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

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A crack in a free-free bar affects its natural frequency by altering the stiffness at the crack location, which cannot be assumed to be zero. To accurately determine the natural frequency, a detailed finite element model that includes the crack is necessary. Simply splitting the bar and treating each side as free may not yield precise results. The behavior of the crack during vibration cycles, whether open or closed, adds complexity to the analysis. Accurate modeling is essential for understanding the impact of the crack on the bar's dynamic properties.
tony harrison
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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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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?
 
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.
 

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