Natural Frequency for torsional vibration

In summary, the formula for calculating the natural frequency for torsional vibration of a fixed-fixed beam is =1/2*3.142 sqrt(K*g/mr^2) hz, where K=J*G/L and G=Modulus of rigidity. This equation may need to be adjusted if the beam is changed from fixed-fixed to fixed-free, depending on the assumptions made about the beam's mass and support conditions.
  • #1
har_rai
10
0
I am trying to calculate natural frequency for torsional vibration of fixed fixed beam using following formula.

=1/2*3.142 sqrt(K*g/mr^2) hz

Where K=J*G/L

and G=Modulus of rigidity

g=acceleration due to gravity=386.4 in/se2

m=mass hanging on the beam at distance 'r' from the longitudenal axis

My question is how does the equation above (if its right) is affected if I change the beam from fixed fixed to fixed -free.

thanks
 
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  • #2
I can't verify your equation, but, if the beam is considered massless in this calculation, then the equation for a cantilever beam of length 'r' should apply (I don't have a reference for that equation) since the unrestrained section of the beam suffers no torsional stress, assuming the simply supported end is the equivalent of a supported frictionless rotational bearing.
 

1. What is natural frequency for torsional vibration?

Natural frequency for torsional vibration refers to the frequency at which a system naturally oscillates or vibrates when subjected to an external force. It is determined by the physical properties of the system, such as the mass, stiffness, and damping.

2. How is natural frequency for torsional vibration calculated?

Natural frequency for torsional vibration can be calculated using the formula: fn = (1/2π) √(K/I), where fn is the natural frequency, K is the torsional stiffness, and I is the moment of inertia of the system.

3. What is the significance of natural frequency for torsional vibration?

The natural frequency for torsional vibration is an important parameter in understanding the dynamic behavior of a system. It can help determine potential areas of vibration or resonance, which can lead to failure or damage if not addressed.

4. How does natural frequency for torsional vibration affect the performance of mechanical systems?

The natural frequency for torsional vibration can have a significant impact on the performance of mechanical systems, especially those that involve rotating parts. High natural frequencies can cause excessive vibrations and wear, leading to decreased efficiency and potential failure. On the other hand, low natural frequencies can result in resonance and instability, also affecting performance.

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

Natural frequency for torsional vibration can be controlled by adjusting the physical properties of the system, such as the stiffness and damping. Additionally, adding external dampers or using materials with different properties can also help reduce or shift the natural frequency. Proper design and maintenance can also play a crucial role in controlling natural frequency and preventing potential issues.

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