Relevant bibliographies by topics / Wings – Mathematical models

Academic literature on the topic 'Wings – Mathematical models'

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Published: 4 June 2021
Last updated: 4 February 2022

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Journal articles on the topic "Wings – Mathematical models"

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Alexander, R. McN. "Modelling approaches in biomechanics." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358, no. 1437 (August 6, 2003): 1429–35. http://dx.doi.org/10.1098/rstb.2003.1336.

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Conceptual, physical and mathematical models have all proved useful in biomechanics. Conceptual models, which have been used only occasionally, clarify a point without having to be constructed physically or analysed mathematically. Some physical models are designed to demonstrate a proposed mechanism, for example the folding mechanisms of insect wings. Others have been used to check the conclusions of mathematical modelling. However, others facilitate observations that would be difficult to make on real organisms, for example on the flow of air around the wings of small insects. Mathematical models have been used more often than physical ones. Some of them are predictive, designed for example to calculate the effects of anatomical changes on jumping performance, or the pattern of flow in a 3D assembly of semicircular canals. Others seek an optimum, for example the best possible technique for a high jump. A few have been used in inverse optimization studies, which search for variables that are optimized by observed patterns of behaviour. Mathematical models range from the extreme simplicity of some models of walking and running, to the complexity of models that represent numerous body segments and muscles, or elaborate bone shapes. The simpler the model, the clearer it is which of its features is essential to the calculated effect.
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Kobelev, Vladimir. "Approximate static aeroelastic analysis of composite wings." Multidiscipline Modeling in Materials and Structures 15, no. 2 (February 21, 2019): 365–86. http://dx.doi.org/10.1108/mmms-02-2018-0019.

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PurposeThe purpose of this paper is to consider divergence of composite plate wings as well as slender wings with thin-walled cross-section of small-size airplanes. The main attention is paid to establishing of closed-form mathematical solutions for models of wings with coupling effects. Simplified solutions for calculating the divergence speed of wings with different geometry are established.Design/methodology/approachThe wings are modeled as anisotropic plate elements and thin-walled beams with closed cross-section. Two-dimensional plate-like models are applied to analysis and design problems for wings of large aspect ratio.FindingsAt first, the equations of elastic deformation for anisotropic slender, plate-like wing with the large aspect ratio are studied. The principal consideration is delivered to the coupled torsion-bending effects. The influence of anisotropic tailoring on the critical divergence speed of the wing is examined in closed form. At second, the method is extended to study the behavior of the large aspect ratio, anisotropic wing with box-like wings. The static equations of the wing with box-like profile are derived using the theory of anisotropic thin-walled beams with closed cross-section. The solutions for forward-swept wing with box-like profiles are given in analytical formulas. The formulas for critical divergence speed demonstrate the dependency upon cross-sectional shape characteristics and anisotropic properties of the wing.Research limitations/implicationsThe following simplifications are used: the simplified aerodynamic theory for the wings of large aspect ratio was applied; the static aeroelastic instability is considered (divergence); according to standard component methodology, only the component of wing was modeled, but not the whole aircraft; the simplified theories (plate-lime model for flat section or thin-walled beam of closed-section) were applied; and a single parameter that defines the rotation of a stack of single layers over the face of the wing.Practical implicationsThe simple, closed-form formulas for an estimation of critical static divergence are derived. The formulas are intended for use in designing of sport aircraft, gliders and small unmanned aircraft (drones). No complex analysis of airflow and advanced structural and aerodynamic models is necessary. The expression for chord length over the span of the wing allows for accounting a board class of wing shapes.Social implicationsThe derived theory facilitates the use of composite materials for popular small-size aircraft, and particularly, for drones and gliders.Originality/valueThe closed-form solutions for thin-walled beams in steady gas flow are delivered in closed form. The explicit formulas for slender wings with variable chord and stiffness along the wing span are derived.
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Zafirov, Dimo. "Electric vertical take-off and landing fixed wing unmanned aerial vehicle for long endurance or long range?" Aerospace Research in Bulgaria 31 (2019): 99–107. http://dx.doi.org/10.3897/arb.v31.e08.

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An analysis of requirements to electric vertical take-off and landing unmanned aerial vehicle with fixed wings is carried out in this article. These aircraft have to fulfil requirements of users and to be convenient for operation in any field conditions. Long flight duration and long flight range are important for most missions. Mathematical models for both cases are presented and it has been found that the requirements for the wing load are different. It is recommended to use a type of UAV (Unmanned Aerial Vehicle) that is modular and allows performing flights with different configurations and payload depending on the mission in order to fulfill these requirements.
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Mosunov, V. A., R. V. Ryabykina, V. I. Smyslov, and A. V. Frolov. "Experience of computational research on the flutter of an unmanned aerial vehicle." Journal of «Almaz – Antey» Air and Space Defence Corporation, no. 2 (June 30, 2018): 18–25. http://dx.doi.org/10.38013/2542-0542-2018-2-18-25.

