Cantilever Vibration Analysis 2

[Atomic25]

I'm researching how to analyze a cantilever for vibration problems in SAP 2000. How do you guys/gals approach these problems when they come up? The vibrations I'm talking about are for human occupants and not high frequency machines.

I've been looking into the AISC design guide for vibration in conjunction with other references and seem to come up with the following procedure. I don't know if it's even close to being correct. All criticism is welcome.

1: Apply a very accurate amount of dead load/mass to the cantilever

2: Apply a carefully determined amount of Live load and also include a portion of it as mass.

3: Run a modal analysis to identify frequencies where the system resonates. Try to stay above 6hz.

4: Run a steady state case with the live load at those particular frequencies. Measure deflection.

I have a feeling I should also be determining the vibration accelerations too, and I've been looking into Time-history analysis but aren't sure how to interpret the results.

Any other references you could provide would be helpful.

 

[PEinVA]

There is an article by Murray and Hendrick titled "Floor Vibrations and Cantilevered Construction". I just printed it yesterday from AISC. Its old, 3rd Quarter, 1977, but if you haven't read that, it may be a good start to review your process.

RC

RC
All that is necessary for the triumph of evil is that good men do nothing.
Edmund Burke

 

[271828]

"1: Apply a very accurate amount of dead load/mass to the cantilever"

Good.

"2: Apply a carefully determined amount of Live load and also include a portion of it as mass."

Put about as much LL on there as mass as you REALLY think will be there, not the design live load. The AISC Design Guide 11 gives guidance for this. Fairly typical numbers are around 10 psf. Not sure what you mean by "Apply...Live Load..." At this stage, you're trying to get the mass right.

"3: Run a modal analysis to identify frequencies where the system resonates. Try to stay above 6hz."

Good, although 6 Hz isn't a magic number in general.

"4: Run a steady state case with the live load at those particular frequencies. Measure deflection."

The steady state analysis is necessary, but I don't see the usefulness of measuring deflection. Instead, have the analysis plot the acceleration vs frequency. You're predicting the accelerance frequency response function magnitude and phase. The mag is almost always necessary when using a FE program to analyze a floor because the modal analysis will often spit a very large # of modes back at you in a 10 Hz bandwidth and you absolutely cannot tell which one(es) cause significant response at a given location just by looking at the freq and shapes. The FRF magnitude will show you exactly which modes are causing the response.

Here's the order I recommend (mostly similar to yours):

1. Create your model as absolutely detailed and accurate as you possibly can--NOT like a model used for strength & stiffness. These models are extraordinarily sensitive to modeling assumptions that don't make a hill of beans for a typical strength & deflection model. Cladding should be considered, for example. If you have CMU partitions, add a line element with the same MOI and shear area. Your beam-to-girder and girder-to-column joints should be rigid regardless of conn type. Use orthotropic shells to represent the slab and transformed sections to represent beams and girders (beff according to AISC DG11).

Even your best attempt won't be very accurate compared to what you'll get if you do vibe tests on the structure. A typical level of detail as used for typical models creates a model that is absolutely worthless for vibrations.

2. Use the modal analysis to get freq and mode shapes.

3. Use the steady-state analysis to figure out which modes are really important for response at locatons of interest.

4. Apply a harmonic load representing whatever activity you're considering -- walking, rhythmic activities, etc. The DG11 offers some of these, but they're a bit dubious at this point in history. Updated loading functions are in the UK SCI 2007 DG. I'd dare say that there's been more vibe research done from 1997 (DG11) to 2007 than all of the pre-1997 research combined.

5. Either use the steady-state analysis or response history to predict the peak acceleration (or rms if you're in Europe) and compare to tolerance limits in the AISC Design Guide if you're in the USA or the SCI Design Guide if you're in Europe.

The UK SCI 2007 DG has extremely detailed guidance for doing all of this, BTW.

 

[GalileoG]

Tagging this thread for future reading.

 

[JKStruct]

Agree with 271828 on all accounts.. he knows what he's talking about. I'll also add that the AISC DG11 is also incomplete when it comes to the parameters for a footfall forcing function. It leaves something to be desired. There has been later research that I've read by Eric Ungar (who coincidentally co-wrote DG11), which better defines footfall parameters. And I echo the sentiment that the UK has spearheaded research in this area, and any US engineer interested in vibrational analysis should research the work performed by our neighbors across the pond.

