Why do we only care about the lowest modes of Vibration 3

[gharli]

Hi All,

Hope everyone is Covid19 safe and well.

I'm doing a dynamic analysis check on a foundation supporting a motor. There are many guidelines and codes out there specify how far out your natural frequency needs to be from the forcing frequency.

My question is, why do we only consider the lower (say first 3) modes of vibration?

I have found that in my case the modes and corresponding frequencies are as follows:

1

​

16.9 Hz
2

​

18.5 Hz
3

​

24.7 Hz
4

​

25.4 Hz
5

​

33.2 Hz
6

​

40.0 Hz
7

​

53.8 Hz
8

​

73.4 Hz
9

​

81.9 Hz
10

​

91.9 Hz
11

​

99.2 Hz
12

​

100.2 Hz
13

​

104.3 Hz
14

​

115.4 Hz
15

​

120.4 Hz
etc.

It is very possible that the motor is operating at say 6900 RPM (115 Hz) which is all the way up at mode 14...

Are higher modes less likely to ever be excited for a large foundation? Or what is the reasoning behind the rule-of-thumb?

Thanks.

_________________
Jones & Wagener

http://www.jaws.co.za

 

[Ron]

Vibrations induce stress. In general, the lower the frequency, the higher the stress. Lower frequencies induce more "pounding-like" stresses, whereas higher frequencies induce more "buzz-like" stresses. For solid materials such as metals, the whole range of frequencies can be significant. For loose matrix materials, such as soils, the higher frequencies are attenuated quickly and produce little effect.

Further, as loose matrices are subjected to vibration, they consolidate (think compaction), but they generally have air voids and moisture which both mitigate and attenuate vibrations, particularly higher frequencies.

 

[robyengIT]

I am not an expert in foundations but I know, by experience, that the vibration frequencies have to be overtaken as quick as possible. In your situation working at 6900 RPM (115 Hz) means almost equal to the 14th natural frequency of your foundation (115.4 Hz): I would avoid it !

 

[canwesteng]

Short answer - we don't.

Long answer - you need to look at the modes of vibration and mass participation to see what modes matter. Is this a combustion motor or electric?

 

[WARose]

As canwesteng said, the mass participation is a very important aspect to look at.

That being said, in general (for a stiff foundation block supported on the ground) the first few modes are typically the most dominant.

 

[1503-44]

14 x natural frequency is not going to be a problem. Higher frequencies have the smaller amplitudes. Machines and human beings don't experience much discomfort at the high frequency-low amplitude ranges as they do at large ampliitude, low frequencies. If operating speed will be 6900 rpm, your only concern should be not spending too much time passing through the first three modes of machine-foundation resonance on your way up to speed, or when shutting down. Large machine-foundation-soil systems generally have natural frequencies somewhere between 600 to 1200 cpm, and you want to have op speeds at least 40% outside of whatever first resonance speed is, so that would signal you are probably in the clear after you pass 1600 rpm.

“What I told you was true ... from a certain point of view.” - Obi-Wan Kenobi, "Return of the Jedi"

 

[r13]

axie,

Very good explanation. The other thread pointed out a foundation grating had noticeable noise from vibration, and it ceased to vibrate when stepped on it. Do you think it was caused by higher, or lower mode of frequency?

 

[ThomasH]

Hi

I would say that you should consider all relevant frequencies. In some cases that may be three but in most cases I think it is more.

One reason to use three is possibly that they are easy to calculate. Stiffness in three directions, mass, and there you have it.

Avoiding resonance is always a good approach, in some cases more or less necessary. But it depends on the application. For engines start and stop can be the issue if it runs at "high" rpms.

But to limit the analysis at three frequencies would not be my general approach.

Good Luck

Thomas

 

[1503-44]

Grating noise: I think that it might have been caused by the higher freqs, as grating typically has short spans, their natural frequency is relatively high, however that can usually be avoided by tack welding the grating to the supports.

“What I told you was true ... from a certain point of view.” - Obi-Wan Kenobi, "Return of the Jedi"

 

[gharli]

Great, thanks for the responses guys. Always a help.

Questions always lead to more and this instance is no different.

Do any rules of thumb exist for how much mass participation is deemed necessary? Is it 1%, 99% ? I can imagine there may be some instances where only a small percentage is involved for a specific mode but it still may prove problematic? Isn't resonance, resonance? i.e. if a low percentage of mass is involved resonance could have dire consequences.

I'm aware of the cumulative mass participation 80% rule for the total number of modes shapes to consider.

Perhaps it all boils down to engineering judgement and the specific problem at hand...



_________________
Jones & Wagener

http://www.jaws.co.za

 

[GregLocock]

"14 x natural frequency is not going to be a problem"

A rather dangerous statement. A resonant frequency at the rotational speed of the motor will be excited by any imbalance in the motor.

Cheers

Greg Locock


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

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

 

[1503-44]

Theoretically you are correct and I think it is more important to consider them when the machine is supported on a lighter frame, aircraft jet engines, etc., that have limited dampening capacity, but when supported by high damping mass of concrete and soil, that resonance is quickly damped out. Reciprocating loads, metal stamping plants and slow reciprocating compressors, in the range of much nearer the foundation frequency itself, those at 900, 1500, 1800 rpms that are the worst offenders. I have designed many foundations for high speed rotary equipment, pumps, compressors, gas and steam turbines, motors and generators and never had problems with excessive amplitudes at anything so far above the primary mach-fdtn resonance frequency. The amplitudes so high up are just very small.

Yes there are general rules of thumb for providing sufficient mass and for determining the foundation geometry, volume, width and height, but there are a number of them that cover different machine types, speeds and power ratings.


“What I told you was true ... from a certain point of view.” - Obi-Wan Kenobi, "Return of the Jedi"

 

[gharli]

Points well noted ax1e, thanks.

My question regarding the mass was more to do with the mass participation in a specific mode rather than the 2x, 3x ,etc. minimum mass requirements.

Thanks.

_________________
Jones & Wagener

http://www.jaws.co.za

 

[1503-44]

That consideration might be more relevant to the mass distribution of the rotating components, rather than of the foundation, as foundations are preferably designed to act as rigidly as possible in all directions against the net combined X,Y,Z forces and moments acting about the machine-foundation's one center of gravity. But if the foundation is thin enough to be considered as flexible, making it necessary to consider different loads acting at their respective points on the foundation, you will begin to start seeing the effects of the foundation's mass distribution in relation to those independent forces and moments. A rigid foundation tends to be kinder towards future maintenance issues as it minimizes differential movements and tends to keep drives and gearboxes in alignment. The rules of thumb for vibratory machine foundations tend to proportional geometries that favor rigid foundations for that very reason.

“What I told you was true ... from a certain point of view.” - Obi-Wan Kenobi, "Return of the Jedi"

 

[gharli]

Makes a lot of sense. Thank you.

_________________
Jones & Wagener

http://www.jaws.co.za

 

[1503-44]

Not to mention that the analysis of a rigid foundation is far easier than for a flexible foundation.

“What I told you was true ... from a certain point of view.” - Obi-Wan Kenobi, "Return of the Jedi"