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The paper focuses on the sequence of computational and experimental investigations on the flutter. We set the initial data for the unmanned aerial vehicle and built the mathematical models. Furthermore, we did parametric analysis of symmetric and antisymmetric flutter shapes of the wings and the tail, studied the aerodynamics effect on the body of the vehicle, gave the examples of the calculation data on the base of KS-M and MSC. Nastran software.
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Bayly, P. V., and S. K. Dutcher. "Steady dynein forces induce flutter instability and propagating waves in mathematical models of flagella." Journal of The Royal Society Interface 13, no. 123 (October 2016): 20160523. http://dx.doi.org/10.1098/rsif.2016.0523.

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Cilia and flagella are highly conserved organelles that beat rhythmically with propulsive, oscillatory waveforms. The mechanism that produces these autonomous oscillations remains a mystery. It is widely believed that dynein activity must be dynamically regulated (switched on and off, or modulated) on opposite sides of the axoneme to produce oscillations. A variety of regulation mechanisms have been proposed based on feedback from mechanical deformation to dynein force. In this paper, we show that a much simpler interaction between dynein and the passive components of the axoneme can produce coordinated, propulsive oscillations. Steady, distributed axial forces, acting in opposite directions on coupled beams in viscous fluid, lead to dynamic structural instability and oscillatory, wave-like motion. This ‘flutter’ instability is a dynamic analogue to the well-known static instability, buckling. Flutter also occurs in slender beams subjected to tangential axial loads, in aircraft wings exposed to steady air flow and in flexible pipes conveying fluid. By analysis of the flagellar equations of motion and simulation of structural models of flagella, we demonstrate that dynein does not need to switch direction or inactivate to produce autonomous, propulsive oscillations, but must simply pull steadily above a critical threshold force.
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Eshghi, Shahab, Vahid Nooraeefar, Abolfazl Darvizeh, Stanislav N. Gorb, and Hamed Rajabi. "WingMesh: A Matlab-Based Application for Finite Element Modeling of Insect Wings." Insects 11, no. 8 (August 18, 2020): 546. http://dx.doi.org/10.3390/insects11080546.

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The finite element (FE) method is one of the most widely used numerical techniques for the simulation of the mechanical behavior of engineering and biological objects. Although very efficient, the use of the FE method relies on the development of accurate models of the objects under consideration. The development of detailed FE models of often complex-shaped objects, however, can be a time-consuming and error-prone procedure in practice. Hence, many researchers aim to reach a compromise between the simplicity and accuracy of their developed models. In this study, we adapted Distmesh2D, a popular meshing tool, to develop a powerful application for the modeling of geometrically complex objects, such as insect wings. The use of the burning algorithm (BA) in digital image processing (DIP) enabled our method to automatically detect an arbitrary domain and its subdomains in a given image. This algorithm, in combination with the mesh generator Distmesh2D, was used to develop detailed FE models of both planar and out-of-plane (i.e., three-dimensionally corrugated) domains containing discontinuities and consisting of numerous subdomains. To easily implement the method, we developed an application using the Matlab App Designer. This application, called WingMesh, was particularly designed and applied for rapid numerical modeling of complicated insect wings but is also applicable for modeling purposes in the earth, engineering, mathematical, and physical sciences.
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bin Ibrahim, Mohamad Faizul, Ovinis Mark, and Kamarudin bin Shehabuddeen. "An Underwater Glider for Subsea Intervention: A Technical Feasibility Study." Applied Mechanics and Materials 393 (September 2013): 561–66. http://dx.doi.org/10.4028/www.scientific.net/amm.393.561.

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An underwater glider is a type of autonomous underwater vehicle that moves based on small changes in its buoyancy, maneuvering using it wings as it glides through the water. These gliders, currently used in oceanographic sampling, may potentially be used to deliver payloads for subsea intervention at a lower net transport economy (NTE). Net transport economy, is a measure of the cost of transport in terms of the energy consumed per meter traveled, for each kilogram of loaded mass in air or net buoyancy underwater. The current method of payload delivery is either by using customized support vessel or remotely operated vehicle. This paper presents a technical feasibility study of extending the use of these gliders for subsea intervention, with emphasis on payload delivery. Important aspects of an underwater glider such as its volume (size), speed, wing area, wing span, operational depth and net transport economy were considered. The analysis was based on mathematical models governing existing gliders such as legacy gliders and the XRAY Liberdade. The results obtained were validated by extrapolating the present state of the art in underwater gliders to the proposed future use of these gliders, which is for payload delivery. In conclusion, the use of underwater gliders for subsea intervention is feasible based on factors considered in this study.
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Jaworski, Justin W., and N. Peake. "Aeroacoustics of Silent Owl Flight." Annual Review of Fluid Mechanics 52, no. 1 (January 5, 2020): 395–420. http://dx.doi.org/10.1146/annurev-fluid-010518-040436.

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The ability of some species of owl to fly in effective silence is unique among birds and provides a distinct hunting advantage, but it remains a mystery as to exactly what aspects of the owl and its flight are responsible for this dramatic noise reduction. Crucially, this mystery extends to how the flow physics may be leveraged to generate noise-reduction strategies for wider technological application. We review current knowledge of aerodynamic noise from owls, ranging from live owl noise measurements to mathematical modeling and experiments focused on how owls may disrupt the standard routes of noise generation. Specialized adaptations and foraging strategies are not uniform across all owl species: Some species may not have need for silent flight, or their evolutionary adaptations may not be effective for useful noise reduction for certain species. This hypothesis is examined using mathematical models and borne out where possible by noise measurements and morphological observations of owl feathers and wings.
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Dececchi, T. Alexander, Hans C. E. Larsson, and Michael B. Habib. "The wings before the bird: an evaluation of flapping-based locomotory hypotheses in bird antecedents." PeerJ 4 (July 7, 2016): e2159. http://dx.doi.org/10.7717/peerj.2159.

