Structural Vibrations due to "Beat" Frequency

[bootlegend]

I'm trying to get a better understanding of vibrations due to machinery. My general approach has been to make sure that a structure has a natural frequency that doesn't line up with a piece of equipment's operating frequency, in a nutshell.

However, suppose I have a structure that supports two pieces of machinery that operate at similar (but not the same) frequencies. Call those frequencies f1 and f2. My understanding is that I would need to then design my structure around f1 and f2 but also around the "beat" frequency of (f1-f2). Is this understanding correct? Does anyone have any references that would help a structural guy get a better background with this?

 

[JAE]

Wouldn't the resonance of the two frequencies be critical as well?
So f1 x f2?

So if you had a frequency of 2 and a frequency of 3, you'd have resonance at 6, 12, 18, etc.

Check out Eng-Tips Forum's Policies here:
faq731-376

 

[WARose]

Beating can occur with a single forcing function (with a single forcing frequency). Beating occurs because the frequency of the forcing function is so much larger than the difference between the natural frequency and the forcing frequency.....you get rapid oscillation with a slow varying amplitude. It's very obvious looking at the time-history plot.

You wouldn't want the frequency(s) of your structure to be anywhere near f1 or f2. (And that should cover any "beat" problem.) But depending on the complexities of your structure......the individual pieces could give you as much trouble as the whole thing. That's where FEA comes in.

 

[drawoh]

JAE,

I was looking into this one myself. thread384-430013

I was modelling six vibrations very close to each other. At some point, amplifications all add to each other. If you randomly vary each vibration frequency, you get some very weird beat frequencies. I do not understand how significant this is.

--
JHG

 

[WARose]

I was modelling six vibrations very close to each other. At some point, amplifications all add to each other.

The displacements are additive.....but excluding a coupling situation.....the various forcing frequencies shouldn't mean much relative to each other.

Of course, I am thinking of very simple systems here.....it goes back to having a good model in FEA for time-history.

 

[bootlegend]

Beating can occur with a single forcing function (with a single forcing frequency). Beating occurs because the frequency of the forcing function is so much larger than the difference between the natural frequency and the forcing frequency.....you get rapid oscillation with a slow varying amplitude. It's very obvious looking at the time-history plot.

The beat frequency that I am referring to is discussed in the following link and is the result of two similar forcing frequencies. You can hear and feel vibrations as the frequencies go in and out of phase.

http://www.vibrationschool.com/mans/Plots/SPlots21.htm

I've attached a clip as an example as well. In it you can hear the and see the light gauge tool box vibrate as the two machines on the structure come in and out of phase. There was no issue when only one machines were running. Luckily this one was easily fixed by slightly altering the gap in operating frequencies of the two machines.

it goes back to having a good model in FEA for time-history.

I have tried time-history but find it open to engineering judgement. How much displacement is too much? How much acceleration is too much? I see plenty of info on how to perform time history analysis for forcing functions but not so much on how to interpret and use the results and determine whether you have a problem.

 

[WARose]

I have tried time-history but find it open to engineering judgement. How much displacement is too much? How much acceleration is too much?

A bunch of engineering texts & codes have charts for acceptable vibration limits for people and machinery (with displacement & acceleration as a limiting criteria on some charts). They include:

'ACI 351.3R-04', by: ACI

'Vibration of Soils and Foundations', by: Richart, Woods, and Hall. (1970)

'Design of Structures and Foundations for Vibrating Machines', by S. Arya, M. O'Neill & G. Pincus. (1979)

 

[Agent666]

You'll also get resonance if your forcing frequency matches the harmonic frequencies or sub-harmonic frequencies. For example 'n' times f1 or f2, or f1/n or f2/n (where n = 1, 2, 3....etc). Often as a measure you will look at the root mean square acceleration to take account of these effects with appropriate weighting being given to each of the harmonic frequencies. As you can imagine with two frequencies, it can mean quite a lot of potential frequencies where resonance can occur.

One way to think of the harmonic frequencies getting excited is that instead of the forcing frequency coinciding with every cycle of the natural frequency of the system, they are only in phase for resonance every 'n'th cycle.

 

[rb1957]

how about isolating one, or both, machines from your structure ?

another day in paradise, or is paradise one day closer ?

 

[GregLocock]

You need to design for the total of the two amplitudes. You'll hit it at the beat frequency. So for fatigue your number of cycles is very low but the amplitude is high. Beating, or heterodyning is a fairly unintuitive phenomenon in my opinion. You'll notice there is no sign of the beat frequency on your spectrum (if your analysis is good) yet the enhanced maximum amplitude, which is related to the maximum strain in your structure is a real thing.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[WARose]

[blue](JAE)[/blue]

Wouldn't the resonance of the two frequencies be critical as well?
So f1 x f2?

So if you had a frequency of 2 and a frequency of 3, you'd have resonance at 6, 12, 18, etc.

Not sure I follow that statement. Are you saying that forcing frequencies of (for example) 2 Hz & 3Hz would produce a resonance condition if the natural frequency of a system was 6 Hz (with 100% of the mass participating at 6 Hz)? I don't think that is right. Or are you talking about the beating phenomenon?

[blue](Agent666)[/blue]

You'll also get resonance if your forcing frequency matches the harmonic frequencies or sub-harmonic frequencies. For example 'n' times f1 or f2, or f1/n or f2/n (where n = 1, 2, 3....etc).

I don't follow that either. "n" times f1 should never get the same response that occurs when f1=the natural frequency of the system. That is unless we are talking about a system with more than one mode here. (I may be misinterpreting your statement.) Or are you talking about the beating phenomenon?

 

[GregLocock]

I agree with WARose, neither of those is mathematically or physically possible in a linear system, unless they are very poorly worded.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?