JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Volume 133, September 2022, 105351 https://doi.org/10.1016/j.jmbbm.2022.105351Get rights and content ABSTRACT Insect wings can

undergo significant chordwise (camber) as well as spanwise (twist) deformation during flapping flight but the effect of these deformations is not well understood. The shape and size of

butterfly wings leads to particularly large wing deformations, making them an ideal test case for investigation of these effects. High-speed videogrammetry was used to capture the wing

kinematics and deformations. The movements of selected markers on the wings of a living insect was observed. Created characteristics showing the displacement in a three-dimensional

geometric and structural models of the Attacus atlas butterfly wing with various degrees of simplification were developed. Using these models, Fluid-Structure-Interaction (FSI) simulation

studies were performed in the commercial Ansys software environment (Fluent and Mechanical). Computations of the wing beat cycle were carried out, obtaining pressure distributions,

streamlines, vortex regions and cumulative force waveforms. INTRODUCTION THE remarkable aerodynamic efficiency of flapping insect wings has fascinated researchers for many years. It has now

become an anecdote that, according to calculations using classic aircraft aerodynamics models, a bumblebee should not be able to fly, since it is too heavy and its wings are too small. One

of the first significant publications that attempted to explain the key issues related with the aerodynamics of flapping insect wings was a series of six articles by prof. C. Ellington

published in Philosophical Transactions of Royal Society B - Biological Sciences under a collective title: “The aerodynamics of hovering insect flight” (Ellington, 1984). The authors

thoroughly describe the phases of an insect's wing during a flapping flight, relating this motion to the motion characteristics of bat and hummingbird wings. The article (Shigeru et

al., 1993) is an example of a paper devoted to the issue of butterfly wing kinematics and aerodynamics. Its authors describe wing motion using two vectors (for the front and rear wing). The

description did not cover wing deformations or insect in-flight position. It should be noted that the wing angle of attack in butterflies directly implies that their lifting surfaces undergo

deformation, which does not happen in such insects as flies, wasps or bees. In (Fry et al.(2005), Fry, Sayaman and Dickinson present insect flight research results (on the example of a

_Drosophila melanogaster_ fruit fly). The authors distinguish three flapping wing motion phases - beat, break-off and rotation, while noting that the wing motion in each insect is a species

feature. The article (Wilson and Albertani, 2014) presents a series of studies of displacements, as well as forces and torques acting on the wings of the Idea leuconoe butterfly in flapping

flight. As a result of the conducted analyses and calculations, the authors of this paper proffer displacement graphs for body end and the wing ends as a function of time. The analysis

discussed in Piechna (1997) indicates that the lift force in a fly is generated mainly in the course of wing motion downwards, and the thrust during wing motion upwards. Furthermore, in

butterflies, the wings meet in the upper position first at the front, followed by the other parts of the wing, from front to back – generating something called the “pumping effect”. The

wings start spreading from the front with the largest driving force generated at this moment. This enables an increase in thrust by up to 40%. It should be noted that butterflies are

classified as insects with low beat frequency, large area and span of the wings (Hu and Wang, 2010). Based on analyzing the source literature data, the authors of (Hu and Wang, 2010) state

that a butterfly flying forward always flaps, while combining flapping with gliding, in order to improve flight efficiency. They consider gliding as an important element of a butterfly’s

flight, which utilizes vortices generated by flapping. Experimental studies of vortex structures generated by the wings of a Papilio ulysses were also reviewed in (Hu et al., 2009). The

authors of (Chatard et al., 2022; Okamoto et al., 2009) discuss the relationships between specific wing geometry and inflight behavior. In (Senda et al., 2012), Senda et al. calculate

aerodynamic force by applying a model composed of numerous rigid elements, and compare the results with a force measured in the course of the experiment. A two-dimension analysis of flexible

wing flow was presented in (Bluman and Kang, 2017), where the authors attempt to show that wing flexibility leads to increases in its lift force. Fluid Structure Interaction (FSI) analyses

were discussed in (Namhun et al., 2018; Reade and Jankauski, 2020). FSI calculations were conducted for a schematically nerved wings with an arbitrarily adopted geometry. The venation was

aimed at reproducing a different stiffness of the leading edge and trailing edge. The authors of that publication evidenced the direct impact of flapping frequency on aerodynamic forces.

