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.

References

References
1.
Lepora
,
N. F.
,
Verschure
,
P.
, and
Prescott
,
T. J.
,
2013
, “
The State of the Art in Biomimetics
,”
Bioinspiration Biomimetics
,
8
(
1
), p.
013001
.
2.
Ward
,
T. A.
,
Rezadad
,
M.
,
Fearday
,
C. J.
, and
Viyapuri
,
R.
,
2015
, “
A Review of Biomimetic Air Vehicle Research: 1984–2014
,”
Int. J. Micro Air Veh.
,
7
(
3
), pp.
375
394
.
3.
Ellington
,
C. P.
,
1999
, “
The Novel Aerodynamics of Insect Flight: Applications to Micro-Air Vehicles
,”
J. Exp. Biol.
,
202
(
23
), pp.
3439
3448
.http://jeb.biologists.org/content/202/23/3439.short
4.
Alexander
,
R. M.
, and
Bennet-Clark
,
H.
,
1977
, “
Storage of Elastic Strain Energy in Muscle and Other Tissues
,”
Nature
,
265
(
5590
), pp.
114
117
.
5.
Harne
,
R.
, and
Wang
,
K.
,
2015
, “
Dipteran Wing Motor-Inspired Flapping Flight Versatility and Effectiveness Enhancement
,”
J. R. Soc. Interface
,
12
(
104
), p.
20141367
.
6.
Lau
,
G.-K.
,
Chin
,
Y.-W.
,
Goh
,
J. T.-W.
, and
Wood
,
R. J.
,
2014
, “
Dipteran-Insect-Inspired Thoracic Mechanism With Nonlinear Stiffness to Save Inertial Power of Flapping-Wing Flight
,”
IEEE Trans. Rob.
,
30
(
5
), pp.
1187
1197
.
7.
Chin
,
Y.-W.
, and
Lau
,
G.-K.
,
2012
, “
‘Clicking’ Compliant Mechanism for Flapping-Wing Micro Aerial Vehicle
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), Vilamoura, Portugal, Oct. 7–12, pp.
126
131
.
8.
Boettiger
,
E. G.
, and
Furshpan
,
E.
,
1952
, “
The Mechanics of Flight Movements in Diptera
,”
Biol. Bull.
,
102
(
3
), pp.
200
211
.
9.
Pringle
,
J.
,
1957
,
Insect Flight
, Cambridge University Press, Cambridge, UK.
10.
Dickinson
,
M. H.
, and
Tu
,
M. S.
,
1997
, “
The Function of Dipteran Flight Muscle
,”
Comp. Biochem. Physiol., Part A: Mol. Integr. Physiol.
,
116
(
3
), pp.
223
238
.
11.
Thomson
,
A. J.
, and
Thompson
,
W. A.
,
1977
, “
Dynamics of a Bistable System: The Click Mechanism in Dipteran Flight
,”
Acta Biotheor.
,
26
(
1
), pp.
19
29
.
12.
Brennan
,
M.
,
Elliott
,
S.
,
Bonello
,
P.
, and
Vincent
,
J.
,
2003
, “
The ‘Click’ Mechanism in Dipteran Flight: If It Exists, Then What Effect Does It Have?
,”
J. Theor. Biol.
,
224
(
2
), pp.
205
213
.
13.
Tang
,
B.
, and
Brennan
,
M.
,
2011
, “
On the Dynamic Behaviour of the ‘Click’ Mechanism in Dipteran Flight
,”
J. Theor. Biol.
,
289
, pp.
173
180
.
14.
Pfau
,
H. K.
,
1987
, “
Critical Comments on a Novel Mechanical Model of Dipteran Flight
,”
J. Exp. Biol.
,
128
(
1
), pp.
463
468
.http://jeb.biologists.org/content/128/1/463
15.
Miyan
,
J. A.
, and
Ewing
,
A. W.
,
1985
, “
Is the ‘Click’ Mechanism of Dipteran Flight an Artefact of CC14 Anaesthesia?
,”
J. Exp. Biol.
,
116
(
1
), pp.
313
322
.http://jeb.biologists.org/content/116/1/313
16.
Miyan
,
J. A.
, and
Ewing
,
A. W.
,
1985
, “
How Diptera Move Their Wings: A Re-Examination of the Wing Base Articulation and Muscle Systems Concerned With Flight
,”
Philos. Trans. R. Soc. London, Ser. B
,
311
(
1150
), pp.
