Why is a vibration that reaches natural frequency so detrimental?

[k.udhay]

Why are we not supposed to operate a machine on its natural frequency condition? I read max. energy transfer happens at this condition. What exactly does it mean?

When we swing a pendulum it just oscillates on its natural frequency. Nothing goes wrong there. So what makes it different for a machine? Thanks.

 

[Simon Bridge]

Hint: look up "resonance".

When you run a machine you are constantly adding energy to it - imagine you keep giving a pendulum bob a little tap (adding energy) in time with it's natural frequency as opposed to out of time with it: what happens?

 

[tygerdawg]

Explained another way...

The pendulum is "unexcited" or "not excited"...no additional impetus to motion is added to it. It just swings.

Your drum-style washing machine is turned by a motor. Without any unbalance, the drum simply rotates. But put enough soggy clothes in one location, then the drum starts to oscillate a bit. At low speed, probably nothing much happens. At sufficiently high speed and unbalanced load, the momentum of spinning that unbalanced load makes the drum sway in its moorings. The sway or oscillation increases a little bit at a time until we get the "bonk bonk bonk" of the drum hitting the housing.

The Tacoma Narrows Bridge received an excitation that by chance happened to be a the bridge's natural frequency. Wind blowing through the structure caused the phenomena of vortex shedding, first one side and then the other. Each vortex caused a little bit of impetus to the structure. The rest is a black & white film of bridge collapse caused by fatigue failure brought on by extreme structure oscillation.

 

[k.udhay]

Thanks a lot Simon and tygerdawg. I get your points... This is like rocking a swing at the same frequency which keeps increasing the swing angle at the end of every cycle, right? But a similar thing happens in a two stroke engine piston as well. The vibration frequency of the piston (or the rocking frequency) and the firing frequency (exciting frequency) are just the same. But that does not cause any detrimental damage to the piston, does it? Am I comparing with a wrong example?

 

[Simon Bridge]

Does the piston have a natural frequency without the combustion stage? (i.e. if you had an ideal friction-free motor, and you just gave the piston one shove, would it tend to a particular frequency like the pendulum does?)
What happens to the firing frequency when you open the throttle?

 

[russ_watters]

But a similar thing happens in a two stroke engine piston as well. The vibration frequency of the piston (or the rocking frequency) and the firing frequency (exciting frequency) are just the same. But that does not cause any detrimental damage to the piston, does it? Am I comparing with a wrong example?

It could - my car has a tachometer redline and a governor to prevent overspeeding the engine.

Resonance is not automatically a bad thing (especially for musicians!), it is only bad in certain circumstances where it causes an unconstrained amplitude increases that damages something.

When I was in basic training, a company was marched over a footbridge (despite being instructed not to) and the resonance from the bouncing snapped one of the telephone poles that spanned the creek. It was replaced with steel.

 

[AlephZero]

The resonance itself doesn't make anything fail. The failure is caused by the stresses in the structure. The stresses are usually bigger when the object is resonating simply because the motion has bigger amplitude.

So, you have two options when designing something: either you make it strong enough to withstand the stresses when it resonates, or you design it so the resonant frequencies are not excited - for example by keeping them outside of the normal operating frequency of the machine.

In the bridge example, it would be possible to make a bridge strong enough to survive the resonance, but it wouldn't be economic because if the increased cost, weight, amount of material required, etc. So long as people obey the "operating instructions" (i.e don't march over the bridge in step) the resonance won't occur. Of course for a different type of bridge (e.g. one carrying vehicle traffic on a public road) avoiding resonances could be a design issue, if you can't (or don't want to) impose restrictions on the way people use the bridge.

The piston engine is not a good example of resonance. The amplitude of motion of the pistons, valves, etc are fixed by the design of the engine. The stresses caused by the acceleration of the moving parts will be roughly proportional to RPM², and keeping those stresses below a safe value is one reason for limiting the RPM of the engine.

 

[Bobbywhy]

Why are we not supposed to operate a machine on its natural frequency condition? I read max. energy transfer happens at this condition. What exactly does it mean?

When we swing a pendulum it just oscillates on its natural frequency. Nothing goes wrong there. So what makes it different for a machine? Thanks.

See this video if you thought nothing would go wrong there:

Tachoma Narrows Bridge collapse


Cheers, Bobbywhy

 

[AlephZero]

Another consideration is the fact that vibration creates stresses which vary with time. Depending on the material, that can cracks etc to develop over time, even if a constant stress of the same level would be harmless. (Google "metal fatigue" for more information). The safe fatigue stress for a material is often quoted for 10⁷ alternating cycles of the stress. That might sound like a big number, but if a machine is vibrating continuously while it is running, compare it with the fact that there are about 3 x 10⁷ seconds in a year.

