me4235 fall 2015 1 student ed
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ME4235
Introduction to Aeroelasticity (ME4235)
Lecture 1
John T. KimNational University of Singapore
Department of Mechanical Engineering
August 11, 2015
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ME4235 Agenda
1. About the instructor John
2. Prerequisites
3. Text books and references
4. Course outline
5. Teaching philosophy6. Grading and class rules
7. Aeroelastic triangle of forces
8. Historical background
9. Aeroelastic tasks in aeronautical industry
10. Simple mathematical description
11. Aeroelastic operators
12. Summary
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About the Instructor John
16.5 years of experience at Boeing Commercial Aircraft.
Specialty: fluid-structure-control interaction, a.k.a.,
Aeroservoelasticity, system identification & reduced-order
modeling, structural dynamics, control of structures, unsteady
aerodynamics, composite structures.
Have taught Computational Methods in Aeroelasticity at
Boeing, NASA Langley, AIAA Conf., NAL Bangalore, India.
Associate Fellow, AIAA (American Institute of Aeronautics and
Astronautics)
Research Associate at GaTech.
Ph.D. from M.I.T. Aero & Astro Dept.
Joined NUS in 2013.
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Prerequisites
ME2134 Fluid Mechanics I ME2114 Mechanics of Materials II
Familiarity with Structure (Vibration, Natural
Modes, Natural Frequencies), Aerodynamics,
(some) Control. Familiarity with Linear Algebra, ODE, PDE.
Some familiarity with airplanes.
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Familiarity with Subjects (Survey)
How many of you are NOT familiar with
Structural Mechanics, Strength of Materials?
Dynamics?
Fluid Mechanics, Aerodynamics?
Linear Algebra?
ODE, PDE? Classical Control Theory?
How many of you ARE familiar with
Structural Dynamics (Eigenvectors & values)?
Calculus of Variation, Energy Methods?
Mechanics of Composite Materials?
Random Processes?
Modern Control Theory?
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Text Books and References
1. Bisplinghoff, R.L., Ashley, H. and Halfman, H.,Aeroelasticity. Dover Science, 1996.
2. Hodges, D.H and Pierce, G.A., Introduction to
Structural Dynamics and Aeroelasticity, Cambridge
University Press, 2011.3. Y.C. Fung,An Introduction to the Theory of
Aeroelasticity, Dover, 1994.
4. Wright, J.R. and Cooper, J.E., Introduction to Aircraft
Aeroelasticity and Loads, John Wiley & Sons, 2008.
5. Dowell, E. H., A Modern Course on Aeroelasticity,Kluwer Academic Publishers, 1989.
6. Craig, R.R., Structural Dynamics: An Introduction to
Computer Methods, John Wiley & Sons, 1981.
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Course Outline
1. Introduction (0.5 wks)2. Structures & Structural Dynamics (3 wks)
3. Aerodynamics (2 wks)
4. Static Aeroelasticity (2 wks)
5. Flutter (3 wks)
6. Gust Response (1 wks)
7. Miscellaneous TopicsAeroservoelasticy, Nonlinear
effects, Experimental Methods, etc. (1.5 wks)
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Grading and Class Rules
HW (50%)+Mid and Final take home (50%).
Students are allowed to work together on HW but the
final work must be individuals effort.
Students are NOT allowed to work together on take
home quizzes.
Attendance is important.
Be diligent in taking notes!
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Teaching Philosophy
Questions are always welcome!
The only stupid question is question not asked.
Understanding the underlying physics is most important.
There will be plenty of mathematics but it is only used as
a tool, is not the end itself.
My class is not a series of seminars, so please do not
expect beautiful, sophisticated slides.
Will present equations on slides, but oftentimes derivethem on whiteboard.
Will try to strike a good balance between physics and
real applications.
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Lessons of Space Shuttle Columbiadisaster (Feb. 2003)
Only engineers and scientists with solid physical
backgrounds can prevent the disasters in the sky!
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AerodynamicForce
InertiaForce
ElasticForce
Flight DynamicsStability
StaticAeroelasticity
Mechanical
Vibration
Dynamic Aeroelasticity(Structural Dynamics)
Flutter Gust Loads Buffet
Aeroelastic Triangle of Forces
Aeroelasticity is a study of structure and aerodynamics, how they interact each
other, how the airplane responds under the fluid-structure interaction, how such
an interaction creates detrimental (or benign) effects on the design and
performance of the airplane, and can lead to a potential failure of the structure.
