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Tuned Mass Dampers

Tuned Mass Dampers. a mass that is connected to a structure by a spring and a damping element without any other support,in order to reduce vibration of the structure. Tuned mass dampers are mainly used in the following applications:

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Tuned Mass Dampers

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  1. Tuned Mass Dampers a mass that is connected to a structure by a spring and a damping element without any other support,in order to reduce vibration of the structure.

  2. Tuned mass dampers are mainly used in the following applications: tall and slender free-standing structures (bridges, pylons of bridges, chimneys, TV towers) which tend to be excited dangerously in one of their mode shapes by wind, Taipeh 101

  3. stairs, spectator stands, pedestrian bridges excited by marching or jumping people. These vibrations are usually not dangerous for the structure itself, but may become very unpleasant for the people,

  4. steel structures like factory floors excited in one of their natural frequencies by machines , such as screens, centrifuges, fans etc.,

  5. ships exited in one of their natural frequencies by the main engines or even by ship motion.

  6. SDOF System eigenfrequency: damping ratio of Lehr:

  7. Thin structures with low damping have a high peak in their amplification if the frequency of excitation is similar to eigenfrequency → High dynamic forces and deformations Solutions: Strengthen the structure to get a higher eigenfrequency Application of dampers Application of tuned mass dampers

  8. Strengthen the structure to get a higher • eigenfrequency Eigenfrequency of a beam: Doubling the stiffness only leads to multiplication of the eigenfrequency by about 1.4. Most dangerous eigenfrequencies for human excitation: 1.8 - 2.4 Hz

  9. Application of dampers

  10. Application of tuned mass dampers

  11. 2 DOF System

  12. differentialequations: solution:

  13. linear equation system by derivation of the solution and application to the differential equations:

  14. static deformation: eigenfrequencies: ratio of frequencies: Damping ratio of Lehr: mass ratio:

  15. All lines meet in the points S and T

  16. → → →

  17. Optimisation of TMD for the smallest deformation: → Optimal ratio of eigenfrequencies: → Optimal spring constant Minimize → Optimal damping constant:

  18. Ratio of masses: The higher the mass of the TMD is, the better is the damping. Useful: from 0.02 (low effect) up to 0.1 (often constructive limit) Ratio of frequencies:  0.98 - 0.86 Damping Ratio of Lehr:  0.08 - 0.20

  19. Adjustment: • Different Assumptions of Youngs Modulus and Weights • Increased Main Mass caused by the load

  20. Problem: • Large displacement of the damper mass •  Plastic deformation of the spring •  Exceeding the limit of deformation

  21. Realization

  22. damping of torsional oscillation

  23. 400 kg - 14 Hz

  24. Millennium Bridge

  25. Mass damper on an electricity cable

  26. Pendular dampers

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