Research Papers

Transient and Stable Chaos in Dipteran Flight Inspired Flapping Motion

[+] Author and Article Information
Chandan Bose

Department of Applied Mechanics,
Indian Institute of Technology Madras,
Chennai 600036, India
e-mail: cb.ju.1991@gmail.com

Vikas Reddy

Department of Aerospace Engineering,
Indian Institute of Technology Madras,
Chennai 600036, India
e-mail: yettellavikas@gmail.com

Sayan Gupta

Department of Applied Mechanics,
Indian Institute of Technology Madras,
Chennai 600036, India
e-mail: gupta.sayan@gmail.com

Sunetra Sarkar

Department of Aerospace Engineering,
Indian Institute of Technology Madras,
Chennai 600036, India
e-mail: sunetra.sarkar@gmail.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received August 5, 2017; final manuscript received November 4, 2017; published online December 14, 2017. Assoc. Editor: Katrin Ellermann.

J. Comput. Nonlinear Dynam 13(2), 021014 (Dec 14, 2017) (9 pages) Paper No: CND-17-1359; doi: 10.1115/1.4038447 History: Received August 05, 2017; Revised November 04, 2017

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 behavior 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 trailing edge wake patterns.

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Fig. 1

Schematic of flexible insect flight motor model: (a) Click mechanism, (b) Duffing oscillator model

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Fig. 2

Schematic of lumped vortex model

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Fig. 3

(a) Comparison of peak lift coefficients, estimated using LVM (present method) and from Navier–Stokes simulation ([23]) and (b) comparison of relative phase angles between the lift coefficient and the heaving motion (ϕL), estimated using LVM (present method) and Navier–Stokes results [23]

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Fig. 4

Temporal convergence of coupled system responses at F¯=0.08

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Fig. 5

Displacement time histories and corresponding phase portraits: F¯=0 (a) and (d), F¯=0.02 (b) and (e), F¯=0.08 (c) and (f)

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Fig. 6

Transient chaos at F¯=0.14: (a) displacement time history and (b) phase portrait; period doubling cascade: (c) zoomed period-2 response and (e) period-2 attractor for F¯=0.14, (d) zoomed period-4 response and (f) period-4 attractor for F¯=0.146

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Fig. 7

Transient chaos at F¯=0.16: (a) displacement time history, (b) frequency spectra, (c) zoomed window of chaotic transient, (d) zoomed window of period-1 oscillation, (e) phase portrait and Poincaré section for chaotic transient, and (f) phase portrait and Poincaré section for period-1 oscillation

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Fig. 8

Periodic windows: (a) period-1 oscillation and (b) period-1 attractor at F¯=0.20; (c) period-5 oscillation and (d) period-5 attractor at F¯=0.212

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Fig. 9

Intermittent time history of displacement at F¯=0.232

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Fig. 10

Sustained chaos at F¯=0.24: (a) displacement time history, (b) frequency spectra, (c) zoomed window of chaotic response, and (d) phase portrait

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Fig. 11

Poincaré sections of the response at F¯=0.24: strange attractors

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Fig. 12

Largest Lyapunov exponent of the response at F¯=0.24

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Fig. 13

RP for the period-1 response at F¯=0.08

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Fig. 14

RP for the transient chaos at F¯=0.16

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Fig. 15

RP for the intermittent response at F¯=0.232

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Fig. 16

RP for the chaotic response at F¯=0.24

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Fig. 17

Scalogram of the wavelet coefficients: (a) period-1 response at F¯=0.08, (b) transient chaos at F¯=0.16, (c) intermittent response at F¯=0.232, and (d) chaotic response at F¯=0.24

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Fig. 18

Sustained chaotic behavior of lift coefficient at F¯=0.24: (a) time history of Cl, (b) frequency spectra, (c) zoomed time history, and (d) phase portrait and Poincaré section

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Fig. 19

Transition in the flow pattern: (a) Periodic flow pattern at F¯=0.20 and (b) chaotic flow pattern at F¯=0.24



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