1. Order-Tuned and Impact Absorbers for Rotating Flexible Structures

2. Background Self-tuning Impact Damper Tuned Dampers Sleeves Chamber & End Caps Turbine Blade

3. Order-Tuned Vibration Absorbers –Den Hartog, Denman, Shaw et al., Borowski, Duffy, … Impact Absorbers –Caughey, Masri, Shaw, Brown & North, Duffy, … Vibration Characteristics of Bladed Disk Assemblies –Many,… Relevant Previous Work

4. Order-Tuned Vibration Absorbers Idealized Model IMPACTS

5. Mathematical Model Model Features

6. Mathematical Model

8. Linear Isolated Absorber Response y

9. Free Linear Response Frequencies versus Rotor Speed Blade Frequency Engine Order Absorber Frequency Natural Frequency Resonance Zone

10. Linear Response Engine Order

11. Linear Response The Effects of Detuning

12. Linear Response The Effects of Detuning

13. Linear Frequency Response

14. Impact Response – Single Sector Ideal Collision Model y x y

15. Impact Response Typical Steady-State Response – Absorber (y) and Blade (x) Phase Planes x = Blade y = Absorber Impacts

16. Impact Response – Single Sector Impact Force Threshold vs. Rotor Speed Impacting Non-Impacting f* 

17. Impact Response Impact Force Threshold vs. Rotor Speed Impacting Non-Impacting f* 

18. Periodic Impact Response Analytical Results vs. Rotor Speed Blade Displacement Absorber Velocity At Impact Stable Unstable W/ Absorber W/O Absorber  

19. Impact Response Blade Displacement and Absorber Velocity vs. Rotor Speed Grazing & Chaos “Simple”   x MAX Blade Displacement Absorber Velocity At Impact

20. Impact Response Sample Response Transitions Simple Chaos Near-grazing

21. Impact Response Interesting Chaos Observed Blade Time Response Blade Poincare Map Chaotic Envelope

22. Impact Response Absorber Parameter Design Charts x MAX vs. force amplitude Vary Increase  Decrease e

23. Summary Non-impacting Response –Absorbers effective –No-resonance zone Impacting Response –Absorbers reduce resonance –Chaos near resonance, but still effective –Absorber parameters: e, , tuning Acknowledgment: Funded by NSF CMS-0408866

24. Directions for Future Work Non-impacting Response –Effects of Damping –Effects of Imperfections –Parameter Studies –Multi-mode sector models Impacting Response –Parameter Studies –Multi-sector analysis –Multi-mode sector models Experiments