Structural damping renders the insect exoskeleton mechanically insensitive to non-sinusoidal deformations

Abstract

Muscles act through elastic and dissipative elements to mediate movement, but these elements can introduce dissipation and filtering which are important for energetics and control. The high power requirements of flapping flight can be reduced by the insect's exoskeleton, which acts as a structurally damped spring under purely sinusoidal deformation. However, this purely sinusoidal dynamic regime does not encompass the asymmetric wing strokes of many insects or non-periodic deformations induced by external perturbations. As such, it remains unknown whether a structural damping model applies broadly and what implications it has for control. We used a vibration testing system to measure the mechanical properties of isolatedManduca sextathoraces under symmetric, asymmetric, and band-limited white noise deformations. We measured a thoracic stiffness of 2980Nm−1at 25 Hz and physiological peak-to-peak amplitude of 0.92 mm. Power savings and dissipation were indistinguishable between symmetric and asymmetric conditions, demonstrating that no additional energy is required to deform the thorax non-sinusoidally. Under white noise conditions, stiffness and damping were invariant with frequency, which is consistent with a structural damping model and suggests the thorax has no frequency-dependent filtering properties. A simple flat frequency response function fits our measured frequency response. This work demonstrates the potential of structurally damped materials to simplify motor control by eliminating any velocity-dependent filtering that viscoelastic elements usually impose between muscle and appendage.

Moth resonant mechanics are tuned to wingbeat frequency and energetic demands

“…When controlling for phylogenetic relatedness using Phylogenetic Generalized Least Squares (PGLS), we find a significant relationship but with a slope that suggests negligible biological significance (predicts less than a percent decrease in k between fastest and slowest insects measured) (Fig 3c, Table 1). Stiffness measurements were lower than some previous measurements, which we attribute to the fabrication of 3D printed mounts that better match the DLM attachment surfaces, thus resulting in more realistic deformations ( 12, 30 ). The current results are in close agreement with recent independent measurements from Manduca ( 37 ).…”

“…). Stiffness measurements were lower than some previous measurements, which we attribute to the fabrication of 3D printed mounts that better match the DLM attachment surfaces, thus resulting in more realistic deformations(12,30). The current results are in close…”

“…We do not consider contributions of active muscle stiffness which are relatively small in hawkmoths compared to exoskeletal stiffness ( 5, 29 ). Recent work on the thorax of Manduca sexta has demonstrated that stiffness and material damping in the thorax are frequency-independent ( 12, 30 ). As such, we ignore internal damping in resonance calculations, as it does not affect the location of the resonant peak, and we use the stiffness measured at wingbeat frequency as the thorax stiffness for each species.…”

Viscoelastic materials are most energy efficient when loaded and unloaded at equal rates

“…Although the literature has historically focused on tendon stretched at symmetric rates, the growing body of literature suggests that tendons undergo diverse patterns of asymmetric loading rates during natural behaviours (figure 1). These observed differences in loading and unloading rates have motivated studies to explore the response to asymmetric rates in tendon [30] and other biological springs [33] over a relatively narrow range of asymmetry.…”