# What is the Den Hartog Criteria for Tuned Mass Dampers?

• Dustinsfl
In summary, the conversation is about finding a resource that explains the Den Hartog criteria for a tuned mass damper. The Den Hartog criteria is related to the ratio of total mass to damper mass, and there are two distinct masses, M and m, in the system. The conversation also mentions a paper that includes an equation for the ratio and provides figures showing the distinct masses. The person is looking to design a tuned mass damper for a specific system with given mass and natural frequency.
Dustinsfl

## 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?

## The Attempt at a Solution

jedishrfu said:

It has
$$\mu = m/M$$
Is ##M## total mass of the system prior to the damper or is the total mass plus the damper mass of m?

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##.

## 1. What is a Tuned Mass Damper (TMD)?

A Tuned Mass Damper (TMD) is a device used to reduce the effects of vibrations and oscillations on a structure. It is typically composed of a mass, spring, and damper, and is attached to a structure to counteract the motion caused by external forces.

## 2. Who developed the Den Hartog Criteria for Tuned Mass Dampers?

The Den Hartog Criteria for Tuned Mass Dampers was developed by Dutch-American mechanical engineer and physicist, Gustavus Den Hartog, in the 1940s. He studied the effects of vibration in mechanical systems and proposed this criteria to optimize the design of TMDs.

## 3. What is the purpose of the Den Hartog Criteria for Tuned Mass Dampers?

The purpose of the Den Hartog Criteria for Tuned Mass Dampers is to provide guidelines for the design of TMDs to effectively reduce vibrations in structures. It takes into account factors such as the damping ratio, natural frequency, and mass ratio to determine the optimal design for a TMD.

## 4. How does the Den Hartog Criteria for Tuned Mass Dampers work?

The Den Hartog Criteria for Tuned Mass Dampers works by calculating the optimal parameters for a TMD based on the characteristics of the structure it is attached to. By determining the appropriate mass, spring stiffness, and damping ratio, the TMD can effectively counteract the vibrations and reduce their impact on the structure.

## 5. What are the advantages of using the Den Hartog Criteria for Tuned Mass Dampers?

The Den Hartog Criteria for Tuned Mass Dampers offers several advantages, such as providing a standardized method for designing TMDs, improving the effectiveness of TMDs in reducing vibrations, and potentially reducing the cost and complexity of TMDs. It also allows for the optimization of TMDs for specific structures, leading to better overall performance.

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