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Aeroservoelasticity
Aeroservoelasticity includes the effect of flight control
systems.
Auto-pilot, ride control, flutter suppression, gust andloads alleviation, etc.
NOTE: Most of airplanes nowadays have fly-by-wire
controls.
Flexible Airplane Dynamics
SensorInputs
Automatic Flight Control System
Control Surface Motion
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Topics in Aeroelasticity
Topics covered: Divergence, load distribution, controlsurface effectiveness, flutter, gust response, random
loads, aerodynamic forces on wings, wind effects on
buildings, aeroelastic tailoring, aeroservoelasticity,
nonlinear effects, experimental methods and flutter
testing. Static divergence and flutter are the most critical issues
and FAA specifically demands all airplanes be free of
them.
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ME4235 What is Flutter?
Flutter:A rapid self-feeding motion, potentially destructive,excited by aerodynamic forces, in aircraft structures,control surfaces and bridge engineering - Wikipedia
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ME4235 continued
http://www.youtube.com/watch?gl=SG&hl=en-GB&v=m686UO68AXI
Tacoma Narrow Bridge Collapse (Tacoma, WA USA, 1940):
http://www.youtube.com/watch?v=xox9BVSu7Ok
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ME4235 continued
Glider in flutter:
http://www.youtube.com/watch?v=kQI3AWpTWhM
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Historical Background
Samuel P. Langleys failed launch of Large Androme A on the
Potomac River (1903)torsional divergence in the wing.
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continued
The Wright brothers utilized warping of the wings to achieve
lateral control (1903).
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continued
Handley Page 0/400 bomber experienced an antisymmetric tail
flutter caused by lack of a torque tube connecting both sides of
elevators (WW I.)the first official record of flutter.
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continued
Fokker D-8 experienced both static wing divergence and wing
bending-torsion flutter.
Read B.A.H. Ch. 1
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theoretical development ( continued)
1. Hans Reissner (1926)theory of wing-load distribution andwing divergence.
2. Roxbee Cox & Pugsley (1932)theory of loss of lateral control
and aileron reversal.
3. Glauert, Frazer, Duncan, Kussner, and Theodorsen (1920-30)potential flow theory for flutter prediction
4. Finite element, computational fluid dynamics (CFD),
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Is Aeroelasticity Still Important?
Yes! As modern aircraft is designed to be lighter, bigger, and more
flexible, Aeroelasticity has become the most critical issue in
aeronautical engineering. Furthermore, addition of control
systems complicates the things, and requires understanding of
Aeroservoelasticity.
A380
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Aeroelastic Tasks in Aeronautical Industry
Static Loads
- static aeroelastic Flutter
- open-loop flutter
- closed-loop flutter
- LCO with nonlinear free-play
- LCO with nonlinear controller
Dynamic Flight Loads
- PSD (linear), TDG (linear & nonlinear)
- Monte Carlo (nonlinear)
Ground Loads
- gear & taxi loads
Engine and Vibration- engine vibration, wind milling, etc
Methods Development (R&D)
NOTE: LCOLimit Cycle Oscillation
http://www.google.com.sg/url?sa=i&source=images&cd=&cad=rja&docid=gL6Y8R4h1YfS6M&tbnid=s7tUwhDOB0Tx8M:&ved=0CAgQjRwwAA&url=http%3A%2F%2Fwww.aircraft-commerce.com%2Fconferences%2FMIA%2FSpeakers.asp&ei=PcAJUsKeKsf_lAW9qoDIDg&psig=AFQjCNF3ttbDKm1MPjuT7ZTnr8Ezaqa0dA&ust=1376457149755295http://www.google.com.sg/url?sa=i&source=images&cd=&cad=rja&docid=fn2AtZSuNw1caM&tbnid=En6DSP7soufMPM:&ved=0CAUQjRw&url=http%3A%2F%2Flogoshistory.blogspot.com%2F2010%2F12%2Fall-boeing-logos.html&ei=578JUq7jMcqfiQfv44CICw&psig=AFQjCNHcDzLY9C-7SPUyFN5kj4WfX7-b9Q&ust=1376457055484275 -
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Functions of the Flutter Engineering Group
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Flutter Design &
Certification
Testing
Wind Tunnel Flutter ModelsGround Vibration Testing
Flight Flutter Testing
Components Testing
Flutter AnalysisDesign and Certification
Analysis of Flutter Models
Analysis of Flight Test Airplanes
Others
Others
Fleet Support (service bulletins)Research: Methods and Process
Program planning
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ME4235
The coupled fluid-structure can be thought of as aplant(structure) with feedback loop (fluid) and thedynamic pressure as the gain factor.
