High or low resonance
High or low resonance
(OP)
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,
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,





RE: High or low resonance
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Greg Locock
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RE: High or low resonance
If you do expect shock loads, design some damping functionality (just add physical dampers)
RE: High or low resonance
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,
RE: High or low resonance
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RE: High or low resonance
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.
RE: High or low resonance
RE: High or low resonance
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.