Biomechanics of a moth scale at ultrasonic frequencies.

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.