adverse stayed within a decibel of B0 across all three positions.The mechanism floor above 1 kHz remained within ±0.8 dB; Table I reports the venation optimization results.Source: B. Wing Venation Testing · p. 7, Table I · p. 7
  • A 5° rib-orientation change separated M1 from M1-adverse, which differed by 7.6 dB at 90° and about 3 dB at the other positions.The two layouts were identical except for rib orientation.Source: B. Wing Venation Testing · p. 7

C. Bioinspired Trailing-Edge Fringes Testing

Short additive trailing-edge fringes reduced broadband swoosh levels, with F2 giving the strongest reported fringe result. The additive design approached cut-serration noise reduction while preserving lift at matched tooth geometry.

C. Bioinspired Trailing-Edge Fringes Testing

  • Short fringes reduced noise more than tall ones: F0 reduced it by 3.1 dB and F2 by 4.1 dB, while F1 reduced it by 1.1 dB and F3 showed no improvement.Increasing tooth height added 3.3 dB on average, whereas doubling pitch changed level by 0.3 dB; taller geometries also produced less lift.Source: C. Bioinspired Trailing-Edge Fringes… · p. 7
  • Averaged over three positions, best fringe wing F2 reduced the band level by 4.1 dB, versus 4.5 dB for the cut serration.At 90° the cut serration was 1.5 dB better than F2; at 0° and 180° they were equal.Source: C. Bioinspired Trailing-Edge Fringes… · p. 7
  • At matched tooth geometry, additive F0 reduced the band level by 3.1 dB and generated about 25% more lift than cut serration.F0 produced 0.113 N cycle-mean lift versus 0.092 N for the cut-serration wing.Source: C. Bioinspired Trailing-Edge Fringes… · p. 7

V. CONCLUSION

The conclusion reports two geometric noise-reduction approaches: optimized venation reduces the reversal click, while an additive trailing-edge fringe reduces broadband swoosh without sacrificing wing area. Venation placement is sensitive, and drive noise above 1 kHz limits overall reduction.

V. CONCLUSION

  • 7.8 dB: venation layout M1 reduced the reversal click in the 80–1000 Hz band versus the baseline, while generating more lift.M1 uses a single rib near the root at 48° to the chord and added 50 mg of carbon-fibre material.Source: §V · p. 8
  • 3–4 dB: 5 mm-high additive fringe teeth reduced broadband noise in the 300–1000 Hz band while maintaining wing area and sufficient lift.The improvement was comparable to a subtractive serrated wing, while generating 25% more lift by not cutting into the membrane.Source: §V · p. 8
  • A 5° rib repositioning relative to M1 removed the noise-suppression benefit, showing that correct venation positioning is crucial.Source: §V · p. 8
  • Drive noise from the flapping mechanism dominated above 1 kHz, limiting the overall noise reduction achievable.Source: §V · p. 8
  • Future work will test a quieter flapping mechanism and whether the venation layout and short additive fringe can work together to suppress noise further.Source: §V · p. 8
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