Elastic-bound conditions for energetically optimal elasticity and their implications for biomimetic propulsion systems

Pons, Arion D.; Beatus, Tsevi

doi:10.1007/s11071-022-07325-6

Cited by 12 publications

(24 citation statements)

References 89 publications

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“…Recent theoretical advances in nonlinear elasticity have demonstrated that insects with sub-stantial series compliance in their flight systems may exhibit wide, band-type resonance ( 45 , 46 ). The likely source of such series elastic effects is the wing hinge, which is also the primary dis-sipative component of the hawkmoth thorax ( 18 ).…”

Section: Discussionmentioning

confidence: 99%

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

Wold

Lynch

Gravish

et al. 2022

Preprint

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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.

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Section: Discussionmentioning

confidence: 99%

“…Recent theoretical advances in nonlinear elasticity have demonstrated that insects with substantial series compliance in their flight systems may exhibit wide, band-type resonance (45,46).…”

Section: Implications Of a Flat Frequency Response Of The Exoskeletonmentioning

confidence: 99%

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

Wold

Lynch

Gravish

et al. 2022

Preprint

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“…The insight that thoracic elasticity can absorb flight motor negative work and thereby decrease motor muscular power consumption [14,46–48] is connected to a more general phenomenon of linear and nonlinear dynamics: the generalized energy-based conception of resonance sometimes referred to as global resonance [27–30]. In a general system, the core condition of global resonance is the absence of negative work in the system overall power requirement: pfalse(tfalse)≥0, normal∀ t.If this condition is satisfied—e.g.…”

Section: Power Consumption and The Global-resonant Frequencymentioning

confidence: 99%

“…Studying the effect of these behaviours on flight motor resonance is a complex process. First, when the system is nonlinear a range of nonlinear resonant phenomena may exist, each may generalize or be approximated by different properties of linear resonance [30,55]. Second, analytical techniques are often insufficient to characterize nonlinear resonant phenomena, making a general treatment of these phenomena more difficult.…”

Section: Effects Of Increasing Model Fidelity 41 Viscoelasticity and ...mentioning

confidence: 99%

“…In this work, we study these aspects of indirect flight motor resonance in more detail and obtain some surprising results. We illustrate how there may be up to eight distinct and mutually exclusive resonant frequencies in the flight motor system, including classical forms of resonance, and the novel form of global resonance [27][28][29][30], defining energetic optimality. Using published data from a range of insect species, we demonstrate how the flight motor elasticity distribution and damping alter these resonant states.…”

Section: Introductionmentioning

confidence: 99%

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Distinct forms of resonant optimality within insect indirect flight motors

Pons

Beatus

2022

J. R. Soc. Interface.

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Insect flight motors are extraordinary natural structures that operate efficiently at high frequencies. Structural resonance is thought to play a role in ensuring efficient motor operation, but the details of this role are elusive. While the efficiency benefits associated with resonance may be significant, a range of counterintuitive behaviours are observed. In particular, the relationship between insect wingbeat frequencies and thoracic natural frequencies is uncertain, with insects showing wingbeat frequency modulation over both short and long time scales. Here, we offer new explanations for this modulation. We show how, in linear and nonlinear models of an indirect flight motor, resonance is not a unitary state at a single frequency, but a complex cluster of distinct and mutually exclusive states, each representing a different form of resonant optimality. Additionally, by characterizing the relationship between resonance and the state of negative work absorption within the motor, we demonstrate how near-perfect resonant energetic optimality can be maintained over significant wingbeat frequency ranges. Our analysis leads to a new conceptual model of flight motor operation: one in which insects are not energetically restricted to a precise wingbeat frequency, but instead are robust to changes in thoracic and environmental properties—an illustration of the extraordinary robustness of these natural motors.

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Band-type resonance: non-discrete energetically optimal resonant states

Pons

Beatus

2022

Nonlinear Dyn

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Elastic-bound conditions for energetically optimal elasticity and their implications for biomimetic propulsion systems

Cited by 12 publications

References 89 publications

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

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

Distinct forms of resonant optimality within insect indirect flight motors

Band-type resonance: non-discrete energetically optimal resonant states

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