Biomechanics of a moth scale at ultrasonic frequencies

Abstract

The wings of moths and butterflies are densely covered in scales that exhibit intricate shapes and sculptured nanostructures. While certain butterfly scales create nanoscale photonic effects, moth scales show different nanostructures suggesting different functionality. Here we investigate moth-scale vibrodynamics to understand their role in creating acoustic camouflage against bat echolocation, where scales on wings provide ultrasound absorber functionality. For this, individual scales can be considered as building blocks with adapted biomechanical properties at ultrasonic frequencies. The 3D nanostructure of a full Bunaea alcinoe moth forewing scale was characterized using confocal microscopy. Structurally, this scale is double layered and endowed with different perforation rates on the upper and lower laminae, which are interconnected by trabeculae pillars. From these observations a parameterized model of the scale's nanostructure was formed and its effective elastic stiffness matrix extracted. Macroscale numerical modeling of scale vibrodynamics showed close qualitative and quantitative agreement with scanning laser Doppler vibrometry measurement of this scale's oscillations, suggesting that the governing biomechanics have been captured accurately. Importantly, this scale of B. alcinoe exhibits its first three resonances in the typical echolocation frequency range of bats, suggesting it has evolved as a resonant absorber. Damping coefficients of the moth-scale resonator and ultrasonic absorption of a scaled wing were estimated using numerical modeling. The calculated absorption coefficient of 0.50 agrees with the published maximum acoustic effect of wing scaling. Understanding scale vibroacoustic behavior helps create macroscopic structures with the capacity for broadband acoustic camouflage.

Keywords: acoustics; moth scale; porous materials; ultrasonics; vibration.

Fig. 1.

Scale arrangement and structure. (A–C) SEM images of B. alcinoe scales: (A) Partly disrupted tiling of scales; (B) perforated top lamina of a scale; (C) cross-section of a fractured scale revealing the intertrabecular sinus between the two laminae. (D–F) Confocal microscopy of the scale: (D) Individual scale used for further analysis. (Magnification 20×.) White square indicates observation area of (E) top lamina and (F) bottom lamina. (Magnification100×.) (G and H) Isosurface 3D visualizations of a midsection shown in the yellow square in D of the individual scale; (G) the top lamina and (H) bottom lamina with longitudinal ridges and cross-ribs. In H the lower lamina faces upward, oriented with the basal socket of the scale to the back and the apical ridge facing toward the front.

Fig. 2.

Schematic showing (A) how the 3D model of the scale was parameterized and (B) the implemented 3D model containing 2 × 10 unit cells.

Fig. 3.

The moth-scale model: (A) The parameterized single unit; B and C show the different boundary conditions. Note that each boundary includes all of the facets on the same plane. (D–I) Simulation results of stress distribution and deformation (solid line frame shows the original shape) in the single unit under different boundary conditions (SI Appendix, Table S2). The unit cell undergoes a pure (D) ${\epsilon }_{xx}$, (E) ${\epsilon }_{yy}$, (F) ${\epsilon }_{zz}$, (G) ${\gamma }_{xy}$, (H) ${\gamma }_{yz}$, and (I) ${\gamma }_{xz}$ strain.

Fig. 4.

Modeled and measured resonances of the moth scale. (A–C) Scanning LDV results of the first three resonances of the scale. Resonance frequencies: (A) 27.6 kHz; (B) 90.8 kHz, and (C) 152.3 kHz. (D–F) Simulation of mode shape of a single scale with curvature radius of 700 μm. The color profile shows the normalized z component (the out-of-scale plane displacement of the vibrating scale). (D) Rotational vibration around the x axis, pivoting at the clamped edge, at frequency 28.4 kHz; (E) twisting vibration around the y axis at 65.2 kHz; and (F) rotational vibration around the z axis, at 153.1 kHz. Gray outline of scale indicates rest position for comparison. Color bar indicates displacement amplitude.

Fig. 5.

Mechanical responses of a scale. The vibrational spectrum was calculated by averaging amplitude spectra over all scanning points. (Inset) Scale shape and the scanning area.

Fig. 6.

(A) Calculated displacement spectra vs. the measured displacement spectra from 20 to 80 kHz. The calculated spectra were under the damping ratio of 4.5%. (B) Calculated reflection, transmission, and absorption coefficients of the moth-scaled wing. The absorption coefficient of a single wing membrane layer was also plotted for comparison.