 

[NascentOxygen]

A much more recent embarrassment was http://en.wikipedia.org/wiki/Millennium_Bridge,_London

 

[k.udhay]

Thanks to all of you and my sincere apologies that I couldn't actively participate in the discussion. All the replies were someway a new information to me. And in between, I sort of found the "my way" to understand
'Why is a vibration that reaches natural frequency so detrimental?' Kindly correct me if I am wrong:

A pendulum case is taken as an example here.
1. A person pokes the bob.
2. The bob starts vibrating (or oscillating) in its natural frequency.
3.If this person keeps pushing on the same frequency, it keeps increasing the amplitude. In this example may be it is not so serious issue (apart from increase in centrifugal force every time when the bob reaches max. velocity of that cycle). But in a case such as a bridge which vibrates, it is.
4. But what when he doesn't excite the pendulum in its natural frequency?
This part is where I was too curious to know and too careless to miss:
[Again to pendulum example] If the person now tries to stroke the bob in a non-natural frequency, when the bob was trying to make its return stroke, he probably pushed it to move onward. This is something like applying a heavy brake on the bob. This in a way, reduces the amplitude of vibration.

I am very sure this explanation looks silly to most of you, as this is a fundamental understanding about vibration. My apologies once I again! :(

 

[Dutchwayne]

Natural frequency causes harmonics. In machinery this is bad because it creates high loads at the cycle peak usually far higher than desired. For pumps, it can cause the bearings and the seals to fail early, damage the drive motor, etc. I have seen harmonic vibrations tear piping systems to shreds, caused a tank to collapse and ravaged other equipment. It is actually a good example of how the real world does not act like the world of calculations.

 

[spectastic]

when I took diff eq, the professor explained resonance with a differential equation. (one of those that doesn't converge, but grow in amplitude - can't think of the word)...

he associated that equation to resonance which led to the collapse of that bridge. I think it was one of these equations where if you tweak one of the variables just right, it changes the behavior of its graph... I don't remember.

if anyone knows what I'm talking about let me know. I'm curious now.

 

[k.udhay]

Hi Dutchwayne... A question related to the answer... What is a harmonic vibration? I have posted a detailed question here: https://www.physicsforums.com/showthread.php?t=769473

Thanks.

 

[FactChecker]

Two examples:
1) Here is the youtube of the bridge that others have referred to: A bridge being excited at it's natural frequency
2) There have been prototype airplanes that, when just sitting on the ground, would start to make tiny motions of it's rear tail surfaces. They grew, and grew, and grew, till the plane was hopping on the ground. (sorry, no video)

 

[OldEngr63]

Natural frequency causes harmonics. In machinery this is bad because it creates high loads at the cycle peak usually far higher than desired. For pumps, it can cause the bearings and the seals to fail early, damage the drive motor, etc. I have seen harmonic vibrations tear piping systems to shreds, caused a tank to collapse and ravaged other equipment. It is actually a good example of how the real world does not act like the world of calculations.

Sorry, Dutchwayne, but natural frequency does NOT cause harmonics. Please look up the definition of harmonics, and you will see that there is no connection at all.

 

[OldEngr63]

Thanks a lot Simon and tygerdawg. I get your points... This is like rocking a swing at the same frequency which keeps increasing the swing angle at the end of every cycle, right? But a similar thing happens in a two stroke engine piston as well. The vibration frequency of the piston (or the rocking frequency) and the firing frequency (exciting frequency) are just the same. But that does not cause any detrimental damage to the piston, does it? Am I comparing with a wrong example?

While not visible at all, the periodic torque pulsations in an IC engine (either two stroke or four stroke) cause torsional vibrations in the engine and whatever machinery is coupled to it. These pulsations arise from (1) gas pressure pulses due to combustion, and (2) inertia variation due to the kinematics of the slider-crank mechanism.

One of the biggest concerns in engineering an engine driven machinery package is to assure that torsional vibration will not cause a fatigue failure. A typical case is an engine-generator set, running hour after hour at 1800 rpm to generate 60 Hz current. For this case, the steady vibratory stresses ust be kept quite low to be safe.

 

[analogdesign]

Two examples:
1) Here is the youtube of the bridge that others have referred to: A bridge being excited at it's natural frequency
2) There have been prototype airplanes that, when just sitting on the ground, would start to make tiny motions of it's rear tail surfaces. They grew, and grew, and grew, till the plane was hopping on the ground. (sorry, no video)

Ironic! From Wikipedia:

"In many undergraduate physics texts the event is presented as an example of elementary forced resonance with the wind providing an external periodic frequency that matched the natural structural frequency, even though the real cause of the bridge's failure was aeroelastic flutter. A contributing factor was its solid sides, not allowing wind to pass through the bridge's deck. Thus its design allowed the bridge to catch the wind and sway, which ultimately took it down."

 

[Simon Bridge]

https://www.physicsforums.com/threads/good-explanation-of-aeroelastic-flutter.624992/
... connection between aeroelastic flutter and resonance.