High or low resonance

[ggoo]

Folks, I have this problem in mind for a long time and wish someone can give me a good hand.

In designing structure to withstand vibration, is it better to design the structure with high or low resonance frequency? The assumption is resonance is unavoidable, that means vibration test frequency range is wider than the resonance frequency of structure. Also, assuming the G level is identical throughout the test frequency spectrum.

This problem led me to read a vibration book from Steinberg. Inside the book I found the following statement to describe the vibration within a circu

“ A high natural frequency means low displacements and low strains, so the transmissibilities are usually higher. Conversely, a low natural frequency means high displacements and high strains, so the transimissibilities are usually lower. “

According to this statement, it seems it is more beneficial to design the structure to lower resonance frequency to leverage on lower transmissibilities. With the uniform input G level, the dynamic loading should be lower at low resonance frequency.

However, based on the following equation provided by Steinberg found in earlier chapter:

Y = 9.8 * Gin * Q / F^2

Where,

Y is displacement
Gin is input G level
Q is transimissubilities
F is natural or resonance frequency

Apparently displacement is proportional to transmissibilities. It seems contradicting to the above statement about circuit board. Anybody can confirm me?

Also, any recommendation for whether the structure should be designed for high or low resonance frequency is appreciated.

Regards,

 

[GregLocock]

The answer depends on a whole host of things. Not limited to - what effect of the resonances are you trying to avoid? what shape is your excitation spectrum? And what sort of excitation is it - displacement, or force, or more realistic?


Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[rob768]

I agree with Greg. You will have to know what forces, and most important, what frequencies you expect. Only if you are designing for shock, your frequencies are indetermined. In that case, I'd go for very stiff, just to avoid large deflections. In other cases, you will be able to define a load and frequency spectrum you can work around.
If you do expect shock loads, design some damping functionality (just add physical dampers)

 

[ggoo]

Thanks for the response.

I would like to make the case as simple as possible. I am really talking about simple sinusodual vibration with unified G level over the spectrum. That means, the G level is identical over the frequency range.

The excitation is done typically in shaker table in vibration lab.

The goal is minimize the dynamic loading on the board.

Let's put some number for the sake of discussion.
The test frequency range is 20 to 2000Hz with uniform G level of 10G. Now I need to design a structure.
I also know the best resonance frequecny I can achieve (the most rigid design) is less than 2000 Hz. I also know the minimium natural frequency I can achieve is more than 20Hz.
Now it is the question of whether I should make it rigid or not.

According to Steinberg statement, a low natural frequency means high displacements and high strains, so the transimissibilities are usually lower. Based on this statement, it seems that design the structure to low resonance frequency is favourable since the transmissibilities is lower. Low transmissibilities means less dynamic force output.

This contradict to my believe that design to higher resonance is more favourable.

Also, any comment about the stuff I wrote about Steinberg book?

Regards,

 

[electricpete]

I haven't thought too much about the question yet, but wouldn't damping determine the vibration at resonance, regardless of resonant frequency? In that case the assumptions about damping (is it proportional to stiffness or what) would be important to discuss.

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[rob768]

I don't know the mass that will be vibrating at 2000 Hz and 10 g, but I wouldn't want to be near. Any idea on the forces involved if the mass is indeed considerate? Use that force as input for the design of the frame, and especially of deformation and related stresses.

And yes: a stiff frame leads to more transmission, since there is less energy consumed in the deformation of the frame. That's why frames with vibrating or reciprocating machinery are often resilitiently mounted. The low natural frequencies of a frame on rubber or springs isolate the frame from its foundation.

 

[2design]

Even if you design for a low frequency, won't there still be some resonances at the higher frequncy range? I believe that all you will be doing is changing your mode shapes, add or subtarcting certian modes, when you design for a high or low resonance.

 

[ggoo]

Thanks for the response.

Electripete, you are correct that Steinberg did mentioned his statement is with the conclusion that the PWB will be flexing more during large displacement and hence damping is high, The consequency is Q is low.

Rob, the effect of mass and stiffness has been included in those Q formula. These parameter is normally replaced by angular velocity term [angular velocity = sqrt(k/m)]. Typcially Q equation involves only velocity ratio and frequency ratio. Another formula I found for Q is
Q=1/c*(sqrt (km)).

2design, you are correct there will be harmonic effect and I think it may be the added advantage to design to high resonance frequency. My experience is the second harmonic has far less damage than the fundamantal frequency.

I have been thinking more about the question I have. Any from the e-mail I received, it's almost concluded it is still more benefitial to design to high frequency.

With regards to Steinberg statement, I now tends to think the following:

-Q is high in high frequency, but the resulting displacement is still low. That means, the dynamic stress on the structure is still low. This is based on the equation given above, the displacement is inversely proportional to the square of frequency. Although the Q is increased in high frequency, but the increase in frequency offset the effect for the increase in Q.