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# Non linear spring with stiffness function of displacement and/or frequency

Valued Contributor

Hi,

1. In a SOL601 I would like to introduce a non-linear lumped spring (eg CBUSH), with the stiffness function of the displacement (eg k(x)=x^2). How can I do that?
2. In a modal analysis SOL103 I would like to introduce a lumped spring, with the stiffness function of the frequency (eg usually the stiffness is frequency indipendent, but I would like to obtain an hardening behaviour such as k(omega)=omega^2). How can I do that?

Regards,

A

6 REPLIES 6

# Re: Non linear spring with stiffness function of displacement and/or frequency

Phenom

1. Define a table with the desired behaviour and allocate to the appropriate k value on the cbush

2. Can’t do that with nx nastran. Might be able with a sensitivity tool/module. You need to do it by hand by changing the appropriate k values and and record the omega value

Production: NX.CAE 9.0.3.4, NX.CAE 10.0.2.6
Development: VB.NET (amateur level !)

# Re: Non linear spring with stiffness function of displacement and/or frequency

Valued Contributor

Dear @selex_ct, more preceselly, where I can set k(x) in the table that you mentioned?

# Re: Non linear spring with stiffness function of displacement and/or frequency

Siemens Phenom

Your image shows the PBUSH dialog with the Nominal Values tab active.

Switch to the Dependent Properties tab. Expand the Nonlinear (bottom) group and define the appropriate table(s).

# Re: Non linear spring with stiffness function of displacement and/or frequency

Valued Contributor

Dear @JimB, I add the force-displacement relation in the appropriate table, but I get the following errors:

```FATAL ERROR
There is no stiffness or damping defined for "CBUSH" elements in mesh "Cbush
Collector(1)::1d_mesh(1)".
Job is not ready to submit to the solver.

ACTION: Edit the physical property specified in the mesh collector to apply a spring
stiffness and/or damping value.

WARNING
There is no orientation specified for mesh "Cbush Collector(1)::1d_mesh(1)".
ACTION: Define an orientation for the mesh in the "Edit Mesh Associated Data" dialog.```

I add the files in order to help me for the debugging phase (it is a very easy model hence it take few minutes).

Thanks a lot!

# Re: Non linear spring with stiffness function of displacement and/or frequency

Siemens Phenom

In this model, you had specified only the PBUSHT force/displacement table. You need to specify the nominal stiffness for PBUSH as well. This will eliminate the first error.

The warning can be ignored since there are only axial frces/displacements. To eliminate the warning, edit the mesh associated data and specify an orientation. For this model, you can simply check the Uniaxial box.

Finally, node 2 is only connected to node 1 with stiffness in the X direction. The other 5 dof are unconnected. You need to define a SPC for DOF 2-6 at node 2.

The attached updated model contains all 3 of these changes and solves without error.

# Re: Non linear spring with stiffness function of displacement and/or frequency

Valued Contributor

Thank you very much @JimB for your very clear explanation!

Last questions are:

1. How do I extract the "nominal stiffness"? Maybe the stiffness linearized around equilibrium position (hence the slope of the first segment in the table)?
2. I do not really understand the meaning and how-it-works the "Uniaxial" and "Enable CSYS override" boxes, can you help me?

Thank you very much for your availability!