Why is stiffer better?
Why is stiffer better?
(OP)
Just a basic theoretical question (or three):
I know that it is desirable to have the natural frequency of a system be far away from any driving frequencies.
-Is there any inherent advantage to having the natural frequency above the driving frequency? If I look at an output magnitude vs. driving frequency plot for a 2nd order system, the magnitude drops off at frequencies above the natural frequency, but I was taught that higher natural frequencies were better.
-Related to that, is there any risk of exciting resonance at harmonics below or above the natural frequency? The simple models don't show it, but it seems likely.
BTW, I am working with pressure fluctuations in a fluid (water) system. Does that affect any of the fundamental equations of a 2nd order system (spring, mass damper)?
Thanks,
Steve
I know that it is desirable to have the natural frequency of a system be far away from any driving frequencies.
-Is there any inherent advantage to having the natural frequency above the driving frequency? If I look at an output magnitude vs. driving frequency plot for a 2nd order system, the magnitude drops off at frequencies above the natural frequency, but I was taught that higher natural frequencies were better.
-Related to that, is there any risk of exciting resonance at harmonics below or above the natural frequency? The simple models don't show it, but it seems likely.
BTW, I am working with pressure fluctuations in a fluid (water) system. Does that affect any of the fundamental equations of a 2nd order system (spring, mass damper)?
Thanks,
Steve





RE: Why is stiffer better?
In answer to your second question, near-resonance effects may be a problem depending upon the sensitivity of your system, and the proximity of the excitation to the resonant frequency.
Maui
RE: Why is stiffer better?
"Is there any inherent advantage to having the natural frequency above the driving frequency? If I look at an output magnitude vs. driving frequency plot for a 2nd order system, the magnitude drops off at frequencies above the natural frequency, but I was taught that higher natural frequencies were better."
I don't see signficant advantage to stiffening far above natural frequency as opposed to unstiffening far below natural frequency (excluding startup concern identified above)... FOR A SIMPLE SINGLE-DEGREE OF FREEDOM SYSTEM YOU DISCUSS.
But the problem is that real world systems rarely fall in this category. Generally there are many more mode natural frequencies (associatd with different modes) above the first one. The idea of stiffening is to identify the lowest one and shift it up above operating speed. If you tried to identify the lowest one and shift it down you may still have others above it shifting down and causing problems.
RE: Why is stiffer better?
RE: Why is stiffer better?
But if you have a very flimsy structure excited by high frequency there will be a variety of complex mode shapes that have to be considered.
My two cents... struggling with the same questions as yourself.. hope to hear if I'm not exactly correct.
RE: Why is stiffer better?
My experience in reciprocating compressors is that while designing the springs we used to keep the system freq less than 10 Hz as my excitation freq is 50 Hz. These compressors are fitted on the commercial appliances so one should take care of vibrations also.
If i am going to add an additional stiffness in the springs defintely it will shift system freq well above the 50Hz but at the same time vibration level will go up which is higly objectionable. So in my application an optimum balance is maintained between system's natural freq and vibration.
regards,
jo'
RE: Why is stiffer better?
RE: Why is stiffer better?
A classic example where that causes problems is the engine mounts - to get them soft enough to isolate at idle they are so soft that as the engine accelerates from startup it runs through the resonance - which is quite noisy. In the good old days we used much stiffer engine mounts and had the resonance above idle but below the normal operating speed range of the engine (what did you thnk the gap between 600 and 1200 rpm was for? It is where we hide all the resonances, seriously).
Electricpete mentioned adding mass - definitely done that. We used to find that adding a 5 kg mass to a mounting point would cure (or at least reduce)many noise issues. One car company put one of those into production!
Oh, I know one case where floppy is better - sumps (oil pans) should be steel, not cast aluminium, for radiated noise. That is a bit of a cheat, the reasons are not quite the same.
Cheers
Greg Locock
RE: Why is stiffer better?
Before we knew math we generally thought that stiffening things would make them vibrate less. Then we learned the single degree of freedom mass spring system and " and learned that it is more important is how far we are from resonance (dynamic stiffness more important than static stiffness).
But don't we often find ourselves and others always slipping into the old mode of thinking stiffer is better?
Have you heard the following:
- Horizontal rotating machines in presence of unbalance typically have lower vibration in vertical direction than horizontal due to the higher vertical stiffness
- A 2-pole motor is more susceptible to twice line frequency vibration than 4-pole because the 4-pole clover-shaped stator deformation modeshape is much stiffer than the 2-pole oval stator deformation modeshape.