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Background:Powered flight is implicated as a major driver for the success of birds. Here we examine the effectiveness of three hypothesized pathways for the evolution of the flight stroke, the forelimb motion that powers aerial locomotion, in a terrestrial setting across a range of stem and basal avians: flap running, Wing Assisted Incline Running (WAIR), and wing-assisted leaping.Methods:Using biomechanical mathematical models based on known aerodynamic principals and in vivo experiments and ground truthed using extant avians we seek to test if an incipient flight stroke may have contributed sufficient force to permit flap running, WAIR, or leaping takeoff along the phylogenetic lineage from Coelurosauria to birds.Results:None of these behaviours were found to meet the biomechanical threshold requirements before Paraves. Neither was there a continuous trend of refinement for any of these biomechanical performances across phylogeny nor a signal of universal applicability near the origin of birds. None of these flap-based locomotory models appear to have been a major influence on pre-flight character acquisition such as pennaceous feathers, suggesting non-locomotory behaviours, and less stringent locomotory behaviours such as balancing and braking, played a role in the evolution of the maniraptoran wing and nascent flight stroke. We find no support for widespread prevalence of WAIR in non-avian theropods, but can’t reject its presence in large winged, small-bodied taxa likeMicroraptorandArchaeopteryx.Discussion:Using our first principles approach we find that “near flight” locomotor behaviors are most sensitive to wing area, and that non-locomotory related selection regimes likely expanded wing area well before WAIR and other such behaviors were possible in derived avians. These results suggest that investigations of the drivers for wing expansion and feather elongation in theropods need not be intrinsically linked to locomotory adaptations, and this separation is critical for our understanding of the origin of powered flight and avian evolution.
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Aideo, Swati N., and Dambarudhar Mohanta. "Unusually diverse surface-wettability features found in the wings of butterflies across Lepidoptera order and evaluation of generic and vertical gibbosity-based models." Physica Scripta 96, no. 8 (May 14, 2021): 085004. http://dx.doi.org/10.1088/1402-4896/abe82e.

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Dissertations / Theses on the topic "Wings – Mathematical models"

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Kim, Goo. "A vorticity-velocity approach for three-dimensional unsteady viscous flow over wings." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/12123.

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Zsoldos, Jeffrey S. "An experimental investigation of interacting wing-tip vortex pairs." Thesis, This resource online, 1992. http://scholar.lib.vt.edu/theses/available/etd-11242009-020215/.

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Berg, Allison M. "The feasibility of sodar wind profile measurements from an oceanographic buoy." Thesis, (37 MB), 2006. http://handle.dtic.mil/100.2/ADA471871.

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Thesis (M.S.)--Massachusetts Institute of Technology at Woods Hole Oceanographic Institution, 2006.
"September 2006." Description based on title screen as viewed on June 8, 2010. DTIC Descriptor(s): Doppler Radar, Wind Velocity, Sound Ranging, Doppler Sonar, Buoys, Measurement, Motion, Oceanographic Equipment, Theses DTIC Identifier(s): Doppler Sodar, Sodar (Sound Detection and Ranging), ASIS Includes bibliographical references (leaf 75). Also available in print.
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Duhaut, Thomas H. A. "Wind-driven circulation : impact of a surface velocity dependent wind stress." Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=101117.

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The use of an ocean surface velocity dependent wind stress is examined in the context of a 3-layer double-gyre quasigeostrophic wind-driven ocean circulation model. The new wind stress formulation results in a large reduction of the power input by the wind into the oceanic circulation. This wind stress is proportional to a quadratic function of Ua--u o, where Ua is the wind at 10m above the ocean surface and uo is the ocean surface current. Because the winds are typically faster than the ocean currents, the impact of the ocean surface velocity on the wind stress itself is relatively small. However, the power input is found to be greatly reduced with the new formulation. This is shown by simple scaling argument and numerical simulations in a square basin. Our results suggest that the wind power input may be as much as 35% smaller than is typically assumed.
The ocean current signature is clearly visible in the scatterometer-derived wind stress fields. We argue that because the actual ocean velocity differs from the modeled ocean velocities, care must be taken in directly applying scatterometer-derived wind stress products to the ocean circulation models. This is not to say that the scatterometer-derived wind stress is not useful. Clearly the great spatial and temporal coverage make these data sets invaluable. Our point is that it is better to separate the atmospheric and oceanic contribution to the stresses.
Finally, the new wind stress decreases the sensitivity of the solution to the (poorly known) bottom friction coefficient. The dependence of the circulation strength on different values of bottom friction is examined under the standard and the new wind stress forcing for two topographic configurations. A flat bottom and a meridional ridge case are studied. In the flat bottom case, the new wind stress leads to a significant reduction of the sensitivity to the bottom friction parameter, implying that inertial runaway occurs for smaller values of bottom friction coefficient. The ridge case also gives similar results. In the case of the ridge and the new wind stress formulation, no real inertial runaway regime has been found over the range of parameters explored.
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Thornhill, Kenneth L. II. "An investigation of the environment surrounding supercell thunderstorms using wind profiler data." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/26958.

