Hi all,

Many thanks in advance for your help.

My understanding of the dynamic analysis theory is: "Modal Analysis" evaluates the natural frequencies and modes, while "Frequency Response Analysis" gives the response of my system to a dynamic load. The first depends only on the system, the latter also depends on the loads.

Let's carry out a modal analysis: let's calculate a natural frequency. Our system is a cantilever beam.

The formula for natural frequency is:

ω_{n}=√(k/m)

Now, here is a problem. What stiffness should I consider?

- If I consider a concentrated force on the beam extremity, the max deflection is Pl
^{3}/3EI, so I would say that the stiffness is k=F/δ_{Max}=3EI/l^{3}
- If I consider a uniformly distributed load, then he max deflection is ql
^{4}/8EI and so I would consider as stiffness k=ql/δ_{Max}=8EI/l^{3}

So I would get different natural frequencies in the two cases. Is that right?

Question n1:

Did not we say that modal analysis is independent on the load? Does it mean that the natural frequency depends on the type of load? So do I need to know what type of load I am going to apply before evaluating the natural frequency?

However, I carried on with my calculations. I assumed:

length=400mm;E=210000N/mm2; A:4mm2 I=1.33mm4; m=0.0123kg.

and I got:

- for the concentrated load at extremity Tn=2π/ω
_{n=}2π/√(k/m)=2π/√(3EI/l^{3}/m)=0.19s
- for the distributed load Tn=2π/ω
_{n=}2π/√(k/m)=2π/√(8EI/l^{3}/m)=0.12s

Then I used a FEA software, input the same values for l, E,A, etc. and it gave me the results in the picture.

As you can see the results are different from mine, so:

Question n2&3:

- Why FEA gives different results from my calculations? Did I make a mistake in the way I interpret the theory?
- The FEA software did not ask for any loads when calculating these modal frequencies. But previously, did not we say that we need to know the type of load to estimate the natural frequency?

Thank you very much for your great help

1## Re: Natural frequence cantilever Beam