What resonant frequency is sufficient? 1

[flapjack1]

Hi all,

I'm primarily a mechanical design engineer working on a structural engineering problem, so I'm working with a lot of concepts here that I haven't seen since college. I've designed a support frame for a heavy (~5000 lb) scientific instrument, and I've been doing analyses to determine whether my design is sufficient. One thing that I've been looking into is the resonant frequency of the system, i.e. the support structure plus the load on top. I've calculated a value in Hz, but I don't know whether my number is good or bad. Is there a minimum resonant frequency value I should make sure to stay above? Is there a range? Does it depend on the specific details of the system?

Thanks!
fj1

 

[FSB1]

Hi,

If no minimum natural frequency requirement is provided to you, and you are assessing that yourself, natural frequency analysis is not enough.

The analysis you just did only gives you an idea of the dynamic behavior expected from the structure.

Since vibration is of your concern, I recommend you to use a suitable random environment for your structure and evaluate the strength.
Based on this you can re-design the system as necessary by increasing the stiffness in regions the structures fails under the random environment.
You do it by re-iterating on the normal modes analysis of your structure and checking if you suppress the undesired resonance modes.

It is not clear from your question if you are analyzing the frame with the heave instrument, or if you are analyzing only the frame.

 

[GastonLagaffe]

It really depends on your specific equipment - if you contact the manufacturer they should be able to give you info on natural frequency restrictions. If there's no heavy moving parts it may not be an issue.

If it's a matter of measurement sensitivity, it may also be in terms of allowable accelerations, which you could calculate depending on what kind of loading you're expecting. It'll be very different if you're near a busy railroad vs just people walking on the floor. But a 5,000lb super-sensitive scientific instrument sounds very expensive and hiring a vibration consultant is probably a fraction of the cost.

Keep in mind that calculated natural frequencies are almost never even close to the real structure. There's just too many variables at play.

 

[drawoh]

flapjack1,

I have done a lot of design for optics, although nothing that weighs 5000lb.

What will cause vibrations in the vicinity of your system? If you have a forcing function at 60Hz, your structure had better not have a mode at 60Hz.

How will your system fail under vibration? Maybe some or all of it needs to be isolated from vibration?

If your system is vibrated, how much movement can you tolerate? If you know the displacement or acceleration, you can work out the acceleration or displacement.

x(t) = X sin [ω]t
v(t) = X[ω] cos [ω]t
a(t) = -X[ω][sup]2[/sup] sin [ω]t

If you know what the acceptable motion is, you know how stiff your structure must be. My experience with optics has been that if it is stiff enough, I don't need to worry about strength.



--
JHG

 

[flapjack1]

Thanks for the quick responses everyone. Wanted to clarify one thing - the support stand won't be used while any scientific data is being collected. It's only used during assembly and then the instrument is removed before the experiment starts. So the goal here isn't reduction of noise or high frequency vibration, but rather to get a sense of how stable the structure will be - i.e. can we feel 110% confident about crawling under the instrument to work on it while it's resting on this support stand. Two senior engineers/scientists have come up with an estimate for the minimum resonant frequency just based on their experience, but I'm curious to know if anyone on here has any thoughts. Figured I'd hold off on letting you know what their number is and see if anyone else independently estimates something close. Incidentally this will go through a rigorous analysis by experts before it's actually used, but my goal at this point is just to reduce the chances that they find anything to complain about.

Thanks,
fj1

 

[FSB1]

For structure failure you want to do a quasi-static analysis with 1g applied vertically down, together e.g. 0.2g in each in-plane direction, just for safety.
You should use a factor of safety, e.g. F=2, meaning your structure should be able to withstand 2x its weight.

The natural frequency analysis gives you the frequency and shape of the deformation only. The values of displacement provided by the analysis software is just for representation and they don't mean anything, because the normal modes analysis is an eigenvalue problem, and the actual displacement of the structure depends on the nature of the external force applied.
To get the expected deformation of the structure you want to run frequency response analysis, with 1g in applied and extract the displacement of the structure.

However if you want to just have preliminary results, you want to increase the stiffness as much a possible. The higher first natural frequency, the stiffer the structure is.

 

[drawoh]

flapjack1,

If your system must be crawled under safely, you should be concerned about buckling. I can imagine that people will be nervous about crawling underneath a wobbly 5000lb structure. I certainly would be. This has nothing whatsoever to do with resonant frequencies.

Is your instrument pointed at anything? Work out how stiff it must be to remained pointed at stuff while scientists crawl up on it and turn wrenches.

Are there constraints on the size and weight of your structure? Steel is cheap, strong and easy to weld. Use lots of it.

--
JHG

 

[flapjack1]

We've already done a static structural analysis, and the vertical support members are plenty strong enough to support the load. However, that analysis is valid even if the vertical support members have no horizontal cross members connecting them together to make a frame; it's just looking at tensile buckling and compression. This frequency analysis is looking beyond that basic static structural analysis to get a sense of how stable the system as a whole is, taking into account the vertical posts, the connecting cross members, and the load sitting on top.

