Natural Frequency in Finite Element Method

[Hassan2]

Hi all,

A fixed-free bar has a single natural frequency. When we discretize such a bar in the finite element method, then the natural frequencies are the eigenvalues and an nχn matrix where n is the number of the degree of freedom which is usually large. Thus we obtain up to n natural frequencies. I don't know which one of the frequencies is the (nearly) true one. Anyone has an Idea?

Your help would be appreciated.

Edit: I think I was wrong and the natural frequency of the bar depends of the point of force(s).

 

[AlephZero]

A fixed-free bar has a single natural frequency.

No, a real bar also has an infinite number of natural frequencies. You probably have a formula that gives the lowest one. The three lowest bending frequencies of a cantilever are in the ratio 1.0 : 6.27 : 17.55.

The lowest frequencies from a finite element model should correspond to the lowest frequencies of the real bar. Remember the FE program may be also be finding axial and torsional modes, and bending modes in both planes of the beam. It's a good idea to look at plots of the mode shapes to check what they are.

If all the FE model frequencies look completely wrong, a common reason is using the wrong units for the material properties, especially if you are using US units where "pounds per square inch" for Youngs modulus and "pounds per cubic inch" for density are NOT consistent units (unless the FE program let's you input the conversion factor between mass and weight units as a separate input quantity).