Slender, Straight Wings Divergence
Improved Modeling
Account for some three-dimensional nature of the
structure and airflow over a finite wing
Model Characteristics
No sweepback
Wing is rigidly fixed at its root
Straight continuous elastic axis, per

Ryerson University
Department of Aerospace Engineering
AER722 Aeroelasticity Project II
Due: November 24, 2014
A two-dimensional, two-degree-of-freedom thin airfoil of unit span and semi-chord b is mounted in a wind
tunnel via spring and damping system as

AER 722 Aeroelasticity
Problem Set 1
1. A rigid wind tunnel model of a uniform wing is pivoted in pitch about the mid-chord. The
model is elastically restrained in pitch by a translational spring with spring constant of 40
kN/m mounted at the trailing edg

Ryerson University
Department of Aerospace Engineering
AER722 Aeroelasticity Project II
Due: November 24, 2014
A two-dimensional, two-degree-of-freedom thin airfoil of unit span and semi-chord b is mounted
in a wind tunnel via spring and damping system as

Ryerson University
Department of Aerospace Engineering
AER722 Aeroelasticity Project I
A cantilever wing model is positioned in a wind tunnel. The span of the model is s = 2m, and its chord
has a piecewise linear variation as shown in the figure. Leading

Aircraft Design
Lecture 10:
Aeroelasticity
G. Dimitriadis
Aeroelasticity
Introduction
Aereolasticity is the study of the interaction of inertial,
structural and aerodynamic forces on aircraft, buildings,
surface vehicles etc
Inertial Forces
Flight Dynami

Unsteady Aerodynamics
aerodynamic forces and moments
calculation for
wings undergoing oscillatory motions
Origin of Unsteady Effects
We can get a good understanding of the origin of the
unsteady aerodynamic effects by considering the simple
case of an air

Introduction to Aeroelasticity
Prof. Hekmat Alighanbari, PhD, PEng
Department of Aerospace Engineering
Ryerson University
Important Note
Please note that the materials posted on the
blackboard are only a preview of the
subjects covered in class.
You nee

Aileron Elastic Efficiency
Elastic efficiency is defined as
E
L
L
L
and using q r
AE
AD BC
and q d
BC
2q
substitute
( E / q ) D A and
0 elastic
We find
E
0 elastic
0 rigid
L
0
2 qA
rigid
E
D
1 q q r
1 q q d
Aileron Elastic Efficiency Cont

Two Dimensional, Three Degree-of-Freedom
Divergence
From the previous aileron reversal analysis divergence
was again given by
qd K (ec 2 sC L )
This is only correct if the flap is rigidly fixed to the airfoil
If the flap is attached via a torsional spr

Wing Aileron Reversal
This is a simple analysis based on the strip
theory aerodynamics
1- rolling power of a rigid wing
U
L
s
p
y1
y
2
L rolling moment
p angular rolling velocity
Wing Aileron Reversal
Strip theory aerodynamic
C L C L C L
CM CMo CM
C L 0

Assumed Mode Method cont.
Multiple-modes
Instead of using just one mode, we can use any
number of modes
As number of modes is increased the estimate of qd will
continually decrease in an asymptotic manner towards
the exact solution
Modes will be added

Static Aeroelasticity
The study of the mutual interactions among
aerodynamic and elastic forces.
Characteristics of Static Aeroelasticity
Time is not an independent variable
Do not have to consider inertia of the system
Steady aerodynamics (zero frequency

Slender, Straight Wings Flutter
Model Characteristics
No sweepback
Wing is rigidly fixed at its root
Straight continuous elastic axis, perpendicular to
the fuselage centreline
The wing will be treated as a cantilever beam with
freedom to move in the

Airfoil Divergence cont.
If C L 0 = C M 0 = = 0
i.e. a camberless airfoil with zero initial AOA
for q < qd , = 0
at q = qd ,
0, 0
1.0
qd q
Compressibility Effect
(subsonic)
Previous analysis was based on incompressible flow for
Mach Number M < 0.3
For

Flutter of a Two Degree-of-Freedom Airfoil
Consider a rigid airfoil of chord c, semi-chord b, mass m and
moment of inertia I flexibly mounted at its elastic axis via a
translational spring kh and torsional spring k as shown.
At this point no mechanical da

Dynamic Aeroelasticity
Unstable (static)
Disp
placement
Displ
lacement
The study of the mutual interactions among
aerodynamic, elastic and i ti f
d
i
l ti
d inertia forces.
Unstable (Dynamic)
time
time
Dynamic Aeroelasticity
Flutter
Buffet
Galloping
Aeroe

Equilibrium and Stability
Consider a ball on three different surfaces.
surfaces
(a)
(b)
(c)
In all three cases the ball is in EQUILIBRUM position
such that
forces =0 and
moments = 0.
Are all the above ball positions STABLE?
(a)
(c)
(b)
Stable: given a sma

Flutter Overview
In this chapter we discuss various
forms of flutter which can occur on
aircraft and the effect of some
parameters on these flutter
mechanisms.
mechanisms
Binary Flutter
We examined the mechanism leading to binary flutter of
the wing tors