Abaqus natural frequency error with a tip mass, values not matching

[boredbot]

I have a simple problem: a cantilever beam with a tip mass of 0.0634 Kilograms has some vibrational response from an impact, and from that data I used a FastFourierTransform to get the natural frequency, which turned about to be 10.5882 Hz. And the beam's dimensions are as follows - L = 0.186 m, B = 0.03 m, H = 0.001 m (a thin beam). So my natural frequency should be sqrt(k/m), where k for a cantilever beam is 3EI/L^3. From the natural frequency obtained from the FFT of the data, we get E as 2.369e11 Pa.

I am supposed to validate this using FEA, but my natural frequency falls way short only when using a 3d solid model. Using a wire model with assigned sections and no mass, and just an inertia at the tip is perfect. But the second I transition to a 3d solid model, it stops working completely.

Here's what I have tried:

1) Assign an arbitrarily low mass density, create a node set, define an inertia > non-structural mass for the nodal set with the tip mass
2) Assign a mass density such that the total mass is the same as the mass of the tip
3) Create a tip mass with an RP and arbitrarily low mass density.


All of them predict my natural frequency to be incredibly low.

Any suggestions as to why this is?

I don't want to create a part on top of the beam with the tipmass, I want the nodes at the end to have some mass, should I look into kinematic coupling?

 

[FEA way]

Double-check the units. A model equivalent to the beam element one (the same section properties and mass at the tip) should work. Point mass/inertia applied to RP connected to the free end of the beam via rigid body constraint or kinematic coupling makes sense.

 

[GregLocock]

Check the spring rate of your 3d solid model

 

[SWComposites]

many solid element types are not good in bending.

run a static analysis of the beam vs solid model

 

[boredbot]

Double-check the units. A model equivalent to the beam element one (the same section properties and mass at the tip) should work. Point mass/inertia applied to RP connected to the free end of the beam via rigid body constraint or kinematic coupling makes sense.

So here's the plan:

1) Double-check my units
2) Create an RP in space such that it matches the Center of Mass for the accelerometer
3) Zero mass density for the beam
4) Kinematic coupling for the RP and the nodeset where the accelerometer is supposed to be sitting
5) Point mass/ inertia on the RP

Good to go? Honestly I'm worried the whole 0 mass density could break things, not too sure how Abaqus handles the mass matrix for these kinda situations

 

[boredbot]

many solid element types are not good in bending.

run a static analysis of the beam vs solid model

I was not aware of this, will do!

 

[boredbot]

Check the spring rate of your 3d solid model

I compared the stiffness values of my 3d solid model by giving an element a simple displacement and then also getting the history output for the reaction forces on that same element. The sitfness was off by a mangtidue and also on the values (so completely wrong)

Not sure whats going on!

 

[boredbot]

I also found an issue in the analytical side of things

So far, I have been experimentally getting my natural frequency and then deciphering the properties using omega = sqrt(k/m)

But this site tells me otherwise:

Axial Vibration Frequency and Transverse Vibration Frequency of the Beam with a Weight

 

[GregLocock]

I expect in the case of the website that is you set m to 0 then it agrees with root(k/M). As to the incorrect stiffness value with the 3d elements, isn't a static test the FIRST thing you do with an FEA model? Or am I just old fashioned?

 

[SWComposites]

isn't a static test the FIRST thing you do with an FEA model? Or am I just old fashioned?

you are old fashioned like me. drives me nuts to read all the various FE related posts on this site where people are diving into complicated non-linear contact, fracture mechanics, non-linear materials models as their very first model. guess the idea of running small test case models is just to boring and simplistic (and not recommended by the random YouTube FE videos). sigh.

 

[GregLocock]

As a sometime test engineer I'd point out that measuring the stiffness of structures is often difficult, whereas the dynamic test (bash it with a hammer and get the frequencies) is amazingly robust. But the reverse is often true when we move into the analytical world.