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# Vibration Limits

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## Vibration Limits

(OP)
I am trying to figure out how to specify an acceptable limit
when I do a dynamic analysis on a structure. For instance,
there is a beam supported at the ends. Someone walks across
the beam that is very flexible. The person walking on the beam
bounces too much. So the beam is made stiffer until the bouncing
is limited to a small amount.
Is there a way or an equation that can incorporate the structure
stiffness and deflection to determine a limit on the dynamic
deflection?

Thanks,

### RE: Vibration Limits

#### Quote:

The person walking on the beam bounces too much. So the beam is made stiffer until the bouncing
is limited to a small amount.

If I understand correctly, the goal is to design a structure that limits dynamic deflection to a given value (based on some assumed dynamic loading pattern). Is that the goal?

If so, first question I'd ask about the beam problem - is the frequency of the excitation limited. Can you redesign/stiffen the beam so the first resonant frequency is above the highest excitation and how far.

If you can't push resonant frequency above highest excitation, then you need to know the damping... that is what will limit ampliltude of resonant vibration.

From a simplistic standpoint, if you can push the first resonant frequency far above highest excitation frequency, then the system acts spring controlled and can be analysed as static. If you can't push resonant frequency far above excitation then you need dynamic analysis.

=====================================
(2B)+(2B)' ?

### RE: Vibration Limits

Plenty of information by searching:
Google: acceptability criteria for occupant-induced floor vibrations
Google: generalisation of criteria for floor vibrations for industrial

Most floor construction above grade whether wood, steel or concrete can/usually have natural frequencies in the excitation range of human foot-fall, vehicle traffic, and machinery; so it would be unwise to do a simple static analysis if the concern is vibrations.

Walt

### RE: Vibration Limits

Good point W. Strong.

#### Quote (electricpete)

If you can't push resonant frequency above highest excitation, then you need to know the damping... that is what will limit ampliltude of resonant vibration.
I should clarify damping would limit amplitude of resonantly excited vibration in sinusoidal steady state. On the other hand if it is known that the excitation is applied for a limited time, you might be able to estimate an upper bound for vibration if you could estimate expected energy input during that limited time. (btw I am not a guy that designs things, just throwing out some thoughts)

=====================================
(2B)+(2B)' ?

### RE: Vibration Limits

(OP)
Thanks for your replies.I don't necessarily have a beam. It could be any mechanical
structure that is vibrating due to a forcing function. I was just trying to provide
a generic example.

About 15 years ago I did some analysis on an existing mixer in a tank. They didn't
know the components were going to shake excessively until the first time the
switch was turned on. I got an equation from someone I worked with that converted
the structure stiffness and dynamic deflection into a sound decibel value. This value
was then compared to the sound level from charts that show sound levels for...like..
jet engines or lawn mowers or people talking, Adjustments were made and the components
worked great but those reports have been lost since then.

I found the guy who provided the info before but for some reason he doesn't know what
I'm talking about. Yes, I searched the internet and there is a lot if information but
I was looking for that equation I used a long time ago.

### RE: Vibration Limits

dynamic equation to cover a generic unspecified geometry?

Other than the obvious building blocks (F=MA), I'm not aware of anything like that. Unless maybe the systems you are interested in can all be simplified to SDOF? In that case there is an equation to compute dynamic deflection of SDOF system given the amplitude & frequency of the excitation and given the the M/K/C of the system.

=====================================
(2B)+(2B)' ?

### RE: Vibration Limits

I'm not sure I'd count on a vibration level or machine condition being OK simply because it did NOT create an unacceptably high sound level.

Conversely There have been plenty of decent quality roof mounted airhandlers that have created un-ending occupant noise complaints due to mis-application, duct installation errors, or simply not following ASHRAE's guidelines, like not putting airhandlers over conference rooms or even worse the boss's office.

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