Natural Frequency of a structure and foundation. 1

[bsrd]

I have been designing a structure to support a 10,000lb. vibrating conveyor that generates approximately 800lb. horizontal load and the frequency of the equipment is 9.5 Hz. The equipment sits approximately 20ft above the ground.

To keep the structure from resonating the frequency of the support structure has been kept 10 percent away from the 9.5 Hz. Is it better to keep the frequency 10 percent above or below the frequency of the equipment?

I have been using RISA 3d to determine the frequency of the structure. If the structure will be sitting on a concrete slab what is the best way to determine the affects of different slab thickness? Specifically how does this change the frequency. To determine the frequency of the structure and the slab the slab can not have any springs; would modeling the slab as two way with just edge supports be a good way of modeling this? Is there a minimum frequency of the slab and structure that should be maintained?

 

[JoshPlumSE]

The slab can have springs.... just not compression only springs.

Think of it this way, when the structure is subject to light dynamic loading then the amplitude of the deflection is minor enough that the foundation will will always be in contact with the soil. So, a regular two-way spring is perfectly valid. You will get a good natural frequency of the structure for this case using the two way springs.

When the amplitude of vibration is very large (and the structure goes into partial uplift), then some springs would be active and others would not be. You could get some results for this with a non-linear time-history analysis maybe. But, the problem is that the natural frequency would vary with the amplitude of vibration.

 

[aggman]

In regards to the natural frequency range the answer is that it depends. If you are above the range, additional mass (material transferred, etc.) will lower the frequency and could bring it right into play. If you are lower than the added mass will not hurt you, but it will pass through it on start-up and shut-down causing some moving around. Furthermore I would strive for more than 10% variation. You will have to be a really good modeler for things to be that close on the vibration side. We typically push for 50%, but don't always get there.

 

[KootK]

If you go with a lower frequency, will the machine have to pass through it as it starts up?

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[bsrd]

Thanks JoshPlum, I wasn't thinking of that because I was just thinking that part of the slab would be in tension or lifting, but this is not the case.

Aggman,

The material coming through the is recycled plastics and may amount to about 120 lbs

The way I modeled it with a 22" slab supporting the structure I am getting a natural frequency of about 5.5 or about 42 percent less than the equipment. Now I need to ask myself am I a good modeler. I modeled the bracing members pinned to the main columns and connected concentrically. If I spend the time of offsetting the ends of the members according to the actual connection details will this greatly affect my frequency?

Should the additional movement stop after the frequency of the machine passes through the frequency of the structure during start up?

 

[aggman]

bsrd,
It would be pretty common to have the structure pass through the natural frequency during start up and shut down. It will shake for a few moments, particularly on shut down as it is a coast down process. The start up will be more or less non-existent. I would take the time to verify that the natural frequency of the screen does not match up with your structure. The manufacturer should be able to give you the resonant frequency of the spring system. If that and your structure match up it will get a little hairy...

 

[KootK]

I think that you can pick which side of resonance you want to be on and then make modelling choices that would tend to push you closer to resonance. Other things being equal, more flexibility will result in a longer period. In this respect it's easier to work with a period longer than resonance because it's fairly simple to create a model that comfortably overestimates stiffness.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[WARose]

First off, I don't know that 10% above or below one of the natural frequencies is a big enough difference. Usually I shoot for the ratio to be 1.4 or greater (for a "low-tuned" structure) or about 0.7 (for a "high tuned" structure). But in many cases that it's unavoidable: as others have pointed out, one of the frequencies of your structure (there will be one per mode) will probably have significant mass participating during the transient phase of motion (during start-up). What you are looking to avoid is the steady state motion having high amplitude. (As far as what is preferable, it's probably "low-tuned" because it tends towards lower dynamic amplitudes.)

Speaking of that, I don't know that comparing frequencies alone will be satisfactory. (I know in many instances equipment manufactures give certain guidelines but they often don't know enough about what will be supporting the equipment or Structural Dynamics to say much else.) In many cases, I have designed a structure and overall the frequency ratios (for the whole structure) compared favorably to the forcing function but individual members were shaking like crazy. So it's probably best to do a Time-History analysis in something like STAAD to get the whole picture. (I'm not sure what RISA's capabilities are there so I cannot comment.) As far as to the impact of the thickness of the slab (which I assume is your foundation) on frequency......I really could not say. I'd shoot for the total mass of the supporting structure to be at least 5 times the mass of the supported equipment. One of the most critical aspects of that however will be your dynamic spring constants which you will need from the Geotechnical engineer. In most instances he has to take some specific measurements out there to come up with an accurate value of that.

By the way for the concrete members of this supporting frame (including the slab), I'd check and see what the effective moment of inertia is and use those values (typically I do that by adjusting those members modulus of elasticity). And I don't understand what you mean when you say you can't get a frequency from a system with springs. Is this a limitation of RISA?

I know this is broad but I hope it helps.

 

[JoshPlumSE]

I've not worked on conveyors much as I never work on a mining / metals project. So, I don't know typical practice for their dynamic loading. But, typical heavy industrial (petroChem or Power) equipment is done in one of a few ways:

Heavy Reciprocating Compressors: You just have to do a time history analysis. They start up slowly and will typically pass through the natural frequency of structure as you ramp up to the normal operating frequency. Therefore, you need the analysis to demonstrate that they pass through quickly enough that it doesn't damage the structure...or that the displacement stays small enough that the equipment still operates properly.

Well Balanced Rotating Fans and relatively light equipment: This equipment starts up very quickly and achieves its operating system before any significant resonance can occur (if the structure natural frequency is lower than the equipment's operating frequency). For these cases, it is normal to just look at the natural frequency of the support structure and make sure that it is not within a certain percentage (10 or 20% in my experience) of the natural period of the equipment.

Heavy Turbine Generators for power plants: This is another case where you just have to do a time-history analysis. Not so much for stress, but rather for deflection. You want to make sure the structure never vibrates enough to cause issues with the equipment operation.

Personally, I would think that conveyors would be somewhat closer to the well balanced fans. But, at a much lower frequency. I do see a lot of conveyor models in RISA-3D tech support. So, I suspect that's what most people are doing. That's still a guess, of course. But, hopefully an educated one. I imagine that you would occasionally get some larger forces than you'd get for a fan. That's based on material being added/ crushed or shifting suddenly. However, I don't know that this would be truly harmonic. Just my 0.02$