Why is stiffer better? 1

[htsmech]

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

 

[Maui]

The inherent advantage of designing your system so that the natural frequency lies well above the typical operating range is that you don't have to force the system to pass through the natural frequency in order to reach the operating range. This reduces the probability of damage to the system due to resonant frequencies.

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

 

[electricpete]

My two cents on question #1... please bear in mind I am electrical by education so might be off base:

"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.

 

[electricpete]

... I have heard of field modifications of rotating machinery go either direction to resolve a resonance condition... stiffening or adding mass. But adding mass may require a little more analysis to make sure the additional mass can be supported without problem by existing structure.

 

[electricpete]

Followup to my first post... the lowest frequeny modes are easiest to identify... they usually have the simplest mode shape.

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.

 

[jomandar]

I don't feel that the natural freq of the system should be always greater than excitation freq.
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'

 

[EnglishMuffin]

There are a number of machines that are knowingly designed such that the natural frequency is lower than the excitation frequency. One of these is a spin drier - by doing this it is also possible to achieve self balancing. Another is the steam turbine. Ever since the first steam turbines were developed by Charles Parsons at the beginning of the 20th century, it was found impossible to make the rotor stiff enough such that its resonant frequency was above the very high rotation speed. So friction dampers were placed on the bearings to avoid the problem that maui mentions. Modern gas turbine engines often have squeeze film oil dampers to accomplish the same thing. And once you get way above resonance, the vibration amplitude becomes very low, so perhaps there is something to be said for doing this, provided you have a way to cope with the "maui" problem.

 

[GregLocock]

In cars we usually go for the 'stiffer is better' solution, except for when we are trying to isolate things when we often try to make the isolators as soft as possible.

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

 

[electricpete]

I guess I have kind of a similar pet peeve question that is bugging me.

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?

 

[jomandar]

Dear Greg & Electricpete,
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'

 

[DanT]

>snip<
-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 &quot;above resonance&quot; but the motion of M1 is larger. For unbalance it approaches the mass eccentricity. I used to imagine (hope?) that the &quot;below resonance&quot; 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)?

 

[hacksaw]

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.

 

[GregLocock]

I've just realise why we might tend to go with 'stiffer is better' - if you look at the mobility on a spectrum the average level across the entire frequency range will be lower if the first resonance is high in frequency.

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

 

[electricpete]

Greg - what's mobility? Is it different than dynamic stiffness?

 

[GregLocock]

Mobility is velocity per unit force. I think we use it because (a) force times velocity is power, and (b) sound pressure is a direct function of panel velocity, not acceleration.

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

 

[Rob45]

Here's another thought: numerous structures simply can't be made stiff enough to be above the driving frequency range.
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.

 

[drawoh]

Are we talking about vibration isolation here, or structural design? My assmption has been that a structure with a high natural frequency is very stiff, and that the mechanical displacement under vibration is low enough that I can ignore it. If I am isolating vibration, then I want my operating freqency to significantly exceed 1.4n so that vibration is indeed isolated.

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

 

[zzy]

For the second question regarding excitation at harmonics, it is better to understand it by using Fourier theory. For Example, your narural frequency is f0 and your excitation frequency f1=0.5*f0. If the excitation waveform is purely sine or cosine wave, the resonance with f0 will not be excited. But, remember there is raraly pure sine wave in the real world. In that case, by Fourier theory, any periodical waveform can be decomposed into a series of harmoncis with its frequencies as f1, 2*f1, 3*f1, ..... Now the second harmonics in your excitation with a frequency of 2*f1 happens to coincide with the natural frequency, f0. It is primarily that component of waveform that excites your vibration.

 

[vanstoja]

Having dealt with vibration in complex powerplant fluid piping systems for many years and struggled to understand and apply the sparce guidelines on &quot;resonance avoidance&quot;, it is somewhat disconcerting to read so many references to &quot;THE (presumably one and only) natural frequency&quot; of complex mechanical, electromechanical and hydromechanical systems. The individual components of such systems as well as the whole system and its subassemblies each have a multitude of structural response frequencies in flexural (bending), torsional, extensional and combined modes, not to mention the hydroacoustic modes of any fluids running through these systems (which fluids sometimes stiffen or soften the confining or immersed structural components). For systems with separate major components like pipe branches, pumps, valves, pressure vessels, etc., the major problem in resonance avoidance is assuring that the components not only do not destroy themselves by self-induced vibrations but can also withstand the external vibration inputs from other adjacent or connected components in the system. To achieve both goals, one must deal with structural and perhaps hydroacoustic resonances scattered throughout the frequency range from about 5 to 10,000 Hz. It is a formidable task just to identify the important vibration modes to be analyzed in complex systems and the prospects of using single degree of freedom equations to provide reliable results is rather limited. Even the classical beam, plate, column, shell equations for structural vibration responses rarely apply to the actual end constraint conditions of complex mechanical sytems or their components, subassemblies and parts. Finite and boundary element analyses are essential in many of these circumstances. For fluid-loaded structures stiffening/softening effects on calculated structural resonant frequencies depend on the mode of structural vibration (eg., torsional modes are generally unaffected by fluid loading) and the area extent of fluid coverage of the structure.
All of these complications make a &quot;cookbook&quot; approach to resonance avoidance in complex systems a virtual impossibility and the related sub-issue of &quot;stiffening/softening&quot; to avoid &quot;THE natural frequency&quot; about as timely as Tyrannosaurus Rex.

 

[vgarzani]

A couple of basic considerations:

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.