vibrating plate nat. Freq question 6

[AndrewUK]

I’ve been doing some tests on a set-up at work, vibration is not my area of expertise but I’m keen to develop it so any ideas are welcome.

The set up is a thin plate restraint on all edges, the plate as small holes drill in it (0.2mm dia, by 0.2mm deep [blind holes]). I’m vibrating the plate to remove
Air bubbles when it is submerged in a tank of plating liquid.

I did some modeling on solid works and cosmos and got five modes; 23Hz, 39 Hz , 57Hz, 67Hz, 77Hz. I also did an impact test got a lot of noise put a clear peak at 55 Hz.

I ran some tests and found that running the exciters at 23Hz and 39 Hz didn’t do much but when I got to 57Hz it shifted the air bubbles, can anyone explain that?


As far as work is concerned the problems fixed but for myself I’m left wondering. Any info on this would great.

I’ll have to pop to the library this weekend; I guess I’m looking for natural frequencies but is there any theory on cases like this?

 

[AndrewUK]

to make it clear I'm wondering why the bubbles didn't shift at 23 and 39 HZ. Is it because ther is more energy at 57 Hz and the thus greater deflection in the plate?

 

[CESSNA1]

ANDREWUK: It probably has to do with the mode of vibration. When you did the analysis it should have also shown you the mode shapes. A manual analysis will give you the fundamental mode shape and frequency. You can find the methods in any vibration text book.

Regards
Dave

 

[GregLocock]

Agreed, you need to look at your mode shapes. I don't think it is any surprise that running the rig at the same frequency that you identified with an impact test is most effective.



Cheers

Greg Locock

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[Drej]

As a starting point, have you checked that the boundary conditions from your rig tie with those of your FE model?

And, yes, this is a leading question...


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[AndrewUK]

well as best I could the panels fit into plating rig which holds the panels in a 'comb' like slider. This comb allows some movement which I factored into the model, but of course could change.

With the panel able to move slighty (1 to 3mm) this would change the stiffness but would the panel 'bounce' around setting of new freq's?

Could I use beam formula to find the natural freq or is there one for a plate? 608mm x 453mm x 1mm.

Also getting myslef confussed, is this "sinusoidal vibration " or "Simple harmonic vibration" , I've been working on SHM but the vibration motor is rotary. sorry if I sound dumb now but its bugging me! thanks again

 

[GregLocock]

Guessing that you are holding a PCB in a rattly sort of assembly fixture, I wouldn't worry overmuch about your FEA, it got within a factor of 2, and without a good model of the BCs you will be hard pushed to get it better than that - you might want to do 3 runs, one free-free, one pinned, one clamped at all edges, to see how much difference it makes.

Your motor will produce roughly sinusoidal input, but may well have some harmonics.

"With the panel able to move slighty (1 to 3mm) this would change the stiffness but would the panel 'bounce' around setting of new freq's?"

Moving by several times the likely amplitude of flexural vibration is not 'slightly'!

A google search on "flexural modes of a rectangular plate" will probably give you an analytical solution for the simple cases, Blevins covers it more thoroughly.

Given that you have a fluid loaded plate, with indeterminate boundary conditions, I think you will be lucky to get better than a ballpark approximation.













Cheers

Greg Locock

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[AndrewUK]

thanks for help guys.

Imanged to get FFT on my site here

http://www.andrewflower.plus.com/scan.jpg

The peak witht he dot is 65 Hz the peak to the left of that is 54Hz.

Gregg, I think you're right I'n not going to get much better with my FE model.

What I don't understand is why the actual plate didn't shift the bubbles at is lower fundemental freq's?

With the rattly rig the stiffness would decrease rasing the nat freq. hence not even occuring until 55Hz, or just too little energy in it at 23HZ?
Any comment on the noise to the right would be could, trying to get on a course for this anyone of a a good pratical course in the UK?

 

[GregLocock]

The best vibration course I ever went on was at ISVR at Southhampton.

I'm inclined to think your lower resonant frequencies predicted in your FEA model are in error. You need to compare mode shapes between your FEA and your impact tests to check that out.



Cheers

Greg Locock

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[AndrewUK]

thanks for that, I've emailed ISVR as they have a few short courses running.

Do you think my first natural freq is actually 55 Hz as opposed to the 27Hz from the mode? I guess this could be due to change in stiffness from the model restraints to actual.

trying to remmeber dispalment equ for modes
1st x =AsinWt
2nd x^(dot)=AWcost
3rd x^(double dot)= AW^2sint

is that correct forgive my questions and inaccurate terms I'm a little rusty at this.

 

[IRstuff]

The ping test is definitive. Your other modes are either artifacts of your analysis conditions or you are not using it or pinging it the same way you're analyzing it.

TTFN

 

[AndrewUK]

thanks for input guys, but does anyone know this?>>>

trying to remmeber dispalment equ for modes
1st x =AsinWt
2nd x^(dot)=AWcost
3rd x^(double dot)= AW^2sint

is that correct forgive my questions and inaccurate terms I'm a little rusty at this.

Would a the 2nd modal (fundemental) freq. depart more or less energy to a plate than the 1st modal freq.?

 

[electricpete]

If x is as shown, your x' and x'' are correct except you need as minus sign as shown:
1st x =AsinWt
2nd x^(dot)=AWcost
3rd x^(double dot)= -AW^2sint

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[GregLocock]

I agree with IRstuuf, most likely 50-60 is your actual fundamental mode.

which mode is most efficient depends on the exciter location, but typically the fundamental is the easiest to drive, for very good reasons.





Cheers

Greg Locock

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[electricpete]

Harris' Shock and Vib Handbook p7-32 Table 7.9

wn = 2*Pi*fn = C * sqrt([D*g]/[gamma*h*a^4])
where
a = 608mm
b = 453mm
a/b~1.3

C = table lookup. Bottom row of table has all edges clamped. C= 36 for a/b=1.0, 1.5 for a/b=27, for your case ballpark eyeball interpolation C = 31.

D = E*h^3 / [12*(1-mu^2)]
E = modulus of Elasticity
mu = poission's ratio
h = 1mm
gamma = weight density

g is not defined - I assume this may be attempt to assist English unit conversion factor related to lbf's and lbm's. (I hate when they do that... we can do the units ourselves). I suspect if you leave out g and supply needed unit conversions, it will work.

Give it a try and see what you come up with. You haven't told us E or mu or gamma.

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[electricpete]

small correction...reversed some numbers in discussion of C but doesn't affect the final answer. Corrected version:

"C = table lookup. Bottom row of table has all edges clamped. C= 36 for a/b=1.0, 27for a/b=1.5, for your case ballpark eyeball interpolation C = 31."

You can do your own interpolation if you'd like. Just in case you want to visualize the shape of the curve here are all the points given in the table:
a/b C
1 35.98
1.5 27.00
2.0 24.57
2.5 23.77
3.0 23.19
Inf. 22.37


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[electricpete]

Actually there are two types of boundary conditions available within the table. The one I gave above is clamped on all 4 edges. There is another for simply-supported on all 4 edges. It is the same equation but different C

a/b C (simply supported edges)
1 19.74
1.5 14.26
2.0 12.34
2.5 11.45
3.0 10.97
Inf. 9.87

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