How does a crack in a free-free bar affect its natural frequency?

So, I'm not sure what the best approach would be.In summary, when trying to find the natural frequency of a free-free bar with a crack located along its length, it is not accurate to assume that each side of the crack is free/excited due to the stiffness of the material at the crack. To get accurate results, a detailed finite element model that includes the crack would be needed. However, this may be complicated if the crack is open and closed during vibration. Thus, it is unclear what the best approach would be for finding the natural frequency in this situation.
  • #1
tony harrison
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0
if a free-free bar has a crack located somewhere along it's length, in order to find the natural frequency of the bar do you split the bar on either side of the crack and assume each bar is free/excited? What would the equation for natural frequency be in this situation?
 
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  • #2
This is an interesting problem. Assuming each side of the crack is free/free is assuming the stiffness of the material at the crack is zero; which isn't true. Are you trying to come up with an general equation for the frequencies?
 
  • #3
To get "accurate" results, you would need to make a fairly detailed finite element model that includes the crack.

This may get complicated, if the crack is open for half of each cycle of vibration and closed for the other half.
 

FAQ: How does a crack in a free-free bar affect its natural frequency?

What are axial natural frequencies?

Axial natural frequencies are the frequencies at which an object naturally vibrates in an axial direction, meaning parallel to its longest axis. These frequencies are determined by the material properties, geometry, and boundary conditions of the object.

How are axial natural frequencies calculated?

Axial natural frequencies can be calculated using mathematical equations based on the object's material properties, geometry, and boundary conditions. These equations can be solved analytically or numerically using computer software.

Why are axial natural frequencies important?

Axial natural frequencies are important in structural engineering and mechanical design because they can help predict the potential for resonance and failure in a structure. They can also be used to optimize the design for specific performance goals.

How can axial natural frequencies be measured?

Axial natural frequencies can be measured using specialized equipment such as a vibration analyzer or accelerometer. The object is subjected to a controlled vibration and the resulting frequencies are recorded and analyzed.

What factors can affect axial natural frequencies?

The main factors that can affect axial natural frequencies include the material properties of the object, its geometry, and the boundary conditions it is subjected to. Other factors may include temperature, applied loads, and changes in the object's environment.

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