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 insects 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 isolated Manduca sexta thoraces under symmetric, asymmetric, and band-limited white noise deformations. We measured a thoracic stiffness of 2980 Nm-1 at 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.