What is the Den Hartog Criteria for Tuned Mass Dampers?

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SUMMARY

The Den Hartog criteria for tuned mass dampers are essential for designing effective vibration control systems. The criteria define the mass ratio, represented as $$\mu = m/M$$, where $$M$$ is the total mass of the system excluding the damper mass $$m$$. In the context of the discussion, the user is designing a tuned mass damper for a system with a total mass of 55 kg and a damper mass of 5.5 kg, with a natural frequency of 12.061 rad/s and a forcing function frequency of 183.26 rad/s. Understanding these parameters is crucial for achieving optimal damping performance.

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  • Understanding of tuned mass dampers and their applications in vibration control
  • Familiarity with the Den Hartog criteria and mass ratio calculations
  • Knowledge of natural frequency and forcing function concepts
  • Basic principles of mechanical vibrations and dynamics
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  • Learn about the calculation of natural frequencies in dynamic systems
  • Research the application of the Den Hartog criteria in real-world engineering scenarios
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Mechanical engineers, structural engineers, and students involved in vibration control and dynamic system design will benefit from this discussion.

Dustinsfl
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Homework Statement


I have been searching online but I am unable to find a site that explicitly states the Den Hartog criteria for a tuned mass damper.

What is the Den Hartog criteria?

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The Attempt at a Solution

 
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Look at figure 1, it shows M and m are distinct masses so M is not in fact M+m
 
jedishrfu said:
Look at figure 1, it shows M and m are distinct masses so M is not in fact M+m

I am not sure on how I would design a tuned mass damper from the paper though. I am trying to design one for a system with ##M = 55## kg and a tuned mass damper weighing ##5.5## kg. The natural frequency of the system is ##\omega_n = 12.061## and the forcing function has ##\omega = 183.26##.
 

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