Natural Frequency Hand Calculations Resources 4

[tdo79]

Hi everyone, I am trying to locate some good resources for calculating natural frequencies of some simple structures by hand. Any recommendations would be appreciated. I have been asked to find the natural frequency of a thin plate structure. Through some of the information here I have been able to follow the logic behind a simple canteleaver plate but if I want to make something with two or four plates (like a box girder) using hand calculations I am lost. In the end I will be asked to come up with a quick and dirty model of a gearbox using multiple plates (essentially it will be a box with the bottom surface fixed). The idea would be to vary the plate thicknesses and get the corresponding natural frequencies. To date, the company has no FEA software, as the design and testing of these gearboxes is carried out by the original manufacturer. I am begining to think this is not realistic to do by hand but would like to get a second opinion or at least give it shot before making my recommendation. If you know of any resources that have some worked out examples or if you see the futility in the entire endeavor please let me know, so that I can pass the word along and stop beating my head against the wall. Thanks in advance.

T.

 

[C2it]

Getting the natural frequency of your single plate is a fairly simple task. However, once your create a 3d shape with the stiffness of one side (in your case)affecting the behaviour of another, with the obvious interactions, you will be looking at dozens of potential mode shapes. You could get some guidance from Roark, but I'd be pleading for a decent general FE package right now.

Cheers.

 

[sreid]

Get a copy of Blevins "Formulas for Natural Frequency and Mode Shape."

http://www.amazon.com/Formulas-Natu...2839204?ie=UTF8&s=books&qid=1185292106&sr=1-1

From these formulas you should be able to calculate some approximate natural frequencies.

 

[magicme]

not to be all gloom and doom, but hand calculating the vibrations of an operating gearbox will have no credibility at all.
your post says "bottom plate fixed" so i'm imagining you want the vibrations of a bolted-down gearbox due to misalignment, tooth defects, unbalance, external cyclic loads .... that's some serious stuff there.

i love hand calc's as much as anyone, but this won't work. you'll spend lots of time getting the wrong answers.

magicme





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there's no place like gnome.

 

[GregLocock]

Agree, this is a bit too hard to do by hand. You might like to investigate Calculix if money is the problem, or a cheap Nastran for better usability.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[tdo79]

Hi all,

Thanks for all the information. I had assumed that the model (and the resulting calculations) would not be worth much especially considering the amount of work required but it is much more reassuring to hear it from people with more experience. I will have a look at some of the resources you have suggested and pass along the recommendation to pursue other options or purchase and FEA package. Thanks again.

best regards,

T.

 

[jagad5]

Hand calculations provide a ball park answer in just about any situation. An experienced analyst should be able to bound the natural frequency in any regular geometry situation. Unfortunately, few people are involved in designing regular shapes.

Blevins is the best resource for natural frequency formulas, and I second the recommendation to get a copy. Even if your plan is to use FEA, the insights developed through study will be invaluable for making design improvements. If you understand the theory, you can recommend a change that will be better rather than being forced to try a guess in each direction in FEA because you don't know which way the answer will move when you make a change. These days, just about anyone can run an FEA but a true engineer will be able to tell you what the trend is faster than you can create the model and will recognize a bad answer before your prototype fails a test.

Anther excellent resource on vibration is by Dave Steinberg, Vibration analysis of electronic equipment. GO to Bookfinder.com and search for author = steinberg and title = vibration analysis. As low as ~$20 for used. There is an emphasis on topics related to circuit boards and electronic boxes but vibration theory applies and the examples are great. The chapter on random vibe alone is worth the price.



Doug