Biej-Bijenko (1976) considers butterflies as belonging to a group of functionally double winged insects, since during flight, the rear pair remains connected with the front pair and they

work together as a single surface. Essentially, the information required for the purposes of this work is that wings consist of venation that acts as the structure while membranes stretch in

between. Such veins are also arranged in an irregular pattern (not along, not across, sometimes almost radially) (Ha et al., 2011). Furthermore, each vein has a slightly different

structure. Individual features are also important. In the case of large wings, it is possible to study a specific wing section, while small wings must be tested as a whole, without zoning.

This results from the need to develop a universal testing machine, as well as accessories for bending specimens several or a dozen or so milimetres long, and force sensors with a very small

range. This is due to measurement possibilities. Currently (Sun and Bharat, 2011), is the only such comprehensive data source and it only applies to one order of insects. In addition, the

values vary greatly, depending on the wing element and measurement method. They were tested with a nanoindenter, which uses a diamond indenter to determine mechanical properties and

specifies characteristics based on nanohardness measurements. The Attacus atlas was selected as the research subject for the purposes of this work. This insect can be naturally found in

South Asia (China, Indonesia, Malaysia, Ceylon) and is the largest representative of the Lepidoptera. Its significant wing area and low flapping frequency constitute optimal test conditions.

It is essential for a given specimen to be bred and that studying it does not require approval from a bioethical committee. The mechanical properties of this butterfly’s wings were studied

in (Landowski et al., 2020). This paper raises the question of the flapping flight specifics of Attacus atlas butterfly. This article is a second part of complex analysis and mainly contains

informations respecting flexible wings of this moth species. First part consists of the basic experiment description and the influence analysis of object shape on the behavior of the flow.

In broad simplification, it can be said that structure of insect wing contains the following components: System of spars, or venation, being structural elements that carry the load and

stiffen the wing. and membrane spread across the venation that acts as air impermeable surface, lifting area. The stiffness of the second one is nearly zero and is negligible. Conclusions

regarding the application of the correct model result from both an experiment consisting in multiple three-point bending tests of sections of butterfly wings and implementation of models

with various simplification degrees for numerical calculations for the needs of FSI analysis in commercial software Ansys Fluent and Ansys Mechanical. The examination of Young modulus on a

real butterfly wing was conducted for two zones: attack zone and trailing zone across the veins, for various specimens in various humidity conditions (Fig. 1) (Fuchiwaki et al., 2013;

Yokoyama et al., 2013). The humidity was set at 80 and 98% in order to reflect the conditions in the insect’s natural habitat. Averaging the results of the measurements it was set that the

Young modulus for the attack zone is 0.32 GPa and for the trailing zone it is 6.54 GPa (see: previous research) (Fuchiwaki et al., 2013; Kunicka-Kowalska, 2020; Landowski et al., 2020;

Yokoyama et al., 2013). The research leading to the determination of the Young's modulus of the Attacus atlas butterfly wing structure has been described in detail in the paper

(Yokoyama et al., 2013). The Poisson's ratio was adopted based on the literature as 0.49 (Chen et al., 2013; Steppan, 2000). The important source of information was the comparison of

the behavior of simplified models and real motion and deformation of a wing that were filmed and analyzed. During numerical calculations models of various simplification degrees were

applied, each subsequent model better reflects the reality (Table 1): * • model 1 assumed the Young modulus for the attack zone on the whole surface of the wing at fixed thickness, * • model

