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

Pons, Arion D.; Beatus, Tsevi

doi:10.1007/s11071-022-07888-4

Cited by 2 publications

(4 citation statements)

References 116 publications

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“…For some muscular scale factor N, which is as-yet undetermined. Equation ( 5) can be represented as a work loop equation of motion [76,98], allowing solution for elasticity over stroke angle ϕ :…”

Section: Work-loop Analysis and Inverse Problem Solutionsmentioning

confidence: 99%

Solving the thoracic inverse problem in the fruit fly

et al. 2023

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In many insect species, the thoracic exoskeletal structure plays a crucial role in enabling flight. In the dipteran indirect flight mechanism, thoracic cuticle acts as a transmission link between the flight muscles and the wings, and is thought to act as an elastic modulator: improving flight motor efficiency thorough linear or nonlinear resonance. But peering closely into the drivetrain of tiny insects is experimentally difficult, and the nature of this elastic modulation is unclear. Here, we present a new inverse-problem methodology to surmount this difficulty. In a data synthesis process, we integrate literature-reported rigid-wing aerodynamic and musculoskeletal data into a planar oscillator model for the fruit fly Drosophila melanogaster, and use this integrated data to identify several surprising properties of the fly's thorax. We find that fruit flies likely have an energetic need for motor resonance: absolute power savings due to motor elasticity range from 0-30% across literature-reported datasets, averaging 16%. However, in all cases, the intrinsic high effective stiffness of the active asynchronous flight muscles accounts for all elastic energy storage required by the wingbeat. The D. melanogaster flight motor should be considered as a system in which the wings are resonant with the elastic effects of the motor’s asynchronous musculature, and not with the elastic effects of the thoracic exoskeleton. We discover also that D. melanogaster wingbeat kinematics show subtle adaptions that ensure that wingbeat load requirements match muscular forcing. Together, these newly-identified properties suggest a novel conceptual model of the fruit fly's flight motor: a structure that is resonant due to muscular elasticity, and is thereby intensely concerned with ensuring that the primary flight muscles are operating efficiently. Our inverse-problem methodology sheds new light on the complex behaviour of these tiny flight motors, and provides avenues for further studies in a range of other insect species.

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Section: Work-loop Analysis and Inverse Problem Solutionsmentioning

confidence: 99%

Solving the thoracic inverse problem in the fruit fly

et al. 2023

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“…Finally, there is the broad question of model fidelity. The simplest conceivable oscillator model is the parallel-elastic linear oscillator [6,11], royalsocietypublishing.org/journal/rsif J. R. Soc. Interface 20: 20230421 with canonical parameters ω 0 , the structural natural frequency; and ζ, the damping ratio.…”

Section: Modelling Flight Motor Oscillation 21 Modelling Flight Motor...mentioning

confidence: 99%

“…Finally, there is the broad question of model fidelity. The simplest conceivable oscillator model is the parallel-elastic linear oscillator [6,11], leftMx¨+Dx˙+Kx=F, ω02=KM, f=FM, x¨+dx˙+ω02x=f, d=DM, x¨ +2ζω0x˙+ω02x=f, ζ =dω0,with canonical parameters ω 0 , the structural natural frequency; and ζ , the damping ratio. With appropriate definition of force ( F , f ), the kinematic variable x can be taken either as the wingbeat stroke angle ( ϕ ), muscular strain ( ε ), or, a normalized reference (e.g.…”

Section: Modelling Flight Motor Oscillationmentioning

confidence: 99%

“…The landmark experiments of Machin and Pringle [4], on asynchronous muscles attached to a lightly-damped load system, demonstrated characteristics of the self-oscillatory response that would suggest alignment with the system natural and/or resonant frequency [6]. Subsequently, self-oscillation and resonance have become blended terms in the literature [7][8][9], and the dipteran flight motor is widely depicted as resonant [10][11][12]. However, a remarkable feature of the results of Machin and Pringle [4] is now seldom noted: in a general system, there is no particular reason why self-oscillation and resonance should align [13].…”

Section: Introductionmentioning

confidence: 99%

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The self-oscillation paradox in the flight motor ofDrosophila melanogaster

Pons

2023

J. R. Soc. Interface.

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Tiny flying insects, such as Drosophila melanogaster , fly by flapping their wings at frequencies faster than their brains are able to process. To do so, they rely on self-oscillation: dynamic instability, leading to emergent oscillation, arising from muscle stretch-activation. Many questions concerning this vital natural instability remain open. Does flight motor self-oscillation necessarily lead to resonance—a state optimal in efficiency and/or performance? If so, what state? And is self-oscillation even guaranteed in a motor driven by stretch-activated muscle, or are there limiting conditions? In this work, we use data-driven models of wingbeat and muscle behaviour to answer these questions. Developing and leveraging novel analysis techniques, including symbolic computation, we establish a fundamental condition for motor self-oscillation common to a wide range of motor models. Remarkably, D. melanogaster flight apparently defies this condition: a paradox of motor operation. We explore potential resolutions to this paradox, and, within its confines, establish that the D. melanogaster flight motor is probably not resonant with respect to exoskeletal elasticity: instead, the muscular elasticity plays a dominant role. Contrary to common supposition, the stiffness of stretch-activated muscle is an obstacle to, rather than an enabler of, the operation of the D. melanogaster flight motor.

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

Cited by 2 publications

References 116 publications

Solving the thoracic inverse problem in the fruit fly

Solving the thoracic inverse problem in the fruit fly

The self-oscillation paradox in the flight motor ofDrosophila melanogaster

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