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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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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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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Additional excerpts
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