2 assumed the Young modulus for the trailing zone on the whole surface of the wing at fixed thickness, * • model 3 assumed the introduction of two zones with various values of the Young

modulus at fixed thickness, * • model 4 assumed the introduction of three zones with various values of the Young modulus, where one of these zones had an assigned Young modulus interpolated

from the remaining two at fixed thickness, * • model 5 assumed the introduction of a single value of the Young modulus, assuming at the same time linearly changeable thickness: the thickest

wing at the attack edge, the thinnest at the trailing edge. The thickness values were calculated introducing the elasticity constant, that is the thickness and value of the Young modulus

were changed in such a way as to obtain the same elasticity as in reality. In the Young modulus formula with known deflection and force, the value treated as constant was: Ec=F⋅L348⋅sand it

was specified as elasticity constant Ec. With the assumed cross-section (moment of inertia) allowing the creation of a correct mesh, theoretical Young modulus with merely computational

meaning was calculated:Eteoret=EcI * • model 6 was based on model 5; however, its creation consists in maximum decrease of thickness (to 0.01 mm) of the wing in the area where the membrane

occurs by itself and leaving the primary thickness in the area where veins occur. Thus, it can be stated that model 6 simulates a non-uniform location of spars and, what follows, non-uniform

location of zones with elevated Young modulus. This reduces stiffness in certain directions, while leaving it unchanged in others. Obviously, models 1 and 2 are highly simplified. The

simplification is so high, that neglections cause the loss of physical sense of the examined phenomenon. Due to that it was decided that zones mentioned in the assumptions for model 3 will

be designed. In this case, however, it turns out that differences between mechanical properties of the zones are so significant that the model cannot function as a coherent unity. Thus, the

natural conclusion of the conducted approximations was the interpolation of the Young modulus for the third intermediate zone. This was done in model 4. Unfortunately, so called contact

zones were two various conditions met were the places where propagating cracks occurred: due to the stress concentration, mechanical parameters leap and/or insufficient matching of the

calculation algorithm. Butterfly deformable wing simulations surpass the complexity of testing non-deformable wings. This research is an extension of existing knowledge and an introduction

to understanding dependencies in future technologies of this type. SECTION SNIPPETS FSI SIMULATIONS ATTACUS ATLAS WING - MODEL 5 Since model 4 does not reflect the actual state and

introduces material discontinuity, the search for a better solution resulted in proposing model 5. The assumptions of model 5 were realized by adopting the thickness of 0.18 mm in the attack

zone and 0.1 mm in the trailing zone. FSI SIMULATIONS INCLUDING ATTACUS ATLAS WING VENATION – MODEL 6 Due to shown in model 5 inaccuracies related to the stiffness, decision was made to use

model 6. There was no possibility of importing the input geometry from one part of the calculations to another, as it was done in model 5. Consequently, the researchers considered starting

the calculations in the subsequent part once more from a non-deformed wing. It was only possible in the 440th time step. In the previous steps a non-deformed wing moved to the other side of

the plane of symmetry, which CONCLUSIONS The model 6 was characterized by high accuracy and excellent mapping whose detail was so high that it turned out to be too complicated to fully show

its computational usefulness in the applied solver. At this point it should be noted that Ansys software has a wide range of applications and has been successful in conducting calculations

that were very difficult numerically, however, it is not dedicated to model such dynamic phenomena. According to the current state of knowledge there is no such SUMMARY Comparisons and

analyses presented in this paper are a very good starting point for considerations on the technology way of future MAV. From the biological and evolutionary point of view, the wing of an

insect is the best possible solution in given conditions. From this point of view, it is a researcher’s role to examine the best solution and implement it to their needs. At this moment it

would be possible to indicate aspects that will have to be modified for the needs of technology. These FUNDING SOURCES The research was finance by the National Science Centre, within the

project 2014/15/N/ST8/00769, and partially by statutory funds of the Faculty Pawer and Aeronautical Engineering of the Warsaw University of Technology granted for 2020/2021. CREDIT

