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Journal ArticleDOI

Transient and Stable Chaos in Dipteran Flight Inspired Flapping Motion

01 Feb 2018-Journal of Computational and Nonlinear Dynamics (American Society of Mechanical Engineers)-Vol. 13, Iss: 2, pp 021014
TL;DR: In this article, the nonlinear fluid structure interaction (FSI) dynamics of a Dipteran flight motor inspired flapping system in an inviscid fluid were investigated. And the authors employed a potential flow solver to determine the aerodynamic loads and an explicit fourth order Runge-Kutta scheme to solve the structural governing equations.
Abstract: This paper deals with the nonlinear fluid structure interaction (FSI) dynamics of a Dipteran flight motor inspired flapping system in an inviscid fluid. In the present study, the FSI effects are incorporated to an existing forced Duffing oscillator model to gain a clear understanding of the nonlinear dynamical behaviour of the system in the presence of aerodynamic loads. The present FSI framework employs a potential flow solver to determine the aerodynamic loads and an explicit fourth order Runge-Kutta scheme to solve the structural governing equations. A bifurcation analysis has been carried out considering the amplitude of the wing actuation force as the control parameter to investigate different complex states of the system. Interesting dynamical behavior including period doubling, chaotic transients, periodic windows and finally an intermittent transition to stable chaotic attractor have been observed in the response with an increase in the bifurcation parameter. Similar dynamics is also reflected in the aerodynamic loads as well as in the
Citations
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Journal ArticleDOI
05 May 2020-PLOS ONE
TL;DR: The nonlinear dynamics of a bird-like flapping wing robot under randomly uncertain disturbances was studied and showed that the robot is more likely to deviate from its normal trajectory when the randomly uncertain disturbance are applied in a chaotic state than in a periodic state.
Abstract: The nonlinear dynamics of a bird-like flapping wing robot under randomly uncertain disturbances was studied in this study. The bird-like flapping wing robot was first simplified into a two-rod model with a spring connection. Then, the dynamic model of the robot under randomly uncertain disturbances was established according to the principle of moment equilibrium, and the disturbances were modeled in the form of bounded noise. Next, the energy model of the robot was established. Finally, numerical simulations and experiments were carried out based on the above models. The results show that the robot is more likely to deviate from its normal trajectory when the randomly uncertain disturbances are applied in a chaotic state than in a periodic state. With the increase of the spring stiffness under the randomly uncertain disturbances, the robot has a stronger ability to reject the disturbances. The mass center of the robot is vital to realize stable flights. The greater the amplitude of randomly uncertain disturbances, the more likely it is for the robot to be in a divergent state.

3 citations


Cites methods from "Transient and Stable Chaos in Dipte..."

  • ...In the references [14,24,34,35], the dynamic performances of the flapping wing robot were also studied based on different dynamic models....

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  • ...considered the structural model of a flapping flight as a linkage system, and established the dynamic model in the form of a Duffing oscillator, and used the lumped vortex method to calculate the aerodynamic force of the robot [14]....

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  • ...From the results comparison in the references [11,14,24,34,35], the dynamic performances of the robot are different when different models are established....

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Journal ArticleDOI
TL;DR: In this article, the effect of frontal gust on the force patterns of an insect-sized flapping wing in the inclined-stroke plane was assessed using global recurrence plots and windowed recurrence quantification analysis (WRQA).
Abstract: Global recurrence plots (GRPs) and windowed recurrence quantification analysis (WRQA) are two recurrence paradigms which find wide applications to detect the onset of instability in a dynamic system. The present work reports the attempt to employ these recurrence paradigms to assess the effect of frontal gust on the force patterns of an insect-sized flapping wing in the inclined-stroke plane. Horizontal and vertical forces generated by the flapping wing in the presence of gusts of the form $$ \frac{{{\text{u}}_{\text{G}} }}{{{\text{u}}_{\text{w}} }} = \frac{{{\text{u}}_{\infty } }}{{{\text{u}}_{\text{w}} }} + \left( {\frac{{{\text{u}}_{\text{g}} }}{{{\text{u}}_{\text{w}} }}} \right)\sin \left( {2\uppi\frac{{{\text{f}}_{\text{g}} }}{{{\text{f}}_{\text{w}} }}{\text{t}}} \right) $$ were numerically estimated in the 2D reference frame for Re = 150. Nine gusts with combinations of the ratio of gust frequency to wing’s flapping frequency, fg/fw = 0.1, 0.5 and 1 and ratio of gust velocity amplitude to root mean square averaged flapping velocity, ug/uw = 0.1, 0.5 and 1 were considered. Recurrence studies of the forces were carried out to find out the gusty condition, which would trigger an onset of unstable behaviour. Studies indicated a possible onset of instability in the force patterns for gust with fg/fw = 0.1 and ug/uw = 1. The onset of unstable behaviour was prominently captured by WRQA of the vertical force coefficient based on determinism (DET) and laminarity (LAM) series.

3 citations


Cites background from "Transient and Stable Chaos in Dipte..."

  • ...A recent work [48] based on the fluid–structure interaction of flapping wing in forward flight with constant inflow in an inviscid fluid employed recurrence plots to understand the chaotic behaviour of the dynamic system....

