Resonance modes in cylindrical open steel tubes
Resonance modes in cylindrical open steel tubes
(OP)
Hi Fellows,
I like to ask for some help here. I am trying to calculate
the resonant frequencies for a sample of an open stainless steel
tube, free and mounted rigid on one end.
I have done some measurements with and spectrum analyzer
and got a couple resonance peaks.
My goal with the calculations is to predict the resonant
frequencies (or modes) on stainless steel tubing with
different dimensions.
I have encountered some difficulty to find the equations
to solve such problem.
Is there some software available I could use to solve this ?
Thanks
I like to ask for some help here. I am trying to calculate
the resonant frequencies for a sample of an open stainless steel
tube, free and mounted rigid on one end.
I have done some measurements with and spectrum analyzer
and got a couple resonance peaks.
My goal with the calculations is to predict the resonant
frequencies (or modes) on stainless steel tubing with
different dimensions.
I have encountered some difficulty to find the equations
to solve such problem.
Is there some software available I could use to solve this ?
Thanks





RE: Resonance modes in cylindrical open steel tubes
w = an * sqrt{E*I/(MU*L^4)}
a1 = 3.52
a2=22.0
a3=61.7
a4=121
a5=200
I=pi*(OD^4-ID^4)/64
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RE: Resonance modes in cylindrical open steel tubes
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RE: Resonance modes in cylindrical open steel tubes
RE: Resonance modes in cylindrical open steel tubes
electricpete
Thanks for your help, but what is
an
a1=3.52
a2=22.0
a3=61.7
a4=121
a5=200
some fetch factors ?
40818
Also, forgive me but what does FE stand for ? Is this some
simulations software ? If so, can you post a link to it ?
Thanks so much
RE: Resonance modes in cylindrical open steel tubes
You plug a1, a2, a3 etc in for an to obtain the different possible resonant frequencies.
When you solve the Euler Bernoulli problem by separation of variables and apply these boundary conditions, you find that an must satisfy:
COS(SQRT(an))*COSH(SQRT(an))+1=0
The possible values of an that solve the above equation are 3.52, 22.0 etc. We gave them names a1, a2 etc.
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RE: Resonance modes in cylindrical open steel tubes
thanks for clearing this up. I did not understand where
these values came from. I am new to this matter.
So if I understand you right I will have to resolve this equation to f.
f = an * sqrt{E*(pi*(OD^4-ID^4)/64)/(MU*L^4)}/2*pi
I am trying to confirm my Experimental data for the 316 Stainless Steel tube.
Material Data:
Sound velocity (axial) = 4912m/s
Sound velocity (radial) = 5087m/s
Mechanical Impedance = 39290000kg/m^2/s
Young's Modulus = 1.93*10^11N/m^2
Density = 8000 kg/m^3
Poisson's Ratio = 0.26
Tube Data:
OD = 19.16mm
ID = 18.11mm
L = 216mm
I am getting two strong spectrum peaks, one at
3729Hz and the other at 10514Hz.
As I understand other modes may be present yet not as
dominant so they may not be seen in the spectrum.
Also, I was wondering in this equation, the speed of sound
of the material is not been considered.
Thanks again for your help.
RE: Resonance modes in cylindrical open steel tubes
One could also compute resonant frequencies for torsional vibrations (unlikely wihtout torsional excitations), longitudinal vibrations, and air-column acoustic vibrations.
a few questions:
1 - how is the vibration being excited? Bump test? Bump at which location in which direction? Flow? Something else?
2 - Is the base truly acting rigid? i.e. zero vibration of the base?
To find the acoustic resonance, you would need to know speed of sound in air (1100 ft/sec). It is not necessary to know any speed of sound to calculate the lateral, longitudinal and torsional resonances. In some solution methods if you consider the vibration to be a wave or standing wave, there is an associated wavespeed in the material, but it's not a material property (depends on geometry).
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RE: Resonance modes in cylindrical open steel tubes
1. I am using a piece of hard plastic and strike the tube
on it side, somewhere half way in the middle of the tube length.
I experimented with different 'impact' locations along the
length of the tube but it seem to make not a big difference
in terms of spectrum peaks. Once I strike it, I get a quite
long lasting ping, I'd estimate about 1 second or even longer.
I was wondering, if this is a longitudinal resonance or a
breathing resonance over the diameter of the tube.
Or perhaps both ?
2. Well I tried different options.
a) The tube hung with a rubber band.
b) The tube clamped in a small vise at one end.
c) The tube held in the hand at one end.
Also, the spectrum peaks seem not to have moved much, perhaps
a couple hertz but I am not sure as I believe my
measurement setup may not be that precise. I am using
a sound card.
At most it seems more dampened as the ping does not last as
long compared with a 'free' tube.
I am not looking for the acoustical resonance as I believe this is not applicable.