AUTHORSHIP CONTRIBUTION STATEMENT ZUZANNA KUNICKA-KOWALSKA: Writing – original draft, Visualization, Validation, Resources, Project administration, Methodology, Investigation, Funding

acquisition, Formal analysis, Data curation, Conceptualization. MICHAŁ LANDOWSKI: Methodology, Investigation. KRZYSZTOF SIBILSKI: Writing – review & editing, Supervision, Funding

acquisition, Conceptualization. DECLARATION OF COMPETING INTEREST The authors declare that they have no known competing financial interests or personal relationships that could have appeared

to influence the work reported in this paper. ACKNOWLEDGMENTS Authors would like to express their gratitude to Academic Computer Centre CI TASK for granting access to computational

infrastructure built within project PLATON nr POIG.02.03.00-00-028/08 – campus computations service U3 and MAN-HA nr POIG.02.03.00-00-110/13 - “Realization of critical services of high

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* BRANCH SPIRAL BEAM HARVESTER FOR UNI-DIRECTIONAL ULTRA-LOW FREQUENCY EXCITATIONS 2024, Heliyon Citation Excerpt : Butterflies create lift and thrust by upstroke (Fig. 2 (a)) and

downstroke (Fig. 2 (b)) flapping of their wings [30]. At each stroke, the flapping frequency varies due to many factors [30,31] and ranges between 9 and 12 Hz [32]. The butterfly wings'

size and shape help to create large wing deformations during lift and thrust [31]. Show abstract In recent years, there has been a growing interest in piezoelectric energy harvesting

systems, particularly for their potential to recharge or replace batteries in energy-efficient electronic devices and wireless sensor networks. Nonetheless, the conventional linear

piezoelectric energy harvesters (PEH) face limitations in ultra-low frequency vibrations (1–10 Hz) due to their narrow operating bandwidth and higher resonance frequencies. To address this,

researchers explored compact shaped geometries, with spiral PEH being one such design to lower resonance frequencies by reducing structural stiffness. While trying to achieve this lower

resonance frequency, spiral designs overlooked that they were spreading the stress across the structure. This was a significant drawback because it reduced the structure's ability to

stress the piezoelectric transducer. The issue remains unaddressed, limiting the power generation of spiral beam harvesters. Furthermore, spiral structures also fail to broaden the operating

bandwidth, posing additional constraints on their effectiveness. This study introduces a novel solution – the “branch spiral beam harvester,” combining the benefits of both spiral and

branch beam designs. The integration of the branch beam concept into the spiral structure aimed to broaden the effective frequency range and establish a concentrated stress area for the

placement of the piezoelectric transducer. Finite Element Analysis (FEA) was employed to assess operating bandwidth and stress distribution, while experimental studies evaluated voltage and

power generation. Once the workability was confirmed, a statistical optimisation method was introduced to tailor the harvester for specific frequencies in the ultra-low frequency range.

Results indicated that the branch spiral beam harvester exhibits a wider operating bandwidth with six natural frequencies in the ultra-low frequency range. It harnessed significantly higher

output voltages and power compared to conventional linear PEH. This innovation presents a promising advancement in piezoelectric energy harvesting, offering improved performance without the

need for proof masses or additional accessories. * COMPUTATIONAL FLUID-STRUCTURE INTERACTION IN BIOLOGY AND SOFT ROBOTS: A REVIEW 2024, Physics of Fluids * EXPERIMENTAL STUDIES OF THE

FLAPPING MOTION OF A BUTTERFLY WING MODEL 2024, Journal of Theoretical and Applied Mechanics * A REVIEW ON INSECTS FLIGHT AERODYNAMICS, NOISE SOURCES, AND FLOW CONTROL MECHANISMS 2023,

Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering * HIGH-SPEED VIDEOGRAMMETRY FOR SEISMIC PERFORMANCE OF THE SPHERICAL RETICULATED SHELL

STRUCTURE ON THE SHAKING TABLE 2023, Buildings View full text © 2022 Published by Elsevier Ltd.