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Dongaonkar, Ranjeet Manohar. "Integration of microvascular, interstitial, and lymphatic function to determine the effect of their interaction on interstitial fluid volume." [College Station, Tex. : Texas A&M University, 2008. http://hdl.handle.net/1969.1/ETD-TAMU-3114.

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Moodley, Kirshnee. "The fitting of statistical distributions to wind data in coastal areas of South Africa." Thesis, Nelson Mandela Metropolitan University, 2013.

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Coastal South African cities like Port Elizabeth are said to have a strong potential for wind energy. This study aims to model wind data in order to be able assess the power potential belonging to a given site. The main challenge in modelling wind direction data is that it is categorized as circular data and therefore requires special techniques for handling that are different from usual statistical samples. Statistical tools such as descriptive measures and distribution fitting, were re-invented for directional data by researchers in this field. The von Mises distribution is a predominant distribution in circular statistics and is commonly used to describe wind directions. In this study, the circular principles described by previous researchers were developed by using the statistical software, Mathematica. Graphical methods to present the wind data were developed to give an overview of the behaviour of the winds in any given area. Data collected at Coega, an area near Port Elizabeth, South Africa, was used to illustrate the models which were established in this study. Circular distributions were fit to the directional data in order to make appropriate conclusions about the prevailing wind directions in this area.
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Gao, Qian. "A systems biology approach to multi-scale modelling and analysis of planar cell polarity in Drosophila melanogaster wing." Thesis, Brunel University, 2013. http://bura.brunel.ac.uk/handle/2438/7478.

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Systems biology aims to describe and understand biology at a global scale where biological systems function as a result of complex mechanisms that happen at several scales. Modelling and simulation are computational tools that are invaluable for description, understanding and prediction these mechanisms in a quantitative and integrative way. Thus multi-scale methods that couple the design, simulation and analysis of models spanning several spatial and temporal scales is becoming a new emerging focus of systems biology. This thesis uses an exemplar – Planar cell polarity (PCP) signalling – to illustrate a generic approach to model biological systems at different spatial scales, using the new concept of Hierarchically Coloured Petri Nets (HCPN). PCP signalling refers to the coordinated polarisation of cells within the plane of various epithelial tissues to generate sub-cellular asymmetry along an axis orthogonal to their apical-basal axes. This polarisation is required for many developmental events in both vertebrates and non-vertebrates. Defects in PCP in vertebrates are responsible for developmental abnormalities in multiple tissues including the neural tube, the kidney and the inner ear. In Drosophila wing, PCP is seen in the parallel orientation of hairs that protrude from each of the approximately 30,000 epithelial cells to robustly point toward the wing tip. This work applies HCPN to model a tissue comprising multiple cells hexagonally packed in a honeycomb formation in order to describe the phenomenon of Planar Cell Polarity (PCP) in Drosophila wing. HCPN facilitate the construction of mathematically tractable, compact and parameterised large-scale models. Different levels of abstraction that can be used in order to simplify such a complex system are first illustrated. The PCP system is first represented at an abstract level without modelling details of the cell. Each cell is then sub-divided into seven virtual compartments with adjacent cells being coupled via the formation of intercellular complexes. A more detailed model is later developed, describing the intra- and inter-cellular signalling mechanisms involved in PCP signalling. The initial model is for a wild-type organism, and then a family of related models, permitting different hypotheses to be explored regarding the mechanisms underlying PCP, are constructed. Among them, the largest model consists of 800 cells which when unfolded yields 164,000 places (each of which is described by an ordinary differential equation). This thesis illustrates the power and validity of the approach by showing how the models can be easily adapted to describe well-documented genetic mutations in the Drosophila wing using the proposed approach including clustering and model checking over time series of primary and secondary data, which can be employed to analyse and check such multi-scale models similar to the case of PCP. The HCPN models support the interpretation of biological observations reported in literature and are able to make sensible predictions. As HCPN model multi-scale systems in a compact, parameterised and scalable way, this modelling approach can be applied to other large-scale or multi-scale systems.
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Zelenke, Brian Christopher. "An empirical statistical model relating winds and ocean surface currents : implications for short-term current forecasts." Thesis, Connect to the title online, 2005. http://hdl.handle.net/1957/2166.

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Ghazlane, Imane. "Adjoint-based aerostructural sensitivity analysis for wing design." Phd thesis, Université Nice Sophia Antipolis, 2012. http://tel.archives-ouvertes.fr/tel-00925210.