Thanks
RE: Resonance modes in cylindrical open steel tubes
RE: Resonance modes in cylindrical open steel tubes
RE: Resonance modes in cylindrical open steel tubes
htt
RE: Resonance modes in cylindrical open steel tubes
Yes it would, but he said "free and one end rigid". I took that to mean that one of the cases he was attempting to analyze was free-free.
RE: Resonance modes in cylindrical open steel tubes
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RE: Resonance modes in cylindrical open steel tubes
There a number of formulae for the determination of natural frequencies presented by Leissa using different shell theories under different assumptions of type of responses (in-extensional, extensional and bending, etc.), boundary conditions and then compares them to one another. You can program these formulae and arrive at a solution to your problem.
There are a number of qualified shell programs (based on finite difference, finite element and numerical integration techniques) that also give one the ability to analyze any shell configuration.(see http://www.volcano.net/~d.citerley)
The first eight entries under the software tag will give you what you need.
If you are using modal analysis gear to determine the experimental values, you need to very careful about the boundary conditions and where you are impacitng the shell. You can exite many modes with a single strike of a hammer. It is not like you are exciting one dominant mode like a shaker system can. Also, the magnitude of the impact impulse could be so extreme that you could excite a non-linear behaviour--especially with 301 stainless steel.
One vibration component often forgotten are the acoustic modes being excited.
RE: Resonance modes in cylindrical open steel tubes
I am in particular interested in the fixed-free vibration mode.
Is this equation as I had posted above the correct one to
calculate this mode ?
f = an * sqrt{E*(pi*(OD^4-ID^4)/64)/(MU*L^4)}/2*pi
Thanks
RE: Resonance modes in cylindrical open steel tubes
Cheers
Greg Locock
Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.
RE: Resonance modes in cylindrical open steel tubes
fi = (ani^2/2piL^2)(sqrt(EI/M))
M= Mass per unit length
I for a tube = pi(OD^4-ID^4)/4
an1=1.875
an2=4.694
an3=7.854
an4=10.995
RE: Resonance modes in cylindrical open steel tubes
Your L^2 outside the radical corresponds to my L^4 inside
Our equations are the same except for the I. You have 4 in the denominator and I have 64
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RE: Resonance modes in cylindrical open steel tubes
RE: Resonance modes in cylindrical open steel tubes
Attached is a spreadhseet which calculates the 5 modes using the equations I provided above. I have cross-checked it with another program (the beam program from Tom Irvine) and the results agree:
htt
The calculated lateral resonant frequencies for this pipe in fixed/free (cantilevered) configuration using Euler Bernoulli method are:
389 (hz)
2430
6814
13363
22087
Since this is a fairly long thin beam, I think the Euler Bernoulli method should certainly be very close. I don't think something like a method of shells is required. If I am mistaken, I am always willing to learn.
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RE: Resonance modes in cylindrical open steel tubes
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RE: Resonance modes in cylindrical open steel tubes
When n=0, the cross section simply moves in and out (breathing mode) with no circumferental variation (usually at a very high in frequency). When n=1, the motion is a rigid beam motion (generally very low). In both cases, the longitudial variation (sin series) provides multiple modes and are based on the boundary conditions. Many of the calcs. earlier presented by others are for this latter case.
If the shell has an R/h ratio < 10, the behavior is usually a rigid body (beam) motion. For higher ratios, in the order of R/h > 30 to 5000, the cross section begins to respond with a Fourier variation. So high rigid body normal mode frequencies may be higher than those associated with the Fourier normal modes. The higher the excitation frequencies, for cylindrical shells, the closer the response is to a diamond shape on the surface.
You may also subject the shell to a radial and uniform impulse. If it is large enough, the object may first start out with a breathing mode (n=0) and then respond in the lowest Fourier mode. The wave form will have a beating appearance over time. This is called Mathieu instability.
The extent of the "ping" behavior observed in the experiment has to do more with the damping of the material and the non-linear effects of a so called "fixed" BC.
RE: Resonance modes in cylindrical open steel tubes
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RE: Resonance modes in cylindrical open steel tubes
Many Thanks electricpete for the Excel file. This is most helpful.
But I am still a bit confused, as the Excel calculations
indicate Frequencies that do not match my measurements.
I wonder if I am wrong with my measurement ?
Anyway, Thanks everyone for trying to help me.
Cheers
RE: Resonance modes in cylindrical open steel tubes
Why doesn't it match:
A - it could be something other than simple lateral cantilever beam motion. Acoustic, longitudinal, and those complicated modes described by mtnengr
B - There could be a simple error in the material properities that you reported.
I noticed the coincidences that the ratio of your frequencies is 10514/3789=2.8. That also happens to be the ratio of the 2nd and 3rd lateral frequencies above 6813/2430~2.8. That may point toward explanation B. i.e. you may be looking at the 2nd and 3rd simple lateral modes, but some error in the constants creates a multiplicative error (the same error for each frequeency).
