# Torsional Vibration Natural Frequency & Nodal Position

• SeaMist
In summary, the conversation discusses an exercise involving the calculation of the natural frequency of a 3-mass system. The system is supported by bearings and the problem includes determining the natural vibration frequencies and nodal positions using a graphical method. The participant has successfully calculated the natural frequency and nodal position, but is having difficulty understanding the physical meaning of the graphs obtained. They request help in interpreting the graphs and any other comments or points on the solution.
SeaMist
Hi

I was doing an exercise of calculating the "natural frequency" of a 3-mass system. The problem is like:

A shaft has three inertia on it of 6, 4 and 10 kgm2, respectively viewed from left to right. The shaft connecting the first two is 2.6 m long with a stiffness of 12 x 106 Nm/radians and the shaft connecting the last two masses has the length of 2 m and a stiffness of 10 x 106 Nm/radians. The system is supported in bearings at both ends. Ignore the inertia of the shafts and find;
a. The natural vibration frequencies of the system;
b. Locations of the nodes by using a graphical method;

I have calculated the natural frequency of the system and the nodal position alright, but I have difficulty conceptualising/ understanding the "Physical Meaning" of the graphs that I have obtained.

I would alsp appreciate if some one can help me understanding the physical meaning of the graphs attached, and also any interpretation of the graphs.

Thanks
SeaMist

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The first plot looks like mode shapes. However, without units or descriptions on either plot, it's tough to say what you have. The second looks like some kind of displacement plot. Did you normalize it by chance?

Apologies for the late post, got stuck up with some asignments. I am posting the solution graphs for the problem described in the original post.

The units are;
Torq = Nm
Angles (alpha, beta, gamma) = rads

What can we interpret from the graphs that we have obtained from the solution?

Would much appreciate the comments and point.

Thanx

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• a.JPG
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• b.JPG
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• c.JPG
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forgot to attach the graph that deterimes the nodes.

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• d.JPG
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## 1. What is torsional vibration natural frequency?

Torsional vibration natural frequency is the frequency at which a rotating system naturally vibrates when subjected to a twisting force. It is determined by the stiffness and moment of inertia of the system.

## 2. How is torsional vibration natural frequency calculated?

Torsional vibration natural frequency can be calculated using the formula: f = 1 / 2π * √(k/I), where f is the natural frequency, k is the torsional stiffness, and I is the moment of inertia.

## 3. What factors affect torsional vibration natural frequency?

The main factors that affect torsional vibration natural frequency are the torsional stiffness and moment of inertia of the system. Other factors such as material properties, damping, and external forces can also have an impact.

## 4. What is the significance of nodal positions in torsional vibration?

Nodal positions in torsional vibration refer to points where there is no movement or minimal movement in the system. These points are important as they help to determine the natural frequency and mode shapes of the system.

## 5. How can torsional vibration natural frequency be controlled?

Torsional vibration natural frequency can be controlled by adjusting the stiffness and moment of inertia of the system, as well as by using damping techniques such as viscoelastic materials or tuned mass dampers.

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