М.Г.Гоман «Численный анализ нелинейной динамики систем», доклад на 1-й конференции Института математики и приложений (IMA) по фрактальной геометрии, г.Лейстер (Великобритания), 19 сентября 2000 года.
M.G.Goman "Computational Analysis of Nonlinear Dynamical Systems ", presentation at the IMA (Institute of Mathematics and its Applications) 1st Conference in Fractal Geometry, De Montfort University, Leicester, the UK, 19 September 2000.
Web Form Automation for Bonterra Impact Management (fka Social Solutions Apri...
М.Г.Гоман (2000 final) – Численный анализ нелинейной динамики систем
1. 21 September 2000
IMA 1st Conference in Fractal
Geometry
1
Computational Analysis of Nonlinear
Dynamical Systems
M.G.Goman
Institute of Mathematical and Simulation Scineces
De Montfort University, UK
2. 21 September 2000
IMA 1st Conference in Fractal
Geometry
2
Contents:
• Nonlinear Dynamics Problems from Aeronautics
- Multi-Attractor Aircraft Dynamics (computational study)
- Aerodynamic Asymmetry at High Incidence (experimental
results interpretation)
• KRIT Toolbox for Nonlinear Investigation and Examples
of its Application
3. 21 September 2000
IMA 1st Conference in Fractal
Geometry
3
Expanding the Frontiers of Flight
• Design objectives:
- stealth, high incidence and agility, larger scale and
lighter structure, active control approach, etc.
• Increasing role of mathematical modelling in design
process
• Integrated, coupled and nonlinear mathematical models
4. 21 September 2000
IMA 1st Conference in Fractal
Geometry
4
The F/A-18A Hornet HARV
Vortex core
Vortex breakdown
5. 21 September 2000
IMA 1st Conference in Fractal
Geometry
5
The X31 aircraft
Enhanced Fighter Maneuverability (EFM) demonstrator
The Herbst Maneuver
V
a=70
T
Thrust vectoring
16. 21 September 2000
IMA 1st Conference in Fractal
Geometry
16
KRIT GUI for Phase Portrait Design
17. 21 September 2000
IMA 1st Conference in Fractal
Geometry
17
KRIT GUI for Continuation
18. 21 September 2000
IMA 1st Conference in Fractal
Geometry
18
KRIT GUI for Numerical Simulation
19. 21 September 2000
IMA 1st Conference in Fractal
Geometry
19
Aerodynamic Asymmetry for X-31
Flight Tests
Data range
Unmodified forebody
Forebody and noseboom
transition strip
Data range
-.10 -.05 0 .05 .10 -.10 -.05 0 .05 .10
20
30
40
50
60
70
80
Angleofattack(deg)
C C
n0 n0
Trust vectoring
Rudder
20. 21 September 2000
IMA 1st Conference in Fractal
Geometry
20
Delay in Asymmetry Onset
Wind Tunnel Experiment
21. 21 September 2000
IMA 1st Conference in Fractal
Geometry
21
Onset of Vortical Flow Asymmetry
Simplified math model
10
20
1 2-1-2
C /l e
b/e
2
a/e
acr
C > 0l
C = 0l
C < 0l
22. 21 September 2000
IMA 1st Conference in Fractal
Geometry
22
Asymmetrical Vortex Breakdown
Water Tunnel Experiment
23. 21 September 2000
IMA 1st Conference in Fractal
Geometry
23
Vortex Breakdown Hysteresis
Water Tunnel Experiment
24. 21 September 2000
IMA 1st Conference in Fractal
Geometry
24
Asymmetry Onset with Vortex Breakdown
Water Tunnel Experiment
x x1 2
1
0.5
0
-0.5
-1.0
Asymmetry of vortex breakdown points at zero sideslip
- "noisy" tunnel
- "quiet" tunnel
1 2X=X -X
Supposed structure
of vortex breakdown
steady states
chaotic behaviour
20 25 30 40 45
Angle of attack (deg)
35
25. 21 September 2000
IMA 1st Conference in Fractal
Geometry
25
Stability of multiple state vortical flow
at the presence of external disturbances
("potential function" analogy)
- level of disturbances
a)
a)
b)
b)
c)
transmitting
chaotic
behaviour
disturbed
stable
flow
disturbed
bistable
flow
c)
supercritical bifurcation
Clav
=0
delay of
asymmetry
onset
26. 21 September 2000
IMA 1st Conference in Fractal
Geometry
26
Double-Well Dynamical System
0.6 0.7 0.8 0.9 w
0.00
0.04
0.08
0.12
f
Periodical predictable dynamics
Fractal stability boundaries
Chaotic dynamics
27. 21 September 2000
IMA 1st Conference in Fractal
Geometry
27
Conclusion Remarks:
• The KRIT Toolbox in Matlab provides a broad range of
numerical procedures and graphical user interfaces
(GUI) for:
- nonlinear aircraft dynamics investigation,
- post-design control laws assessment
- assistance in piloted simulation
• The Toolbox for general nonlinear dynamics problems
is under development
• The work during last several years was funded by
DERA, UK