- Look at how flimsy that machine support is... no wonder it's vibrating so much.
etc.
I have to admit if I was on a desert island with no equipment and machine was vibrating but don't know above or below resonance ... you tell me I can either stiffen it or weaken it (but only one shot)... my gut says stiffening is better (even though my brain says it's a coin toss depending on whether above or below resonance). Which is right, my gut or my brain?
RE: Why is stiffer better?
Thanks for vibration consideration taken into account.
Also i am agree that dynamic stiffness should be considered
while addressing such issues.
One can really think of stiffening the structer in first
shot.
regards,
jo'
RE: Why is stiffer better?
-Is there any inherent advantage to having the natural frequency above the driving frequency? If I look at an output magnitude vs. driving frequency plot for a 2nd order system, the magnitude drops off at frequencies above the natural frequency, but I was taught that higher natural frequencies were better.
The transmitted force is lower when the forcing frequency is "above resonance" but the motion of M1 is larger. For unbalance it approaches the mass eccentricity. I used to imagine (hope?) that the "below resonance" amplitude was less than the mass eccentricity, but after plugging in numbers a dozen or so times for non-isolated (rigidly mounted) machinery and getting amplitudes of essentially gr-inch/grams I kind of stopped.
-Related to that, is there any risk of exciting resonance at harmonics below or above the natural frequency? The simple models don't show it, but it seems likely.
BTW, I am working with pressure fluctuations in a fluid (water) system. Does that affect any of the fundamental equations of a 2nd order system (spring, mass damper)?
RE: Why is stiffer better?
pressure fluctuations even in a liquid system are rarely modeled with a single spring-mass equivalent unless you know for certain that all of the disturbances and excitations occur at lower frequencies.
where you have well characterized resonances, it is not uncommon to operate between criticals.
RE: Why is stiffer better?
Therefore, for random inputs, and impacts, and things like that there will be less energy in the structure, which on balance is usually a good thing. Obviously in a car many of the inputs are random - road inputs are typically pink noise like, though I think the roll off with frequency is a little greater than 1/f (I can't find the curve at the moment).
Cheers
Greg Locock
RE: Why is stiffer better?
RE: Why is stiffer better?
Our targets are usually in a mixture of stiffness, mobility, and acceleration/force, so we get a fair amount of practice at integrating in the frequency domain.
Cheers
Greg Locock
RE: Why is stiffer better?
Example: an automotive exhaust system will typically have a first mode frequency of 5 Hz or so, with higher modes every 5 Hz, e.g., 10, 15, 20 Hz... The only thing (two) things you can do with it is to isolate it with e.g. rubber hangers, and then to make sure these hangers are not located at anti-nodes of the system for particularly objectionable frequencies - since they're bound to be at an anti-node for SOME frequency.
Then concerning softer engine mounts: you DO want the resonant frequency of the mount system to be as low as possible so that the transmissibility is as low as possible in the acoustic frequency range. Setting engine/mount resonance between idle and running frequencies will give unacceptable transmissibility in the running frequency range.
However, the engine/mount system can't have a resonance so low that it's in the ride frequency range, where it'll be excited by road and running gear inputs. This presents you with a rather narrow window of acceptable frequencies.
RE: Why is stiffer better?
Is this analysis not massively affected by the problem we are trying to solve?
Recently, I analyzed a cover for its lowest vibration mode. The system was shock mounted, so I simply ensured that the cover's natural frequency grossly exceeded the natural frequency of the shock mounting. This ensured that the cover would not see significant amplitude at resonance.
JHG
RE: Why is stiffer better?
RE: Why is stiffer better?
All of these complications make a "cookbook" approach to resonance avoidance in complex systems a virtual impossibility and the related sub-issue of "stiffening/softening" to avoid "THE natural frequency" about as timely as Tyrannosaurus Rex.
RE: Why is stiffer better?
1) The example of many belt driven fan units is to float the whole machine, but to ensure what is isolated is of itself stiff for general reliability - for example there is bracing to limit deflections due to belt pull. Kind of the best of both worlds - attenuation associated with soft mounts, but structural control and local resonance avoidance with stiffness in the assembly.
2) Any time I've ever run into fluid pressure pulsations, the fundemental and a handful of harmonics had to be avoided. Don't forget about the harmonics.