vibration on composite floor

huangyhg

vibration on composite floor
good afternoon,
i have a unique problem to ponder. i have a floor system supporting a 29,000 lb piece of equipment. the equipment usually runs at a relatively high rpm (about 2200 rpm) and does have isolators. the equipment rests on two joists 20 feet long that in the end have a second moment of inertia of 5500 in4. (w24x62 with 8鈥?thick concrete slab on top)
when i look at the floor鈥檚 natural frequency (per aisc design guide 11) i end up with a value of 11 hz, roughly. this equates to 660 rpm. the machine will only see this speed as it鈥檚 ramping up. my first instinct is to place a moment of inertia up so high that the frequency is larger than the 2200 rpm of the machine. that value is insanely high and can鈥檛 be done.
i鈥檓 wondering if it鈥檚 ok to use 660 rpm, since the machine won鈥檛 see that value long. anyone else run into this? is there a good reference to look at for this situation? the machine sits on isolators, but the magnitude of force from the vibration doesn鈥檛 seem to be a factor in the general concept. therefore i think i still need to cautiously prepare of this vibration.
are there full height partitions around this piece of equipment (between the edge of the equipment and the end of the supporting beam)?  this will help dramatically, although i am not sure how to quantify it for purposes of your calcs.  
can you space beams closer together in this area since this will likely help with stiffening the floor system.  it probably wouldn't help with an office floor since the frequency comes from a footfall force on a single beam, but i am assuming that this equipment is rather large and can impart its load to several beams.
in addition to partitions, adding mass would help.
not only 660 rpm but also 660 x 2, 660 x 3, 660 x 4, etc.  tie the structural components together,(in both your calculations and in the building), to increase the mass as much as possible.  increasing the moment of inertia is also desirable, (diagonal braces back to the columns and to other beams).  a damping material for the mounts and a second damping component at the connection of the floor/stucture system to the building may attenuate the transmitted energy.  close tolerances for balancing and counter weights will reduce the initial vibration energy peaks.
is this simply a rotating machine of some type, or does it have some impacts or reciprocating motions too?  sounds like it might really belong installed on grade.
sooner or later i'd expect you will get complaints about either the floor vibration, or the machine vibration, or even both.  2200 rpm is 36 hz, and it won't take much floor vibration to create a nice deep audible tone upstairs and downstairs forming standing waves in rooms with dimensions related to 30 feet.  barely detectable/perceptible/feel-able floor vibration will suffice.
simultaneously adding mass and increasing stiffness can result in no net change in resonant frequency.  if you are running well above floor/machine/system resonance then the vibration of the system will be mass controlled, and adding a mere 29,000 pounds will reduce the vibration by half or so, neglecting the floor weight.
increasing stiffness will raise the resonant frequency, but you already indicate that is impossible.
what are these isolators like? rubber biscuits with .25 inch deflection? that just about matched your floor deflection, so your isolators may combine with the floor deflection to form a 2 mass system with exciting vibration results. for any useful isolation of the machine from the floor the isolators need to have static deflection much greater  than the floor deflection (inches, often).  any piping or ducts must not short circuit the isolation.
the machine has internal drums that spin about a horizontal axis.  i鈥檒l find out more about the isolators, i know they help reduce reactions, but i don鈥檛 know if that also affects the frequency of the reduced reactions.
the client has an identical machine on a mezzanine about 20 feet away.  they will never run together, but rather as a redundant system.  they had this monster running the one day.  it felt pretty smooth, you can actually balance a nickel on edge on the actual machine.
i like the idea of bracing the floor beam to the columns, i have also thought about hydraulic dampeners from beam to floor also.  
i've had installations like this where the isolators under the machines do little except attenuate the higher frequency vibrations, but it depends on vibrator installed.  in effect you have two springs in series where the equivalent system takes on the characteristics of the softer spring in particular if there's a significant difference in the spring constants of each.  the softer spring (where there is the most static deflection) is probably the floor system.  it might help if you put in an isolator with more static deflection but that is only one variable in what is becoming a more complicated dynamic model.
for example, if you model this in 2d as a two mass system, one for the machine and another for floor/slab, you will have two vertical frequencies, two horizontal, and two rocking modes.  if there is a lack of symmetry in the structure it may need to be modeled as a 3d problem.  the result is that there are a lot of vibration modes that could be coincident with the operating frequency of the machine or its upper modes.  these are difficult evaluations to do because of the uncertainties involved in dynamic modeling.
this may or may not help because of the assumptions i made in this discussion, but my point is that it can be a complex design problem.  my first goal would be to establish the support is structurally safe including any possible out of balance forces that could develop during the life of the machine or from unusual usage or improper maintenance of the machine.  be aware of natural frequencies of of the structure that the machine passes through during startup and shutdown and the loads from a possible resonance situation.  
regards,
-mike
ahunt,
i have had an installation similar yours.  it was (4) 500hp vertical axis fans that operated between 25 and 55hz, and they were all mounted on isolators. while it was attempted to engineer the structure to avoid the resonant frequency the variables in the system led us to still have resonance at a possible operating frequency.  
i would provide you with (2) suggestions.
desgin into the system connection multiple points for stiffening braces and have them fabricated.  use the braces to "tune" the structure based on how the owner will operate it to give you the least resonance during operation.  you can do that by altering the brace points along the length of the joist. we just did this with a ped bridge as well.  
in addition, the equipment is probably controlled using vfds via a plc and hmi. enter the electrical engineer.  at my fan installation he saved the day.  we were all standing around quite concerned about the resonance and he programmed the fans to never operate at the resonant frequency but only accelerate or decelerate through it.  it worked like a charm!!  the forcing frequency is only resonant for a split second and the structure did not react fast enough. to do that you will need to have them slowly vary the frequency until you find resonance, then program the machine to never run at that speed. hopefully it isn't 2200 rpm or you will need your tuning columns!   
designing in the ability to react to what the structure does will save you time and analysis $$$.