# Simulation frequency result/analytical mismatch

**1-L7XAXT**Aug 20, 2009 4:03 PM

EDIT:

Problem solved, it was user error. The mass calculation was incorrect (should be mass per unit length not total mass). Doing the frequency calcs in MathCad and not by hand where I could easily keep track of dimensions exposed by mistake. Simulation gives the correct answer now.

Hello,

I'm verifying SW Simulation's capabilities right now and I came up with a problem. I came up with parameters for cantelevered beams that would result in 100Hz in one case and 1000Hz in another case. For the 100Hz beam, the parameters are: length=1m, width=.24491m, height=.122455m. Material is 6061-T6 aluminum.

When I ran this result in Solidworks Simulation frequency analysis, it properly gave me 100.14Hz as the result with the default mesh settings.

However, just to be sure, I created a small beam with the following parameters: rectangular section with width=.00317506m, height=.00158753, length=.07m, also made with 6061-T6 aluminum. When I ran the result for a cantilevered model (one end fixed, no other loads or restraints), simulation came up with a frequency of 265.24 Hz with the default mesh setting, or 2 element thicknesses across the thickness of the beam, and 99.9% of them classify with an aspect ratio < 3. The highest aspect ratio is 4. Increasing the mesh density to the highest allowable doesn't do much. Using a draft setting increases the frequency to around 350hz, but that still isn't nearly right, and is counterintuitive.

This is almost an entire order of magnitude off of the analytical result, which worked nearly perfectly for the other beam.

The equation I am using is from Table 8-1-3 from Formulas for Natural Frequencies and Mode Shape by Blevins:

f_n = y^2 / (2*pi*L^2) * sqrt (E*I/m) where y is the modal constant (for the first mode of a cantilevered beam, y=1.875), L is the beam length, E is the modulus of elasticity, I is the moment of inertia, m is the total mass of the beam.

This equation agrees exactly with the 100Hz beam model.

The reasons I can think that Simulation is not giving the same result are:

1 - There is some tolerance error due to the size of the object in SW

2 - There is a calculation rounding error dude to this size

3 - I have done the calculation wrong (I don't think so, I have checked multiple times

4 - I am missing some fundamental knowledge of vibrations (possible, but I don't think that this is it)

I couldn't find any information on minimum element sizes for SW Simulation, so I'd really like to get this cleared up before I do any real analysis. Meaning, either A: I figure out what I am doing wrong or B: I know limitation on part sizes or relative part sizes so I can determine how to model accordingly.