1. AAE 556 Aeroelasticity Lecture 16
Dynamics and Vibrations
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2. Aeroelasticity – the challenge the shapes to come
New systems, vehicles, shapes, environments & challenges
integrating aerodynamics, structures, controls and actuation to create unbeatable systems

3. In the future Future aircraft will be Multi-purpose and robust
Automated and robotic
Semi-to-fully autonomous
Able to change state
Aircraft will be able to
Cope with environmental change, both man-made and due to nature
Self-repair
Use nontraditional propulsion

4. …but the challenges loom large
Conceptual design of highly integrated systems with distributed power and actuation
Redefining aeroelastic stability concepts for structures that lock and unlock, move, stay fixed and then move again
Calculating loads and transient response
Developing test plans for multi-dimensional structural configurations
Assigning risk

5. Low speed and high-speed flutter
Gloster Grebe
Handley Page O/400
X-15
Electra
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6. Unusual flutter has become usual
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7. Flutter is a dynamic instability it involves energy extraction
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8. Understanding the origin - Typical section equations of motion - 2 DOF
Plunge displacement h is positive downward & measured at the shear center xq
measured at the shear center from static equilibrium position
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9. Coupled Equations (EOM) are dynamically coupled but elastically uncoupled
mg = weight xq
xq is called static unbalance and is the source of dynamic coupling
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10. Prove it! Lagrange steps up to the plate
z(t) is the downward displacement of a small potion of the airfoil at a position x located aft of the shear center
kinetic energy
strain energy
LaGrange's equations promise
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11. Kinetic energy integral simplifies
Sq is called the static unbalance
m is the total mass
Iq is called the airfoil mass moment of inertia – has 2 parts
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12. Equations of motion for the unforced system (Qi = 0)
EOM in matrix form, as promised
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13. Diff Eqn. trial solution -separable
Goal – frequencies and mode shapes
substitute into coupled differential eqns.
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14. Purdue Aeroelasticity
The eventual result
Goal – frequencies and mode shapes
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15. divide by exponential time term
But – we have a derivation first collect terms into a single 2x2 matrix
divide by exponential time term
Matrix equations for free vibration
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16. The time dependence term is factored out
Determinant of dynamic system matrix
set determinant to zero (characteristic equation)
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17. Define uncoupled frequency parameters
nondimensionalize
Define uncoupled frequency parameters
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18. Solution for natural frequencies
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19. Solution for exponent s
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20. solutions for w are complex numbers
and
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21. Example configuration
2b=c
and
and
New terms – the radius of gyration
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22. Natural frequencies change value when the c.g. position changes
c.g. offset in semi-chords
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