Is anybody in Nashville for the NASCC? Tom Murray is giving a vibration talk tomorrow... I'm attending it. I've read a lot of his work. Now that I think about it, I find it ironic that's it's probable that several eng-tippers might be present, but I wouldn't know it because of the online pseudonyms... maybe if we all scratched a "271828" or whatever screen name onto our nametags...

 

[271828]

LOL, my real name is 2.71828 HAHAHAH! The stupid registration thingie wouldn't let me have a decimal so now I am multiplied by 100000 to get 6 sig figs. e is an inside joke...

Thanks for the kind words.

I won't be at NASCC, but I will write e on any conference nametag in the future. If anybody gets that, I think I'll totally crack up.

I have worked with Dr. Murray a lot over the years on floor vibe issues, but then again, there are probably 100 people who can type that. His talk would be great, I'm sure. I am not quite sure what happened with so much research going across the pond. My guess is that it's due to funding. THey had the Millinium (sp?) Footbridge problem, so I'd guess there has been much more funding for vibe research over there. I gather that there's not a lot of funding in the US for that type of research with the push to do infrastructure research.

 

[d2783]

Hello guys,

I have a similar problem as atomic25 mentioned.
But I have a flat slab concrete floor system.
And I have to peform time history analysis for the walking/running load on the floor.
I know ETABS can do it.
But I havent really performed time history analysis before.
I know i have to define a function which represents the impact of the either walking or running load.
But i wanted to know how do i peform the analysis in the software and how to interpret the output.

Can anybody help me regarding the same.

thank you

 

[271828]

d2783, your problem is probably harder because your floor can either be low or high frequency (fn <= 10 Hz or > 10 Hz). The loading functions are very different for these two cases and so are the results and behavior.

Your best bet is to get your hands on the UK SCI 2007 floor vibe design guide. It's called something like Floor Vibrations: A New Hope (oops, I meant "A New Approach"). Use what they call the General Procedure.

Beware that their rho factor is wrong. The exponent numerator should also include h*fp.

Their low freq harmonic loads are also wrong. fp should be replaced by h*fp for the 2nd through 4th harmonics.

 

[RVSWA]

I'm just a caveman engineer, I don't understand all your "time history analysis" ways... could someone recommend a good book or jumping off point for embarking upon my evolution?

 

[271828]

Anil Chopra's book is a good place to start. Hopefully your analysis program's documentation is helpful also.

Here's the basic idea (I know it helps me when someone sums it up early on):

Your model's equations of motion are:

[M]{x}''+[C]{x}'+[K]{x}={F}

[M], [C], [K] are the mass, damping, and stiffness matrices which define your physical system. If you have a 10 degree of freedom system, M, C, and K are 10x10. M is almost always diagonal. The program automatically comes up with M and K.

C is another story entirely, but very often you use "modal" damping for this, which is easier. You specify that each mode gets 1% (or whatever) of critical damping or give each mode different values. Deciding on these values is one of the hardest parts.

{x} is the vector of displacements, one at each DOF. Of course {x}'' is the acceleration vector. These are functions of time.

{F} is the vector of forces, each is a function of time. For floor vibe these are usually sinusoidal forces even for loads that aren't obviously sinusoidal (a series of footsteps for example). Due to the wonders of Fourier analysis, practically any function of time can be decomposed into a series of sinusoids which are then easier to apply to the model.

You define the physical system and apply loads that are functions of time.

The program uses one of various numerical methods to solve this system of equations for {x} as functions of time. For floor vibe and other linear (well we assume linear anyway) analyses, this is pretty easy. It gets harder when there can be dynamic instability or other weird things happening.

That's pretty much it in a nutshell.

 

[271828]

Oh, I forgot the crucial step: playing around with your program to make sure you know what the heck it's doing. This is actually pretty easy. Any decent vibrations or structural dynamics book will have example problems with single masses subject to various kinds of loads. It should be possible to model this mass in the program and duplicate the result from the book. Then go on to a two degree of freedom example, etc. until you're sure you know what it's doing.

 

[RVSWA]

Thank you "e", I appreciate the explanation, I am printing this and saving it for future reference.