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Cette thèse a pour cadre le développement de méthodes numériques pour la conception optimale de forme de voilure en aérodynamique compressible. Ce travail a donné lieu au développement et à la validation d'un adjoint discret aéro-structure pour l'analyse de sensibilité par rapport aux paramètres de forme et de structure interne de l 'aile dont dépend la fonction d'intérêt, qu' elle soit aérodynamique ou structurale. Les développements logiciels ont été réalisés dans le code de simulation numérique de mécanique des fluides elsA et font suite aux travaux de Marcelet portant sur l'adjoint aéroélastique et dont ils sont une extension. Alors que pour l'adjoint aéro-élastique, on considère une aile flexible, de caractéristiques structurales constantes, pour l'adjoint aérostructure, leur variations sont prises en compte. Pour cela, l'extension de la méthode adjointe s' est accompagnée du développement d' un module de modélisation de la structure interne de l'aile. Ce module est linéarisé et vient donc alimenter le système adjoint. Il a été validé par le dimensionnement de la structure primaire d'une configuration de recherche fournie par l' avionneur Airbus. Dans l'état actuel de développement de la méthode adjointe dans le code elsA, on peut donc désormais calculer les sensibilités d'une fonction aérodynamique ou d'une fonction structure par rapport aux paramètres de forme aérodynamique ou de structure interne de l'aile. Le calcul des gradients ainsi obtenus a été validé par des comparaisons systématiques aux différences finies.
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Books on the topic "Wings – Mathematical models"

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Teorii͡a nesushcheĭ poverkhnosti: Matematicheskai͡a modelʹ, chislennyĭ metod, raschet mashushchego poleta. Moskva: Nauka, Fizmatlit, 1995.

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Bina, Bardia. Wing anti-icing system control modelling and sensitivity analysis: A system identification based approach. [Downsview, Ont.]: University of Toronto, Institute for Aerospace Studies, 2003.

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Turk, Thomas Andrew. Aircraft wing anti-icing system: Modelling, integration, and validation. [Downsview, Ont.]: University of Toronto, Institute for Aerospace Studies, 2003.

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Powell, Kenneth G. Vortical solutions of the conical Euler equations. Braunschweig: Vieweg, 1990.

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Hollowell, S. J. Conceptual design optimization study. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division, 1990.

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Klein, Thomas. Katabatic winds over Greenland and Antarctica and their interaction with mesoscale and synoptic scale weather systems: Investigations using three dimensional numerical models. St. Augustin: Asgard, 2000.

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Wuertz, David B. Editing wind profiler measurements. Boulder, Colo: U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, Wave Propagation Laboratory, 1989.

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Wuertz, David B. Editing wind profiler measurements. Boulder, Colo: U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, Wave Propagation Laboratory, 1989.

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Wuertz, David B. Editing wind profiler measurements. Boulder, Colo: U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, Wave Propagation Laboratory, 1989.

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Klaus, Braun. Der Einfluss mesoskaliger Windfelder auf die räumliche Verteilung des Niederschlags: Eine Untersuchung zur Regionalisierung von Niederschlagsdaten mit Hilfe eines mesoskaligen Strömungsmodells. Freiburg: Im Selbstverlag des Institutes für Physische Geographie der Albert-Ludwigs-Universität Freiburg i. Br., 1997.

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Book chapters on the topic "Wings – Mathematical models"

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Rozhdestvensky, Kirill V. "Simple Mathematical Models of Elastic and Flexible Wings in the Extreme Ground Effect." In Aerodynamics of a Lifting System in Extreme Ground Effect, 319–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-04240-3_12.

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Sekimura, Toshio. "An Integrative Approach to the Analysis of Pattern Formation in Butterfly Wings: Experiments and Models." In Springer Proceedings in Mathematics, 121–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-20164-6_11.

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Bacharoudis, Konstantinos, Atanas Popov, and Svetan Ratchev. "Application of Advanced Simulation Methods for the Tolerance Analysis of Mechanical Assemblies." In IFIP Advances in Information and Communication Technology, 153–67. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72632-4_11.

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AbstractIn the frame of a statistical tolerance analysis of complex assemblies, for example an aircraft wing, the capability to predict accurately and fast specified, very small quantiles of the distribution of the assembly key characteristic becomes crucial. The problem is significantly magnified, when the tolerance synthesis problem is considered in which several tolerance analyses are performed and thus, a reliability analysis problem is nested inside an optimisation one in a fully probabilistic approach. The need to reduce the computational time and accurately estimate the specified probabilities is critical. Therefore, herein, a systematic study on several state of the art simulation methods is performed whilst they are critically evaluated with respect to their efficiency to deal with tolerance analysis problems. It is demonstrated that tolerance analysis problems are characterised by high dimensionality, high non-linearity of the state functions, disconnected failure domains, implicit state functions and small probability estimations. Therefore, the successful implementation of reliability methods becomes a formidable task. Herein, advanced simulation methods are combined with in-house developed assembly models based on the Homogeneous Transformation Matrix method as well as off-the-self Computer Aided Tolerance tools. The main outcome of the work is that by using an appropriate reliability method, computational time can be reduced whilst the probability of defected products can be accurately predicted. Furthermore, the connection of advanced mathematical toolboxes with off-the-self 3D tolerance tools into a process integration framework introduces benefits to successfully deal with the tolerance allocation problem in the future using dedicated and powerful computational tools.
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Feng, Kun, and Krzysztof Sibilski. "Analysis of resonant propulsion flapping wing micro aerial vehicle." In Mechanika w Lotnictwie ML-XIX 2020, 327–45. Instytut Techniczny Wojsk Lotniczych, Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2020. http://dx.doi.org/10.15632/ml2020/327-345.