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RE: Resonance modes in cylindrical open steel tubes
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RE: Resonance modes in cylindrical open steel tubes
Cheers
Greg Locock
Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.
RE: Resonance modes in cylindrical open steel tubes
Now, the response is non-linear, coupling between Fourier modes associated with the clamp and the rest of the cylinder.
RE: Resonance modes in cylindrical open steel tubes
RE: Resonance modes in cylindrical open steel tubes
well the material data came from a website, a company that makes ultrasonic transducers. I felt it was quite safe to use data they had posted for SS136.
I had also found material data elsewhere which varied in some parameters but I am not knowledgeable in this field so I don't know if it makes a significant difference. Once I have the right equation, then it should be easy to predict.
GregLocock,
The frequencies I had measured had two very strong spectrum peaks, one at 3729Hz and the other at 10514Hz. I have not been able to calculate any of these as I am not sure what is the correct equation for the to me unknown resonance mode.
Different Material Data for SS316:
Young's Modulus = 2.1*10^11N/m^2
Density = 7800 kg/m^3
Poisson's Ratio = 0.29
Anyway, here are a few pictures of what I have done. I have been using SpectraLab for analysis. For those that are interested, here are the wav. files as well.
Again, many thanks for all the help.
http://
http://
http://
http://
http://
RE: Resonance modes in cylindrical open steel tubes
As a sanity check, pull down and release the free end of the tube and see it it vibrates near the 389 Hz electricpete has given.
RE: Resonance modes in cylindrical open steel tubes
That would seem to point away from the simple lateral beam modes and perhaps towards acoustical resonance.
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RE: Resonance modes in cylindrical open steel tubes
It is set up to identify the length of pipe that will cause a given frequency.
htt
To apply it to this particular problem, proceed as follows:
Go to Calculations tab
* put f=3729hz into the frequency (cell C3)
* Observe the length 217 appears in cell N28 (5th mode for open/open pipe)
* put f=10514 into the frequency (cell C3)
* Observe the legnth 217 appears in cell N35 (14th mode for open/open pipe corresponding to L=Lambda)
The above MIGHT lead you to conclude these are some higher order acoustic resonances. BUT, why would it only respond to just a few of the higher order resonances and completely skip the others? Sounds a little strange to me. Some other caustions:
* I took a guess at air density - depends on humidity and barometric pressure
* The higher order modes are so close together (as a fraction of the frequency) that odds are one of them will be close to a given frequency
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RE: Resonance modes in cylindrical open steel tubes
"(5th mode for open/open pipe corresponding to L=2.5*Lambda)"
(14th mode for open/open pipe corresponding to L=7*Lambda)
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RE: Resonance modes in cylindrical open steel tubes
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RE: Resonance modes in cylindrical open steel tubes
Now there is a problem there, the beam modes of axisymmetric beams are notriously hard to measure with accelerometers. I suggest using two at the same location at 90 degrees.
Cheers
Greg Locock
Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.
RE: Resonance modes in cylindrical open steel tubes
have a look at the picture I had posted. Considering I had used a small vise and considering as you stated fixed does
not equal fixed I am absolutely not sure how fixed it is.
electricpete,
awesome, many thanks for taking the time to help me and to come up with the Excel sheet.
Well there are other peaks in the spectrum as well, but they are not as dominating as the two I had mentioned. I thought it made more sense to try to analyze the dominant modes.
When you speak of acoustic modes, you are hinting that air plays a role. That is really throwing me off, as I thought this would only be applicable if air travels through the pipe or if flowing air under pressure is used to excite the pipe.
Also, in one attempt to tune it, I had milled a 15mm slot 1/8inch wide into one end of the pipe, but it seemed to make
little to no difference where the two dominant peaks occur.
This lead me to believe that the peaks originated in a 'bell' mode and not over the length of the tube.
Thanks
RE: Resonance modes in cylindrical open steel tubes
especially not at 10000 Hz.
I really recommend that you measure the mode shapes, not just the frequencies.
I agree that ring modes of the tube are a possibility. You can measure those, although they are a bit tricky.
Cheers
Greg Locock
Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.
RE: Resonance modes in cylindrical open steel tubes
how should I have to setup and measure the ring modes only ?
Thank
RE: Resonance modes in cylindrical open steel tubes
You'll run into probelsm with this - the modes will rotate until the accelerometers are nodal, so a non contacting method, eg doppler laser, may be more appropriate.
Cheers
Greg Locock
Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.
RE: Resonance modes in cylindrical open steel tubes
I guess that's as far as I can take it with this.
Thanks
RE: Resonance modes in cylindrical open steel tubes
One way to eliminate acosutic modes is to build an enclosure around them and flood it with CO2.
If the modes are acoustic the frequency will change.
Cheers
Greg Locock
Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.