Interesting that you say that resonant frequency has nothing to do with whether people will be nervous crawling underneath the structure. The scientist I work with who suggested this idea feels differently - that a high natural frequency would give a good sense of stability whereas a low natural frequency would make people nervous. I'm not an expert but intuitively that makes sense to me? Assuming that's correct, my goal here is to figure out where to draw that line between safe high natural frequency and unsafe low natural frequency.

I'm not sure what you mean by if the instrument is pointed at anything. It will just be resting on the support structure, which will be resting on the ground. Unfortunately size and weight are big concerns here (as is cost). This stand will be shipped halfway across the world along with the instrument and everything that goes with it, so size and weight reduction is a ubiquitous desirable. Currently I have this designed from aluminum MayTec profile.

Thanks,
fj1

 

[drawoh]

flapjack1,

As I noted above, I worked in optics. Optics generally are pointed at stuff. Subsystems within the optics all have to point at the same thing. If the optics mount is not rigid, you cannot align anything. Your design problems sound different.

The rigidity of automobile chassis is generally/often rated as a vibration frequency, typically something like fifteen to thirty cycles per second. Higher frequencies would be nice, but cars have to be light, we want space inside, and we want unobstructed doors. Frequency is a convenient way to rate a complex problem. Your scientist may be into hot rods. It sounds to me like your problem is more easily defined.

The collapse of a 5000lb structure on top of somebody, is catastrophic. Your failure mode either is buckling, or the failure of one or more joints. Analyse for buckling and apply a generous safety factor. If you do not have cross-members, you do not have a truss, and your joints must withstand bending moments. Again, analyse your joints and apply a generous safety factor. Make sure your frame assembly is simple, easily assembled, and inspectable. Rigidity is important if your system is aimed at or aligned with something. Your required precision will define your rigidity. Will your frame wobble around as people torque down bolts and screws? If you have 5000lb of stuff, probably not.

How will you be attaching and removing your equipment from this frame? Make sure you understand and if possible, define the procedure. This is when your frame likely will collapse, so this probably should drive your structural analysis. Do some DFMA. Can you fiddle the design so that nobody has to crawl underneath it? Can you do the ergonomics to ensure nobody drops your equipment? Perhaps you need a hoist!

In addition to structural failure, there is the possibility that someone climbing on it will fall off and hurt themselves. Can you eliminate climbing? Can you somehow render the climbing safe, and/or design in safe positions on top?

--
JHG

 

[DayRooster]

This is one of the most complex topics in structural engineering. There are so many factors that can affect the result and it can easily be thrown off if any input is wrong. The general idea is to offset the frequency of machine from the natural frequency of the structure + associated masses enough that the amplitude (typically viewed as displacement) is within a tolerable range. It doesn’t matter if the natural frequency is high or low. It only matters how far offset you are from the machine frequency. Also, the final amplitude/displacement result is heavily dependent upon the offset frequency, structural material, and associated damping factors. I, myself, choose to develop a time-history model within a program like STAAD. Also depending upon the structure type I might need to obtain geotechnical guidance with regards to the soil itself. This allows me to see mode shapes, frequencies and displacements all at the same time.

If this leaves you with more questions than answers then I would recommend training on the topic. ASCE has a three day long course on it taught by professors that specialize in it. Also in my opinion the ASCE course is only a crash course on it. You generally need to do even more research and self training after the course is complete too.

Keep in mind most engineers are not fully versed in this topic and will just tell you to make the structure 3-5 times heavier than the rotating or reciprocating components. But that was the old rule of thumb and knowledge has increased on the topic for the better IMHO.

Overall, I’m glad you are at least talking about it. Best of luck on your analysis.

 

[HS_PA_EIT]

Structural is a different branch of engineering. Maybe consider getting someone who knows structural design to design the structure...
have you considered seismic loads?

 

[kingnero]

Are you validating a static structure using a (natural) frequency acceptance criterium?
Because someone had a value that is expressed in Hz in mind?

 

[flapjack1]

kingnero - that's right, a couple people I work with suggested that if the structure with the load on top has a natural frequency of 10 Hz or higher, that would be a good indication that it will be stable. My hope with this forums post was to explore whether that 10 Hz estimate is reasonable.

 

[drawoh]

flapjack1,

If your system is not subject to vibration, natural frequency is not important. Natural frequency does not affect the stability of anything, unless there is a massive forcing function at the natural frequency.

I have designed systems to be mounted in helicopters. I managed to specify anti-vibration mounts that had a natural frequency of around 8Hz. This was far enough below the helicopter's vibration frequency that it isolated everything, and it was stiff enough that the system did not wobble excessively. Without a good understanding of your system, I am not willing to claim that 8Hz or 10Hz will work for you.

If you don't have vibration problems, don't solve vibration problems. Your support might deflect excessively and/or collapse under load. This defines your stiffness and strength. Don't forget to analyse for when your equipment gets sloppily dropped on to your fixture.

--
JHG