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This article is concerned with the resonant property which is exhibited in insect flight, and analyzes how resonant propulsion works when implemented in powering a flapping wing micro aerial vehicle. This article is divided into three parts. In the first part, information regarding to insect flight, the resonant property, and flapping wing micro aerial vehicles are described. In the second part, mathematical models representing the micro aerial vehicle (basing on the model developed by Bolsman) are applied, simplified and built into simulation in MATLAB. Some interesting properties from the simulations are presented.
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Balakrishnan, A. "Nonlinear aeroelasticity, continuum theory, flutter/divergence speed, plate wing model." In Lecture Notes in Pure and Applied Mathematics, 223–44. Chapman and Hall/CRC, 2007. http://dx.doi.org/10.1201/9781420011159.ch11.

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Shubov, Marianna. "Operator-Valued Analytic Functions Generated by Aircraft Wing Model (Subsonic Case)." In Lecture Notes in Pure and Applied Mathematics, 243–57. Chapman and Hall/CRC, 2005. http://dx.doi.org/10.1201/9781420028317.ch17.

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Zangwill, Andrew. "Son of the Heartland." In A Mind Over Matter, 8–24. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198869108.003.0002.

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Anderson’s parents come from academic families in Indiana. Phil and his sister Grace grew up in Urbana, Illinois because their father was a plant pathologist at the University of Illinois (UI). Mother Elsie demanded academic excellence and respect for others. Father Harry was a model of integrity, a fact displayed during the so-called Krebiozen affair. The Depression affected the family relatively little and Phil acquired his lifelong liberal politics from a UI social group called the Saturday Hikers. At age twelve, he accompanies his family to Europe (a sabbatical for his father) where they observe the rise of Nazism. Phil attends and excels at the University High School where he enjoys math, tennis, and speed skating, but not physics. He wins a National Scholarship to attend Harvard University with a plan to major in mathematics.
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Mohammadian, M. "Designing Unsupervised Hierarchical Fuzzy Logic Systems." In Machine Learning, 253–61. IGI Global, 2012. http://dx.doi.org/10.4018/978-1-60960-818-7.ch210.

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Systems such as robotic systems and systems with large input-output data tend to be difficult to model using mathematical techniques. These systems have typically high dimensionality and have degrees of uncertainty in many parameters. Artificial intelligence techniques such as neural networks, fuzzy logic, genetic algorithms and evolutionary algorithms have created new opportunities to solve complex systems. Application of fuzzy logic [Bai, Y., Zhuang H. and Wang, D. (2006)] in particular, to model and solve industrial problems is now wide spread and has universal acceptance. Fuzzy modelling or fuzzy identification has numerous practical applications in control, prediction and inference. It has been found useful when the system is either difficult to predict and or difficult to model by conventional methods. Fuzzy set theory provides a means for representing uncertainties. The underlying power of fuzzy logic is its ability to represent imprecise values in an understandable form. The majority of fuzzy logic systems to date have been static and based upon knowledge derived from imprecise heuristic knowledge of experienced operators, and where applicable also upon physical laws that governs the dynamics of the process. Although its application to industrial problems has often produced results superior to classical control, the design procedures are limited by the heuristic rules of the system. It is simply assumed that the rules for the system are readily available or can be obtained. This implicit assumption limits the application of fuzzy logic to the cases of the system with a few parameters. The number of parameters of a system could be large. The number of fuzzy rules of a system is directly dependent on these parameters. As the number of parameters increase, the number of fuzzy rules of the system grows exponentially. Genetic Algorithms can be used as a tool for the generation of fuzzy rules for a fuzzy logic system. This automatic generation of fuzzy rules, via genetic algorithms, can be categorised into two learning techniques, supervised and unsupervised. In this paper unsupervised learning of fuzzy rules of hierarchical and multi-layer fuzzy logic control systems are considered. In unsupervised learning there is no external teacher or critic to oversee the learning process. In other words, there are no specific examples of the function to be learned by the system. Rather, provision is made for a task-independent measure of the quality or representation that the system is required to learn. That is the system learns statistical regularities of the input data and it develops the ability to learn the feature of the input data and thereby create new classes automatically [Mohammadian, M., Nainar, I. and Kingham, M. (1997)]. To perform unsupervised learning, a competitive learning strategy may be used. The individual strings of genetic algorithms compete with each other for the “opportunity” to respond to features contained in the input data. In its simplest form, the system operates in accordance with the strategy that ‘the fittest wins and survives’. That is the individual chromosome in a population with greatest fitness ‘wins’ the competition and gets selected for the genetic algorithms operations (cross-over and mutation). The other individuals in the population then have to compete with fit individual to survive. The diversity of the learning tasks shown in this paper indicates genetic algorithm’s universality for concept learning in unsupervised manner. A hybrid integrated architecture incorporating fuzzy logic and genetic algorithm can generate fuzzy rules for problems requiring supervised or unsupervised learning. In this paper only unsupervised learning of fuzzy logic systems is considered. The learning of fuzzy rules and internal parameters in an unsupervised manner is performed using genetic algorithms. Simulations results have shown that the proposed system is capable of learning the control rules for hierarchical and multi-layer fuzzy logic systems. Application areas considered are, hierarchical control of a network of traffic light control and robotic systems. A first step in the construction of a fuzzy logic system is to determine which variables are fundamentally important. Any number of these decision variables may appear, but the more that are used, the larger the rule set that must be found. It is known [Raju, S., Zhou J. and Kisner, R. A. (1990), Raju G. V. S. and Zhou, J. (1993), Kingham, M., Mohammadian, M, and Stonier, R. J. (1998)], that the total number of rules in a system is an exponential function of the number of system variables. In order to design a fuzzy system with the required accuracy, the number of rules increases exponentially with the number of input variables and its associated fuzzy sets for the fuzzy logic system. A way to avoid the explosion of fuzzy rule bases in fuzzy logic systems is to consider Hierarchical Fuzzy Logic Control (HFLC) [Raju G. V. S. and Zhou, J. (1993)]. A learning approach based on genetic algorithms [Goldberg, D. (1989)] is discussed in this paper for the determination of the rule bases of hierarchical fuzzy logic systems.
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Conference papers on the topic "Wings – Mathematical models"

