Cantilever Beam Vibration
Cantilever Beam Vibration
(OP)
I have cantilever beam in which I found the modes 1 and 2 by way of FEA (see attachment). How would I go about verifying this by hand?
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Cantilever Beam Vibration
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RE: Cantilever Beam Vibration
RE: Cantilever Beam Vibration
It is not a simple classical cantilever beam.
PERHAPS we could simplify it for order-of-magnitude hand calc by imagining that the center section is flipped past the end to create more of a textbook beam which has roughly twice the length and half the width (of all 3 sections) or original problem.... but it would be very much an open question how close that would be.
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(2B)+(2B)' ?
RE: Cantilever Beam Vibration
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(2B)+(2B)' ?
RE: Cantilever Beam Vibration
RE: Cantilever Beam Vibration
However that system looks like even a moderately skilled analyst could work out the first mode exactly from first principles, assuming constant thickness and that the torsional strength of the bit joining the two is high. I'd guess it would take me a couple of hours.
The first mode is 'almost' a classical beam mode with a 50% reduction in root stiffness.
Another approach would be theory of receptances.
An approach for the second mode would be to work out the mass and moment of inertia of the central tongues, and apply that to the tip of a cantilever, and work out the mode from that. It isn't perfect, it should be close.
Incidentally a front view of each mode shape would be far more informative.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Cantilever Beam Vibration
Which leads me back to my original question? Why? Looking at the image of the structure I figure I could build this FEA model and have many frequencies and mode shapes in less than five minutes. As engineers we often need to balance accuracy against budget and schedule. I would certainly question spending 5 minutes to do an FEA model and then 2 hours of hand calculations to verify it. On the flip side, I would question doing an FEA model of something I could easily figure out within five minutes using a hand calculation. In my mind at least, FEA is not for solving the easily solvable, but for coming up with approximate numerical solutions to highly complex problems that can't be solved easily (or at all) by other means.
In situations similar to this there are a couple of things I might do. Easiest thing you could do is perform a mesh refinement study. Run the model again and again with smaller and smaller elements. If your model is adequately meshed you will see little change in your results between successive iterations. In some cases I might say that I know my results should be between two extremes, so I run the extreme cases to come up with lower and upper bounds on my problem. My results should fall somewhere between the bounds. Another idea along these lines would be to come up with a very simplified and easily solvable model that will give you an idea if you are in the ballpark with your results.
RE: Cantilever Beam Vibration
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Cantilever Beam Vibration
If the consequences of failure are virtually zero then I wouldn't check my work either. Build and break is a very traditional form of design and is quick, informative and fun in the right arena. It also allows you to develop solutions in cases where the optimum is not obvious.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Cantilever Beam Vibration
We can see that the two resonance frequencies are close together - ((3415-3240)/3415)*100 is the relative difference in percent-
This fact can be explained by the theory. Indeed, resonance frequencies only increase with thickness of the beam. Width has no influence on the resonance frequency.
We can think this structure as two beams with the same length, the same thickness and almost the same boundary conditions.
The only difference is the width which has actually no influence.
So the shape of the two modes and the value of the resonance frequencies are quite coherent from a physical point of view.
RE: Cantilever Beam Vibration
I can't follow the rest of your thought process.
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(2B)+(2B)' ?