# Discussion Forum

## How do you know which resonant frequency of the cantilever is the proper one?

 Topics: 4.3, 4.2a, 4.2, Structural Mechanics
RSS feed   |   Turn on email notifications   |   5 Replies   Last post: October 17, 2012 10:53am UTC

Wenqi Deng

October 12, 2012 2:55pm UTC

How do you know which resonant frequency of the cantilever is the proper one?

Hi, everyone.
I'm quite confused. It's a rectangular beam,with one end fixed. Then I do the eigenfrequency study. When I apply different mesh method to the beam, for example, first I use Free Tetrahedral mesh to simulate.Then,in the second study, I use Free Triangular mesh on the bottom boundary and swept the whole domain. The difference of the resonant frequency between two study is about 70000Hz. Is this usual? The resonant frequency of the cantilever with same size and material should be the same right?

Nagi Elabbasi
Certified Consultant
Veryst Engineering

October 12, 2012 5:43pm UTC in response to Wenqi Deng

Re: How do you know which resonant frequency of the cantilever is the proper one?

Yes, the frequencies should be the same. Also when comparing the difference between models it is better to look at the ratio, not the absolute difference.

When a beam is modeled with 3D solid elements you need to be careful with mesh density. Specifically you should have multiple elements through the thickness of the beam. If the beam has a high aspect ratio (length/thickness) that may require non-uniform meshing like the sweep you mentioned.

You should also make sure you are using quadratic (not linear) elements as they are much better in bending. Quadratic elements are the default in solid mechanics in COMSOL so if you haven’t changed it you should be fine.

Nagi Elabbasi
Veryst Engineering

Wenqi Deng

October 15, 2012 9:43am UTC in response to Nagi Elabbasi

Re: How do you know which resonant frequency of the cantilever is the proper one?

My cantilever is a 3D rectangular beam, and the beam has a high aspect ratio. Therefore, it is better to use sweep mesh than free tetrahedral mesh? What's the advantage of using sweep mesh?

What do you mean by when comparing the difference between models it is better to look at the ratio, not the absolute difference?

Sometimes, I found that the frequency I got from eigenfrequency study is a complex value. Does it represent different mode?or I should abs() it to get the actural frequency?

Regards,

Wenqi Deng

Nagi Elabbasi
Certified Consultant
Veryst Engineering

October 16, 2012 5:25pm UTC in response to Wenqi Deng

Re: How do you know which resonant frequency of the cantilever is the proper one?

Hi Wenqi,

I think a sweep mesh gives you better control over meshing so you can make the elements small in the beam cross-section and much bigger along its length. You can probably do something like that without sweep but I find it much easier that way.

Regarding absolute or relative differences, you had mentioned that there was a 70kHz difference in frequencies. If one frequency was 30kHz and the other 100kHz that’s a big deal but if one was 800kHz and the other was 870kHz it’s not as big a deal.

Finally regarding complex values, there should not be present in the eigenfrequencies unless you have damping. Since you probably have no damping check if the imaginary parts are very small. If they are then they are probably due to numerical round-off errors and can be neglected. If not then the solver may not have converged.

Nagi Elabbasi
Veryst Engineering

Wenqi Deng

October 16, 2012 8:44pm UTC in response to Nagi Elabbasi

Re: How do you know which resonant frequency of the cantilever is the proper one?

Hi Nagi,

In my model, I carry out a time-dependent study to use a piezo block to activate the vibration of the cantilever. When I use the resonant frequency I got from eigenfrequency study as the activating frequency to apply a sinusoidal voltage to the piezo, the displacement of the cantilever should be the highest, right? but I seem not to see much difference when I use some other frequencies around the resonant frequency. In this case, does it mean that the resonant frequency of cantilever I got from eigenfrequency study is not right?

Regards,

Wenqi Deng

Wenqi Deng

October 17, 2012 10:53am UTC in response to Nagi Elabbasi

Re: How do you know which resonant frequency of the cantilever is the proper one?

Hi Nagi,

I got the displacement of the cantiliver while I use 81503Hz (resonant freq) and 150000Hz to activate the piezo respectively,but the peak(valley) of the displacement is quite the same. It should not be like this, as the resonant freq should provide larger displacement. Am I right?

Thanks a lot.

Regards,

Wenqi Deng

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