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Cheng, B., and X. Deng. "Mathematical Modelling of Near-Hover Insect Flight Dynamics." In ASME 2010 Dynamic Systems and Control Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/dscc2010-4234.

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Using a dynamically scaled robotic wing, we studied the aerodynamic torque generation of flapping wings during roll, pitch, and yaw rotations of the stroke plane. The total torque generated by a wing pair with symmetrical motions was previously known as flapping counter-torques (FCTs). For all three types of rotation, stroke-averaged FCTs act opposite to the directions of rotation and are collinear with the rotational axes. Experimental results indicate that the magnitude of FCTs is linearly dependent on both the flapping frequency and the angular velocity. We also compared the results with predictions by a mathematical model based on quasi-steady analyses, where we show that FCTs can be described through consideration of the asymmetries of wing velocity and the effective angle of attack caused by each type of rotation. For roll and yaw rotations, our model provided close estimations of the measured values. However, for pitch rotation the model tends to underestimate the magnitude of FCT, which might result from the effect of the neglected aerodynamics, especially the wake capture. Similar to the FCT, which is induced by body rotation, we further provide a mathematical model for the counter force induced by body translation, which is termed as flapping counter-force (FCF). Based on the FCT and FCF models, we are able to provide analytical estimations of stability derivatives and to study the flight dynamics at hovering. Using fruit fly (Drosophila) morphological data, we calculated the system matrix of the linearized flight dynamics. Similar to previous studies, the longitudinal dynamics consist of two stable subsidence modes with fast and slow time constants, as well as an unstable oscillatory mode. The longitudinal instability is mainly caused by the FCF induced by an initial forward/backward velocity, which imparts a pitch torque to the same direction of initial pitch velocity. Similarly, the lateral dynamics also consist of two stable subsidence modes and an unstable oscillatory mode. The lateral instability is mainly caused by the FCF induced by an initial lateral velocity, which imparts a roll torque to the same direction of initial roll velocity. In summary, our models provide the first analytical approximation of the six-degree-of-freedom flight dynamics, which is important in both studying the control strategies of the flying insects and designing the controller of the future flapping-wing micro air vehicles (MAVs).
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Carrera, E., A. Pagani, and M. Petrolo. "Static and Dynamic Analysis of Aircraft Structures by Component-Wise Approach." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-63600.

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This paper proposes an advanced approach to the analysis of reinforced-shell aircraft structures. This approach, denoted as Component-Wise (CW), is developed by using the Carrera Unified Formulation (CUF). CUF is a hierarchical formulation allowing for the straightforward implementation of any-order one-dimensional (1D) beam theories. Lagrange-like polynomials are used to discretize the displacement field on the cross-section of each component of the structure. Depending on the geometrical and material characteristics of the component, the capabilities of the model can be enhanced and the computational costs can be kept low through smart discretization strategies. The global mathematical model of complex structures (e.g. wings or fuselages) is obtained by assembling each component model at the cross-section level. Next, a classical 1D finite element (FE) formulation is used to develop numerical applications. It is shown that MSC/PATRAN can be used as pre- and post-processor for the CW models, whereas MSC/NASTRAN DMAP alters can be used to solve both static and dynamic problems. A number of typical aeronautical structures are analyzed and CW results are compared to classical beam theories (Euler-Bernoulli and Timoshenko), refined models and classical solid/shell FE solutions from the commercial code MSC/NASTRAN. The results highlight the enhanced capabilities of the proposed formulation. In fact, the CW approach is clearly the natural tool to analyze wing structures, since it leads to results that can be only obtained through three-dimensional elasticity (solid) elements whose computational costs are at least one-order of magnitude higher than CW models.
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Chidurala, Manohar, Benjamin T. Dickinson, and Uttam K. Chakravarty. "Dynamic Response of Biomimetic Hair Receptors in Both Steady and Unsteady Flow Environment." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-65250.