271
302
.
17.
Chin
,
Y. W.
, and
Lau
,
G. K.
,
2013
, “
Is Clicking Mechanism Good for Flapping Wing Micro Aerial Vehicle?
,”
Proc. SPIE
,
8686
(86860W), p. 12.https://www.spiedigitallibrary.org/conference-proceedings-of-spie/8686/1/Is-clicking-mechanism-good-for-flapping-wing-micro-aerial-vehicle/10.1117/12.2009627.short?SSO=1
18.
Kok
,
J.
,
Lau
,
G.
, and
Chahl
,
J.
,
2016
, “
On the Aerodynamic Efficiency of Insect-Inspired Micro Aircraft Employing Asymmetrical Flapping
,”
J. Aircr.
,
55
(
3
), pp.
800
810
.
19.
Hilborn
,
R. C.
,
2000
,
Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers
,
Oxford University Press
, Oxford, UK.
20.
Cao
,
Q.
,
Xiong
,
Y.
, and
Wiercigroch
,
M.
,
2013
, “
A Novel Model of Dipteran Flight Mechanism
,”
Int. J. Dyn. Control
,
1
(
1
), pp.
1
11
.
21.
Katz
,
J.
, and
Plotkin
,
A.
,
2001
,
Low-Speed Aerodynamics
, Vol. 13,
Cambridge University Press
, Cambridge, UK.
22.
Fitzgerald
,
T.
,
Valdez
,
M.
,
Vanella
,
M.
,
Balaras
,
E.
, and
Balachandran
,
B.
,
2011
, “
Flexible Flapping Systems: Computational Investigations Into Fluid-Structure Interactions
,”
Aeronaut. J.
,
115
(
1172
), pp.
593
604
.
24.
Lai
,
Y.-C.
, and
Tél
,
T.
,
2011
,
Transient Chaos: Complex Dynamics on Finite Time Scales
, Vol.
173
,
Springer Science & Business Media
, New York.
25.
Grebogi
,
C.
,
Ott
,
E.
, and
Yorke
,
J. A.
,
1983
, “
Crises, Sudden Changes in Chaotic Attractors, and Transient Chaos
,”
Phys. D
,
7
(
1–3
), pp.
181
200
.
26.
Leven
,
R.
,
Pompe
,
B.
,
Wilke
,
C.
, and
Koch
,
B.
,
1985
, “
Experiments on Periodic and Chaotic Motions of a Parametrically Forced Pendulum
,”
Phys. D
,
16
(
3
), pp.
371
384
.
27.
Sommerer
,
J. C.
,
Ku
,
H.-C.
, and
Gilreath
,
H. E.
,
1996
, “
Experimental Evidence for Chaotic Scattering in a Fluid Wake
,”
Phys. Rev. Lett.
,
77
(
25
), p.
5055
.
28.
Tam
,
J. I.
, and
Holmes
,
P.
,
2014
, “
Revisiting a Magneto-Elastic Strange Attractor
,”
J. Sound Vib.
,
333
(
6
), pp.
1767
1780
.
29.
Wolf
,
A.
,
Swift
,
J. B.
,
Swinney
,
H. L.
, and
Vastano
,
J. A.
,
1985
, “
Determining Lyapunov Exponents From a Time Series
,”
Phys. D
,
16
(
3
), pp.
285
317
.
30.
Eckmann
,
J.-P.
,
Kamphorst
,
S. O.
, and
Ruelle
,
D.
,
1987
, “
Recurrence Plots of Dynamical Systems
,”
Europhys. Lett.
,
4
(
9
), p.
973
.
31.
Marwan
,
N.
,
Romano
,
M. C.
,
Thiel
,
M.
, and
Kurths
,
J.
,
2007
, “
Recurrence Plots for the Analysis of Complex Systems
,”
Phys. Rep.
,
438
(
5
), pp.
237
329
.
32.
Grossmann
,
A.
,
Kronland-Martinet
,
R.
, and
Morlet
,
J.
,
1990
, “
Reading and Understanding Continuous Wavelet Transforms
,”
Wavelets
, Springer, Berlin, pp.
2
20
.
You do not currently have access to this content.