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References
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Book
06 Jan 1994
TL;DR: The phenomenology of chaos Towards a theory of nonlinear dynamics and chaos Quantifying chaos Special topics Appendices Index
Abstract: First Edition Preface First Edition Acknowledgments Second Edition Preface Second Edition Acknowledgments I. THE PHENOMENOLOGY OF CHAOS 1. Three Chaotic Systems 2. The Universality of Chaos II. TOWARDS A THEORY OF NONLINEAR DYNAMICS AND CHAOS 3. Dynamics in State Space: One and Two Dimensions 4. Three-Dimensional State Space and Chaos 5. Iterated Maps 6. Quasi-Periodicity and Chaos 7. Intermittency and Crises 8. Hamiltonian Systems III.MEASURES OF CHAOS 9. Quantifying Chaos 10. Many Dimensions and Multifractals IV.SPECIAL TOPICS 11. Pattern Formation and Spatiotemporal Chaos 12. Quantum Chaos, The Theory of Complexity, and other Topics Appendix A: Fourier Power Spectra Appendix B: Bifurcation Theory Appendix C: The Lorenz Model Appendix D: The Research Literature on Chaos Appendix E: Computer Programs Appendix F: Theory of the Universal Feigenbaum Numbers Appendix G: The Duffing Double-Well Oscillator Appendix H: Other Universal Feature for One-Dimensional Iterated Maps Appendix I: The van der Pol Oscillator Appendix J: Simple Laser Dynamics Models References Bibliography Index

1,055 citations


"Transient and Stable Chaos in Dipte..." refers background in this paper

  • ...In such situations, they are successively repelled by the unstable manifold and are attracted to the stable manifold of the saddle point many times in a chaotic manner before settling into a periodic orbit [19]....

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  • ...There are several established routes to chaos [19]....

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Journal ArticleDOI
TL;DR: Design characteristics of insect-based flying machines are presented, along with estimates of the mass supported, the mechanical power requirement and maximum flight speeds over a wide range of sizes and frequencies.
Abstract: The wing motion in free flight has been described for insects ranging from 1 to 100 mm in wingspan. To support the body weight, the wings typically produce 2–3 times more lift than can be accounted for by conventional aerodynamics. Some insects use the fling mechanism: the wings are clapped together and then flung open before the start of the downstroke, creating a lift-enhancing vortex around each wing. Most insects, however, rely on a leading-edge vortex (LEV) created by dynamic stall during flapping; a strong spanwise flow is also generated by the pressure gradients on the flapping wing, causing the LEV to spiral out to the wingtip. Technical applications of the fling are limited by the mechanical damage that accompanies repeated clapping of the wings, but the spiral LEV can be used to augment the lift production of propellers, rotors and micro-air vehicles (MAVs). Design characteristics of insect-based flying machines are presented, along with estimates of the mass supported, the mechanical power requirement and maximum flight speeds over a wide range of sizes and frequencies. To support a given mass, larger machines need less power, but smaller ones operating at higher frequencies will reach faster speeds.

764 citations


"Transient and Stable Chaos in Dipte..." refers background in this paper

  • ...Insects, which constitute nature’s successful flyers, are prime source of inspiration in this regard with the credence of natural selection [3]....

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Journal ArticleDOI
13 Jan 1977-Nature
TL;DR: The elastic materials involved include muscle in every case, but only in insect flight is the proportion of the energy stored in the muscle substantial.
Abstract: Storage of strain energy in elastic materials has important roles in mammal running, insect jumping and insect flight. The elastic materials involved include muscle in every case, but only in insect flight is the proportion of the energy stored in the muscle substantial.

699 citations


"Transient and Stable Chaos in Dipte..." refers background in this paper

  • ...Alexander and Bennet-Clark [4] showed that the ‘click’ mechanism is beneficial in the storage of elastic strain energy....

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  • ...Insect flight motors have been evolved over ages making their flapping flight energetically efficient by storing the kinetic energy as elastic energy in the deformed elastic elements like flight muscles, flight thorax, and wing hinges and recovering it during wing stroke reversal [4]....

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Book ChapterDOI
01 Jan 1989
TL;DR: One of the aims of wavelet transforms is to provide an easily interpretable visual representation of signals that is a prerequisite for applications such as selective modifications of signals or pattern recognition.
Abstract: One of the aims of wavelet transforms is to provide an easily interpretable visual representation of signals This is a prerequisite for applications such as selective modifications of signals or pattern recognition

356 citations


"Transient and Stable Chaos in Dipte..." refers methods in this paper

  • ...The Morlet wavelet [32] has been used in the present analysis....

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Journal ArticleDOI
TL;DR: An extensive database of publications for study with network-based information analysis techniques reveals that biomimetics is becoming a leading paradigm for the development of new technologies that will potentially lead to significant scientific, societal and economic impact in the near future.
Abstract: Biomimetics is a research field that is achieving particular prominence through an explosion of new discoveries in biology and engineering. The field concerns novel technologies developed through the transfer of function from biological systems. To analyze the impact of this field within engineering and related sciences, we compiled an extensive database of publications for study with network-based information analysis techniques. Criteria included publications by year and journal or conference, and subject areas judged by popular and common terms in titles. Our results reveal that this research area has expanded rapidly from less than 100 papers per year in the 1990s to several thousand papers per year in the first decade of this century. Moreover, this research is having impact across a variety of research themes, spanning robotics, computer science and bioengineering. In consequence, biomimetics is becoming a leading paradigm for the development of new technologies that will potentially lead to significant scientific, societal and economic impact in the near future.

260 citations