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The high performance of nature’s creations and biological assemblies has inspired the development of engineered counter parts that may outperform or provide new capabilities to conventional systems. In particular, the wings of bats contain distributed arrays of micro-scaled flow sensitive hair receptors over their surface, which inspires artificial hair sensors (AHS) development in aerodynamic feedback control designs using the micro-electro-mechanical systems (MEMS). One approach investigates the possibility of installing AHS on the leading edges of the wings of small-scaled unmanned aerial vehicles (UAVs) to improve the aerodynamic control. Our major motivation for the present study is that current mathematical models have limited relevance to aerodynamic situations because they are analyzed in steady or purely oscillatory flows. Our overall objective is to understand AHS fluid-structure interaction (FSI) in flow regimes relevant to small-scaled UAVs, for which we speculate a steady baseline flow perturbed by an oscillatory component is an appropriate flow reference condition. Towards understanding the AHS in this situation, we investigate the dynamic response of a hair receptor in a creeping flow environment with a steady and oscillatory component. We present time varying deflection and bending moment of the artificial hair sensors at different freestream velocities. For this, a three-dimensional FSI model is developed for the flexible hair-structure in the airflow, which is coupled with a finite element model using the computational fluid dynamics (CFD). The Navier-Stokes equations including continuity equation are solved numerically for the CFD model. To describe the dynamic response of the hair receptors, the natural frequencies and mode shapes of the hair receptors, computed from the FSI model, are compared with the excitation frequencies of the surrounding airflow. This model also describes both the boundary layer effects and effects of inertial forces due to FSI of the hair receptors. For supporting the FSI model, the dynamic response of the hair receptor is also validated considering the Euler-Bernoulli beam theory including the steady and unsteady airflow.
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Yue, Hong-Hao, Zhan-Qiu Liu, Han Yuan, Yu-Fei Long, and Horn-Sen Tzou. "Analysis and Design of Active Morphing Units Based on SMA Actuators." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-65546.

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Morphing wings can change their shapes in flight to optimize aircraft’s aerodynamics, which increases aircraft’s performance for a given flight stage. This paper introduces an active morphing unit (AMU) which can deform by the two-way actuator comprising two one-way shape memory alloy (SMA) elements. The mathematical model and the forward kinematics of AMU are established. The structure of AMU is design. Then, the paper demonstrates that the combination of AMUs can function as the main spar of distributed multi-freedom active morphing wing. Three different combination strategies of AMUs are analyzed by forward kinematics and realizable variable geometries of wing. A configuration sample of one-dimension morphing wing is presented to demonstrate a combination strategy. The rotation function and stiffness of AMU prototype are tested. Experimental results illustrate that AMU can realize desired deformation and has high stiffness. This research will lay the foundations of next generation morphing aircrafts.
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Gopalan, Harish, Alex Povitsky, Ilias Kotsireas, Roderick Melnik, and Brian West. "High-order Method for Modeling of Aerodynamics of Flapping Wings: Airfoil-Gust Interaction." In ADVANCES IN MATHEMATICAL AND COMPUTATIONAL METHODS: ADDRESSING MODERN CHALLENGES OF SCIENCE, TECHNOLOGY, AND SOCIETY. AIP, 2011. http://dx.doi.org/10.1063/1.3663471.

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Gilani, Omar, and Pinhas Ben-Tzvi. "The Application of Bioinspired Jumping Locomotion Principles to Mobile Robots: Modeling and Analysis." In ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control. ASMEDC, 2011. http://dx.doi.org/10.1115/dscc2011-6108.

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Nature provides various alternative locomotion strategies which could be applied to robotic systems. One such strategy is that of jumping, which enables centimeter to millimeter-scaled insects to traverse highly unstructured environments quickly and efficiently. These insects generate the required high magnitude power through specialized structures which store and rapidly release large amounts of energy. This paper presents an investigation into the morphology of natural jumpers and derives a generalized mathematical model based on them. The model describes mathematically the relationships present in a jumping system which uses a pause-and-leap jumping strategy. The use of springs as energy storage elements for such a jumping system is assessed. The discussion is then further extended to another bioinspired approach that can be applied to a jumping robot: that of gliding using foldable wings. The developed jumping and gliding mobility paradigm is analyzed and its feasibility for mobile robot applications is discussed.
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Henry, Janisa, and Darryll Pines. "A Mathematical Model for Roll Dynamics by Use of a Morphing-Span Wing." In 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2007. http://dx.doi.org/10.2514/6.2007-1708.

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Tarasov, Alexander E., and Mezhlum A. Sumbatyan. "A mathematical model for the thrust force generated by a flapping elastic wing." In 9TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2012. AIP, 2012. http://dx.doi.org/10.1063/1.4765616.

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Trabia, Mohamed B., Woosoon Yim, Zohaib Rehmat, and Jesse Roll. "Flight Characteristics of Flapping Wing Miniature Air Vehicles With “Figure-8” Spherical Motion." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-12427.

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Hummingbirds and some insects exhibit “Figure-8” flapping motion that allows them to go through a variety of maneuvers including hovering. Understanding the flight characteristics of Figure-8 flapping motion can potentially yield the foundation of flapping wing UAVs that can experience similar maneuverability. In this paper, a mathematical model of the dynamic and aerodynamic forces associated with Figure-8 motion generated by a spherical four bar mechanism is developed. For validation, a FWMAV prototype with the wing attached to a coupler point and driven by a DC servo motor is created for experimental testing. Wind tunnel testing is conducted to determine the coefficients of flight and the effects of dynamic stall. The wing is driven at speeds up to 12.25 Hz with results compared to that of the model. The results indicate good correlation between mathematical model and experimental prototype.
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Trong, N. T., D. Shyam Sundar, T. T. Lim, and K. S. Yeo. "Towards a realistic fruitfly wing model with flexibility." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4913139.

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