Aeroelastic effects

1. Aeroelastic effects Wind loading and structural response Lecture 14 Dr. J.D. Holmes

2. Aeroelastic effects • Very flexible dynamically wind-sensitive structures • Motion of the structure generates aerodynamic forces • Positive aerodynamic damping : reduces vibrations - steel lattice towers • if forces act in direction to increase the motion : aerodynamic instability

3. Aeroelastic effects • Example : Tacoma Narrows Bridge WA - 1940 • Example : ‘Galloping’ of iced-up transmission lines

4. Consider a body moving with velocity in a flow of speed U Relative velocity of air with respect to body = Aeroelastic effects • Aerodynamic damping (along wind) :

5. transfer to left hand side of equation of motion : for small total damping term : aerodynamic damping term Aeroelastic effects • Aerodynamic damping (along wind) : Drag force (per unit length) = along-wind aerodynamic damping is positive

6. From vector diagram : Aeroelastic effects • Galloping : galloping is a form of aerodynamic instability caused by negative aerodynamic damping in the cross wind direction Motion of body in z direction will generate an apparent reduction in angle of attack, 

7. Fz = D sin  + L cos  = Aeroelastic effects • Galloping : Aerodynamic force per unit length in z direction (body axes) : (Lecture 8) For  = 0 :

8. Substituting, For , Fz is positive - acts in same direction as Aeroelastic effects • Galloping : negative aerodynamic damping when transposed to left-hand side

9. Aeroelastic effects • Galloping : den Hartog’s Criterion critical wind speed for galloping,Ucrit , occurs when total damping is zero Since c = 2(mk)=4mn1 (Figure 5.5 in book) m = mass per unit length n1 = first mode natural frequency

10. Aeroelastic effects • Galloping : Cross sections prone to galloping : Square section (zero angle of attack) D-shaped cross section iced-up transmission line or guy cable

11. Consider a two dimensional body rotating with angular velocity Apparent change in angle of attack : Vertical velocity at leading edge : Aeroelastic effects • Flutter : Can generate a cross-wind force and a moment Aerodynamic instabilities involving rotation are called ‘flutter’

12. Flutter derivatives Aeroelastic effects • Flutter : General equations of motion for body free to rotate and translate : per unit mass per unit mass moment of inertia

13. Aeroelastic effects • Flutter : Types of instabilities :

14. U/nd U/nd unstable 2 4 6 0 10 8 12 A1* 3 0 stable stable 2 2 -2 1 1 -4 1 1 2 0 H1* -6 0 10 4 6 2 8 12 H2* 0.4 A2* 8 2 0.3 6 1 0.2 4 2 2 2 0.1 0 0 A -2 -0.1 -0.2 1 Aeroelastic effects • Flutter : Flutter derivatives for two bridge deck sections :

15. Aeroelastic effects • Flutter : Determination of critical flutter speed for long-span bridges: • Empirical formula (e.g. Selberg) • Experimental determination (wind-tunnel model) • Theoretical analysis using flutter derivatives obtained experimentally

16. Aeroelastic effects • Lock - in : Motion-induced forces during vibration caused by vortex shedding Frequency ‘locks-in’ to frequency of vibration Strength of forces and correlation length increased

17. End of Lecture 14John Holmes225-405-3789 JHolmes@lsu.edu