Groh, Rainer

Holderied, Marc W

Mendoza Nava, Hernaldo

Pirrera, Alberto

English

A recently discovered sound production system (Aeroelastic Tymbal) located at the base of the hindwings of ermine moths produces bursts of ultrasonic clicks. The sound is produced when a ridge area on the aeroelastic tymbal buckles. The resultant sound has similar characteristics to that produced by the tiger moth, which in a certain genus is capable of jamming a bat biosonar. The biomechanical function of the aeroelastic tymbal is idealised by a simplified one-dimensional compliant mechanism, and the stability of the structure is evaluated using the modified Riks method. The purpose of this research is to take inspiration from evolved biological structures found in insects, for the development of adaptive and well-behaved non-linear structures

Explore Bristol Research

                          Mendoza Nava, H., Holderied, M. W., Pirrera, A., & Groh, R. (2021). Abioinspired mechanical model of the ultrasonic clicks produced byermine moths. Abstract from 25th International Congress ofTheoretical and Applied Mechanics (ICTAM).Peer reviewed versionLink to publication record in Explore Bristol ResearchPDF-documentUniversity of Bristol - Explore Bristol ResearchGeneral rightsThis document is made available in accordance with publisher policies. Please cite only thepublished version using the reference above. Full terms of use are available:http://www.bristol.ac.uk/red/research-policy/pure/user-guides/ebr-terms/XXV ICTAM, 23-28 August 2020, Milano, ItalyA BIOINSPIRED MECHANICAL MODEL OF THE ULTRASONIC CLICKS PRODUCEDBY ERMINE MOTHSHernaldo Mendoza-Nava1, Alberto Pirrera1, Marc Holderied2, and Rainer Groh ∗11Bristol Composites Institute (ACCIS), University of Bristol, Bristol, UK2School of Biological Sciences, University of Bristol, Bristol, UKSummary A recently discovered sound production system (Aeroelastic Tymbal) located at the base of the hindwings of ermine mothsproduces bursts of ultrasonic clicks. The sound is produced when a ridge area on the aeroelastic tymbal buckles. The resultant soundhas similar characteristics to that produced by the tiger moth, which in a certain genus is capable of jamming a bat biosonar. Thebiomechanical function of the aeroelastic tymbal is idealised by a simplified one-dimensional compliant mechanism, and the stabilityof the structure is evaluated using the modified Riks method. The purpose of this research is to take inspiration from evolved biologicalstructures found in insects, for the development of adaptive and well-behaved non-linear structures.A tymbal organ, which is a well known sound production system found in cicadas [1], and also present in differentmoth species [1, 2], allows the production of sounds for social communication or defence purposes. A moth’s tymbalorgan consists of a cuticular membrane typically located at the tegula, thorax (muscular actuated tymbals) or wings(aeroelastic tymbal), and produces a high-frequency clicking sound when it buckles. Also, the tymbal’s membrane canpresent a striated band on one side, leading to the production of bursts of ultrasonic clicks when buckled. It has previouslybeen observed that ermine moths (Yponomeuta) continuously produce two sets of ultrasonic clicks while flying, and suchsound production occurs during the rotational stages of the stroke cycle [3]. Furthermore, it is suggested that this speciesmimics the sound produced by toxic tiger moths; thus, warning their predators (bats) of potential danger. Experimentalapproaches such as the use of high-speed cameras have provided evidence on how a tymbal organ buckles [4]. However,far too little attention has been paid to the structural mechanics associated with such phenomena. An objective of thisstudy is to investigate the aeroelastic tymbal actuation mechanism among ermine moths. The function is modelled usinga one-dimensional compliant mechanism, analysed using the finite element method. This project provides an importantopportunity to explore the feasibility of bio-inspired adaptive or morphing structures.The aeroelastic tymbal is distinguished as a clear patch (due to the absence of scales) at the base of the hindwing(Figure 1A), located between the cubital (Cu) and postcubital (pCu) veins. A micro-computed tomography (micro-CT)shown in Figure 1B indicates the venation and parts of the aeroelastic tymbal. Individual ridges forming the striatedband alongside the pCu vein are referred to as “microtymbals”, the rest of the translucent patch is called the “window”.Throughout the pCu axis, the membrane is folded through a steep angle, and this region is called the “wall”. A set ofmicromanipulators on an ablated hindwing, and a bat detector (to detect ultrasound signals), allowed the identificationof two conditions for the sound production. Folding and unfolding the crease along the pCu vein axis was found as thetriggering mechanism. Both, the initial and buckled states are shown in Figure 1C, and the latter is characterised by thebirefringence of the wing’s membrane.Figure 1: A. Ermine moth (Y. malinellus), with an enlarged image of the aeroelastic tymbal. B. Dorsal view of a micro-CT of thebase of the hindwing (the yellow dotted line along the pCu indicates a folding region, also known as the claval furrow). C. Initial andbuckled states of the aeroelastic tymbal (birefringance is indicated).