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

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
Topics: Flapping (52%)
Citations
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Journal ArticleDOI
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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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.

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....

[...]

• ...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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References
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Journal ArticleDOI
Abstract: We present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series. Lyapunov exponents, which provide a qualitative and quantitative characterization of dynamical behavior, are related to the exponentially fast divergence or convergence of nearby orbits in phase space. A system with one or more positive Lyapunov exponents is defined to be chaotic. Our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems: we monitor the long-term growth rate of small volume elements in an attractor. The method is tested on model systems with known Lyapunov spectra, and applied to data for the Belousov-Zhabotinskii reaction and Couette-Taylor flow.

7,366 citations

Journal ArticleDOI
01 Nov 1987-EPL
Abstract: A new graphical tool for measuring the time constancy of dynamical systems is presented and illustrated with typical examples.

2,585 citations

• ...[30], is a graphical representation of a symmetric binary square matrix (Ri, j) constructed by a binary mapping based on the criteria for recurrence depicted below for various values of i and j (different time instances), where both 0 5000 10000 15000 −1 −0....

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Journal ArticleDOI
01 Jan 2007-Physics Reports
TL;DR: The aim of this work is to provide the readers with the know how for the application of recurrence plot based methods in their own field of research, and detail the analysis of data and indicate possible difficulties and pitfalls.
Abstract: Recurrence is a fundamental property of dynamical systems, which can be exploited to characterise the system's behaviour in phase space. A powerful tool for their visualisation and analysis called recurrence plot was introduced in the late 1980's. This report is a comprehensive overview covering recurrence based methods and their applications with an emphasis on recent developments. After a brief outline of the theory of recurrences, the basic idea of the recurrence plot with its variations is presented. This includes the quantification of recurrence plots, like the recurrence quantification analysis, which is highly effective to detect, e. g., transitions in the dynamics of systems from time series. A main point is how to link recurrences to dynamical invariants and unstable periodic orbits. This and further evidence suggest that recurrences contain all relevant information about a system's behaviour. As the respective phase spaces of two systems change due to coupling, recurrence plots allow studying and quantifying their interaction. This fact also provides us with a sensitive tool for the study of synchronisation of complex systems. In the last part of the report several applications of recurrence plots in economy, physiology, neuroscience, earth sciences, astrophysics and engineering are shown. The aim of this work is to provide the readers with the know how for the application of recurrence plot based methods in their own field of research. We therefore detail the analysis of data and indicate possible difficulties and pitfalls.

2,533 citations

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

• ..., the distance between the two farthest points in the phase space [31]; the transition dynamics is captured well with this value....

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MonographDOI
Joseph Katz1, Allen Plotkin1Institutions (1)
05 Feb 2001-
Abstract: Low-speed aerodynamics is important in the design and operation of aircraft flying at low Mach number, and ground and marine vehicles. This 2001 book offers a modern treatment of the subject, both the theory of inviscid, incompressible, and irrotational aerodynamics and the computational techniques now available to solve complex problems. A unique feature of the text is that the computational approach (from a single vortex element to a three-dimensional panel formulation) is interwoven throughout. Thus, the reader can learn about classical methods of the past, while also learning how to use numerical methods to solve real-world aerodynamic problems. This second edition has a new chapter on the laminar boundary layer (emphasis on the viscous-inviscid coupling), the latest versions of computational techniques, and additional coverage of interaction problems. It includes a systematic treatment of two-dimensional panel methods and a detailed presentation of computational techniques for three-dimensional and unsteady flows. With extensive illustrations and examples, this book will be useful for senior and beginning graduate-level courses, as well as a helpful reference tool for practising engineers.

1,651 citations

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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