Vibration from machinery on steel platforms 1

[aligorsi]

I was looking at AISC Design Guide 11 for checking my structures for vibrations. I deal with machinery with constant RPM so as per the categorization in the Design Guide, my case is that of "Harmonic or sinusoidal loads". However, the design guide only deals with vibrations caused by walking or other human activities like Dancing etc. As far as I can see, there isn't a generalized method for vibration design which I can use for constant vibrations of a single frequency in this document. Any suggestions on where I can find the appropriate procedures?

 

[saplanti]

This subject was heavily discussed in the following thread;

https://www.eng-tips.com/viewthread.cfm?qid=475471

 

[aligorsi]

@saplanti I went through that thread and the issue over there is that the natural frequency of the structure and operating frequency of the machinery are matching which may cause resonance. They are discussing methods for damping so that resonance can be avoided. My issue is different. I have both the natural frequency of the structure and the operating frequencies of the machinery. I want to know how to calculate the a/g ratio for sinusoidal loads so that I can see if there will be any discomfort.

 

[saplanti]

No, contrary the problem was exactly the same. You need the thread from the top to bottom. Then read the following;

https://engfac.cooper.edu/pages/tzavelis/uploads/Vibration Theory.pdf

In most of the steel structures the natural frequency is low and the forcing frequency of rotating machine is high. In case you keep the structural natural frequency of structure 25% lower than the forcing frequency the system will not go into resosnance. You need to chek the same for the second and third of natural frequencies of steel structures since they are still effective.

You can use 2% of damping for welded structures, and 4% of damping for the bolted structures in case you are calculating transmissibility and forces on the structure.

Hope it helps.

 

[saplanti]

Another to read

http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S1021-20192015000100004

 

[HTURKAK]

You looked to the AISC Design Guide 11 .. Is this a steel structure supporting a vibrating equipment ?
Sometimes it is necessary to look vibrating eq. foundations and modelling the system elevated type foundation..

Pls provide more info. regarding the supporting structure and vibrating equipment to get more valuable comments..

 

[wrxsti]

not sure if your manufacturer gave you dynamic loads
you can use that to get the displacement (delta) under the support

please note you need to determine any magnification and apply it to your displacement

mag = mod ( 1/( 1 - f_equip^2/f_natural^2) )

and then calculate the acceleration

a = -(2*pi*f)^2*delta*mag

note: this is a proposal of method

 

[ATSE]

Another consideration:
For just a welded steel structure with no concrete deck or non-structural components attached (like a stand-alone steel frame rigidly anchored to the base), your equivalent viscous damping ratio is closer to 1% (or even 1/2%).
You also need to consider that even for a high (f_equip / f_natural) ratio, for the start up and shut down operation, the f_equip may "cross thru" the f_natural zone. If this phase is slow, you will experience some cycles near resonance, and your equipment and frame have the potential to vibrate violently. This delta time at start up or shut down may govern your design.

 

[ldeem]

aligorsi if you are trying to determine if the vibrations will be felt by the occupants than you will need to do a time history analysis and compare the results to one of the many criteria of acceptance ranges.

Key points to consider
1. What is the acceptance criteria - this must be coordinated with the owner.

2. Structural analysis methods using lumped masses (STAAD or similar programs) are not going to be 100% representative of real world results so you need a healthy safety factor over the acceptance criteria.

3. Make sure to document your results. Don't get put in a position to satisfy some subjective criteria from the owner.

I am involved in a project now where I did a time history analysis and then took detailed field measurements, the results are up to 50% difference.

 

[aligorsi]

@ HTURKAK Yes. This is a steel structure. It will be supporting belt conveyors meant for airport baggage handling systems. The vibrations will be caused by the motors running and the bags periodically passing over them. The primary source of the vibrations will be the bags since the motors are balanced quite well.

 

[aligorsi]

@ wrxsti Thanks. I can get the dynamic loads from the manufacturer and I will try out your method. However, can you provide reference for the this method. I would like to read through the whole thing.

 

[aligorsi]

@ ATSE You are correct. This is a welded steel structure without any concrete slab with pinned base connections. I am using a damping ratio of 3% for my calculations.
Thanks for the suggestion about the start up time. I will consult the equipment manufacturer to get the time required for equipment to reach full speed.

 

[wrxsti]

@aligorsi

check saplanti's link under undamped forced vibration

 

[wrxsti]

@aligorsi

check saplanti's link:

https://engfac.cooper.edu/pages/tzavelis/uploads/Vibration Theory.pdf

check undamped forced vibration to see how magnification is developed (transmissibility for this case) for undamped scenario

the rest is just shm theory

as i said it was a proposal of a method ( a very simplified one )

....................

model with damping which would be more realistic

damping would decrease your magnification

see Rd (magnification under damped system) in 2.33 of saplanti's link

then check 2.37

a = -(2*pi*f)^2*delta*mag(now Rd)


but as @Ideem mentioned these are just approximations due to lumped mass SDOF models

will get more realistic with time history analysis on computer models

also noteworthy to mention is finding all major contributing natural frequencies of your structure
in which resonance may be problematic

 

[r13]

The primary source of the vibrations will be the bags since the motors are balanced quite well.

It seems you are concerned with the vibration generated by the impact. Suggest to find solves from "random vibration theory", that may help. Link

 

[evo10]

im not sure how the acceleration wrxsti posted will correlate to the AISC design guide acceleration
since they are using damping ratio and mass
versus deflection and omegasquared

 

[evo10]