∗Corresponding author. E-mail: rainer.groh@bristol.ac.uk.XXV ICTAM, 23-28 August 2020, Milano, ItalyFrom the micro-CT it can be observed that the tymbal is not a flat structure but a doubly curved membrane. Themembrane’s thickness was found to be less at the interface between the microtymbals and the window. Inspired from howthe aeroelastic tymbal works, a simplified approach is undertaken. Taking a chordwise cross-section of the tymbal, thesystem can be represented by a curved compliant mechanism (Figure 2A). The stability response is then evaluated usingthe modified Riks method in the Abaqus commercial software package. Three design parameters (wt/ww: tymbal-to-window width ratio, tt/tint: tymbal-to-interface thickness ratio and the κ: tymbal’s curvature), and the material properties(E: modulus of elasticity and v: Poisson’s ratio) are considered, while the structure is simply actuated by a transverseforce at the flexure hinge. Assuming the boundary condition (BC) at the Cu vein position is clamped and the BC atthe pCu is simply-supported, the tt/tint ratio is the parameter driving the stability of the structure; which can be tunedto obtain a bistable or monostable behaviour. Assuming an even tymbal thickness, and a width ratio bounded to thetymbal-to-window dimensions, the tymbal response is characterised in terms of the thickness ratio. As a result, theForce-Displacement diagram in Figure 2B demonstrates that when a critical thickness value (tcrit) is achieved, the systembehaves as a bistable structure.Figure 2: A. Compliant mechanism model taken from a cross-section of the aeroelastic tymbal. B. Force-displacement diagram of thestability behaviour of the compliant mechanism.To gain insight into the acoustic response, a modal analysis is performed to obtain the fundamental frequency of thestructure. This value can be tuned by modifying the elastic modulus to match the peak frequency obtained in acousticrecordings. The κ parameter determines the depth of the mechanism, controlling the maximum deflection attained fromthe initial to the secondary stable position. The transverse deflection of the structure is averaged and together with theresonant frequency, the sound pressure level can be calculated from a closed-form structural-acoustic model such as thebaffled-piston [5], assuming the window as the sound radiator. However, this is only a representative result as the actualdynamic and acoustic response are influenced by the tymbal membrane’s mass and the combined spanwise and chordwiseconstraints; added to the consideration that the baffled-piston model is a non conservative approach as it assumes aninfinite baffle boundary.CONCLUSIONSThe function of the aeroelastic tymbal was studied experimentally. Taking inspiration from this system, a curvedcompliant mechanism from a chordwise cross-section was designed. The stability, dynamics and acoustics of the one-dimensional structure were approached successfully to the extent of the assumptions. Further studies are undergoingon the design of a 2D shell structure to better address the function of the aeroelastic tymbal. This would improve theunderstading of the structural and acoustic response towards the design of larger scale adaptive structures.Acknowledgements: Financial support by the Science and Technology National Council (CONACYT - Mexico, CVU/StudentshipNo. 530777/472285) is gratefully acknowledged. This research is funded by the Engineering and Physical Sciences Research Councilthrough the EPSRC Centre for Doctoral Training in Advanced Composites for Innovation and Science (grant number EP/L0160208/1)and supported by the Royal Academy of Engineering under the Research Fellowship scheme (grant no. RF/201718/17178) and the UKEngineering and Physical Sciences Research Council (grant no. EP/M013170/1).This work was carried out using the computationalfacilities of the Advanced Computing Research Centre, University of Bristol (http://www.bristol.ac.uk/acrc/).References[1] J. W. S. Pringle. A physiological analysis of cicada song. JEB, 31(4):525560, 1954.[2] W.E. Conner. un chant dappel amoureux: acoustic communication in moths. JEB, 202(13):17111723, 1999.[3] Liam J. OReilly, David J. L. Agassiz, Thomas R. Neil, and Marc W. Holderied. Deaf moths employ acoustic müllerian mimicry against bats usingwingbeat-powered tymbals. Sci. Rep., 9(1):1444, 2019.[4] Jesse R. Barber and William E. Conner. Acoustic mimicry in a predator-prey interaction. PNAS, 104(22):93319334, 2007.[5] Lawrence E. Kinsler, Austin R. Frey, Alan B. Coppens, and James V. Sanders. Fundamentals of acoustics. Wiley, 4th edition, 2000.

A bioinspired mechanical model of the ultrasonic clicks produced by ermine moths

https://research-information.bris.ac.uk/ws/files/302314387/ICTAM2020Abstract.pdf

A bioinspired mechanical model of the ultrasonic clicks produced by ermine moths

Abstract

Similar works

Full text

Available Versions

Explore Bristol Research