Modelling of vibration of thin/slender beam

[timspencer22]

Hi everyone,

My name is Tim Spencer and I'm a mechanical engineer currently working on the design of a kinetic sculpture. The sculpture consists of a vertical strip that is vibrated at it's base. The following link shows a video of the sculpture in action

https://www.youtube.com/watch?v=X2mFnXpNBwo

That sculpture was built in the early 2000s and the owner wants to build a larger sculpture - the strip or 'blade' is titanium 6al 4v, fatigue is one of the constrating factors on size. The sculpture in the video is fixed in a cantilever arrangement at its base. I have designed and built a test rig with two simple supports separated by a distance to replace the cantilever clamp. This reduces stress while maintaining the mode shapes of the vibrating strip. The two simple supports are mounted to a frame that is shuttled back and forth at a sinusiodal displacement of amplitude 5.55mm. The frequency of this amplitude is controlled by a crank-arm mechanism driven my an electric motor. The blade on the test rig is carbon steel measuring 1934mm by 200mm by 1.8mm thick. The 'free' length of the strip is 1599mm and the support separation is 335mm.

My question is - how can I model my test rig scenario simply in ANSYS to provide me with stress data that I can verify my test rig strain gauge results with? I've used a MODAL analysis to obtain the frequencies at which the natural modes of vibration occur, and I've tried continuing on with a harmonic response analysis to obtain stress data. The main obstacle I've been facing with harmonic response is that I can only apply sinusoidal loads and pressure but not displacements. If anybody has any suggestions as to how to go about modelling this phenomena in ANSYS I would be extremely grateful!

There are large displacements occuring when the blade is in its natural frequencies so I'm guessing that maybe the non linearity of motion will play a big part in what analysis is used.

Any help (I mean ANY!) would be very much appreciated. More information can be provided if required.

Thanks in advance.

 

[kundalin1]

Hi Tim, cool project.
Take what I'm going to say with caution because I'm talking from memory.
I think there are two solution methods for harmonic analysis: full and mode superposition.
With full method you can use non zero harmonic applied displacements, but with mode superposition you can't, because you cannot apply non zero displacements in a modal analysis.

As for the nonlinearity I don't think you can include nonlinearities in harmonic analyses (I think that prestress and nonlinear contact are treated just as an initial condition, so they are "linearized").
If the large deformation nonlinear effect is important you'll have to go full transient (make your model as small as possible). You can make a very simplified test model with harmonic and then with full transient and compare the results.

 

[meshparts]

Hello,

in addition to what kundalin1 said, I think the damping of the air sourrounding the thin blade plays an important role for the amplitude at resonance. Consider defining some damping (Rayleigh, modal damping or constant damping ratio). You will have to play with these values.

The scientific method in your case is to perform some measurements on the real structure (experimental modal analysis) and validate (tune) your model accordingly. Then model the bigger model based on the damping and material parameters of the smaller structure.

Furthermore the soft ball impacting the blade also damps the system. Hard to model that... Syplify by some spring damper elements?

Regards
Alex



MESHPARTS
Tuning Your Simulation

http://www.meshparts.de

 

[timspencer22]

Thank you for that valuable feedback, yes the air damping plays a significant part and some work has been carried out on this mathematically - but is yet to be completed!