Aerodynamics
Structure
qdynamic pressure
wing motion
(output)
aerodynamic
force (input)
Simple Mathematical Description
(plant)
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ME4235
Coupled!
Coupled Fluid-Structure is hom ogeneous , self-exci tedsystem.
2
21
pressuredynamic
V
q
coupled equation ( continued)
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ME4235 dynamic instability ( continued )
et
0
XX
00)( XXA q
i
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ME4235 mode tracking of 2D airfoil (continued)
Root locus plot:
V-g plot:
o
ox
x
V VVf
g(damping)
(freq.)
oPlunging (h) @ V=0Pitching (a) @ V=0x
x
x
o
oRe
Im
V increasing
a
h
Unstable
Unstable
Stable
Stable
V
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Creativity is Intelligence Having Fun.
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Concept of Aeroelastic Operators
Can see unifying features of aeroelasticity by introducing
aeroelastic operators:
3 types
Operators operate on deflectionto produceforces.
a) Structural Operators
Linear Spring:
can writewhere
Inertial
cAerodynami
Structural
kx
koperator,structural
xdeflectionq
FforceQ
)S(
,
,
(q)Q S
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continued
operatormatrixsquarek
matrixcolumnqq
matrixcolumnQQ
ij [)S(
:]
:}{
:}{
Elastic body in finite d.o.f.:
Continuous beam:
}]{[}{ qkQ ij
)('''' beamBernoullipIw
operatoraldifferentidx
dEI
wq
pQ
)S( :4
4
d
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continued
There are also Inverse Structural Operators
Spring:
Elastic body:
Continuous beam:
Inverse operators operate on force to obtain deflections
(Q)q -1S
/
kF
1
/
1
)(
][][)(
}{][}{
11
1
ijij
ij
ck
Qkq
S
peratorintegral odxc
functionnelcdpxcw
l
l
)(S
(
:),()(
)ker)(),(
0
1
0
i d
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continued
b) Aerodynamic operators
2D section in steady flow:
=1
22
( . )
can write
where
,
,
=1
2
2
(q)Q A
i d
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continued
can write
where
,
,
1 1
1/2
NOTE: Inverse operators often convenient in Aerodynamics.
(Q)q-1
A
i d
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continued
More general wing:
where
Also,
V
caupwash
V
wq
V
cadiffpress
q
p
Q
a
a
.@
2/1
0
)V
w(
q
p aa A
0
)qp(
Vw aa
0
1-A
ti d
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continued
c) Inertia operators
For concentrated mass:
can write
where
2
2
)(
,
,
dtdmeratorinertia op
xdeflectionq
FforceQ
)I(
(q)Q I
2
2
dt
xdm
ti d
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continued
Application to Aeroelastic Problems
Force acting on structure:
May then write (DAlmebertsPrinciple):
esdisturbancexternalgivenQ
inertiaQ
caerodynamiQ
D
I
A
ADTOT QQQQq )(
DQqqq
or
)()()( IAS
ti d
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continued
S
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ME4235 Summary
Aeroelasticity deals with interaction betweenaerodynamics and structures and hence covers a broad
spectrum of topics that are critical in design, analysis,
and testing of airplanes, lifting surfaces, bridges,
buildings, etc.
It would not exist if structures were perfectly rigid. It requires a comprehensive understanding of fluids and
structures, how they interact. It also requires system
engineering perspective because it is truly an
interdisciplinaryfield. In aeroelasticity, structure is the plant subjected to forces
created by aerodynamics and external loads.