Flight and Harmonic Vibrations
Name: Cesar M.
I will like to know the concept of harmonic vibrations.
I am a flight instructor and I know for example that the hydraulics pumps
driven by the transmission rotate at different speed to reduce harmonic
vibrations, undesirable because failure and cracks of components and
structure of the helicopter will occur.
Please explain to me how this phenomenon occurs.
Physical structures -- buildings, bridges, automobiles, or aircraft -- can
vibrate. Like a violin, piano, or horn there are certain vibrations that
reinforce one another. These are called resonances. They can cause the
structure to vibrate with large and/or increasing amplitudes. This flexing
puts stress on the same locations of the structure and the moving back and
forth in the same place eventually weakens the structures at these flex
points resulting in damage or failure. In order to obtain a quiet ride in
an automobile designers engineer the suspension to have many different
vibrational modes. Then they tend to cancel one another. If you have ever
seen a car with bad shock absorbers, if you push up and down, the car will
begin to rock in "harmony" with your pushing and will continue to rock
rather than damp out. I'm not sure that it is true, but anecdotal reports
tell that troops marching across a bridge break marching cadence because if
everyone is stepping at the same frequency this harmonic motion can cause
the bridge to begin to vibrate and perhaps collapse.
I am a structural engineer and we also have to deal with vibrations. Perhaps
approaching from our view may help. Bridge designers often incorporate large
springs within the structure to deal with the problem, trying to dampen
vibration, sort of like shock absorbers in a car. With bridges, mainly the
problem is wind. The classic is the Tacoma Narrows bridge ( I think Verazona
straits, try a Google) where there was no thought to vibration, the structure
just designed for wind loading. In , I think the fall when the wind whipped
up, it whistled thought the cable suspension system ( the bridge is similar
to the Golden Gate). Anyway, those vibrations carried down to the deck, the
deck began oscillating, the waves getting more extreme, till the bridge
literally tore apart. The harmony being the addition of like waves. A
phenomena occurs, sometimes even employing signs in applicable regions, an
Army troop marching at full cadence is ordered to stop marching and walk
across, at their own individual gaits. The" in time" stepping produces
vibration, the multitude of soldiers adding to the vibration. So, sound
waves being not visible, to be understandable think of other waves. When
trying to think of waves, as sound waves, picture other waves, like waves in
water. Opposing waves can cancel each other, or like the troops, if in the
same direction , same shape, can add, I guess, hence the word "harmony"
trying to explain that addition, or extra strength.. Hope this helps.
Vibration in general is bad for materials. It can lead to fatigue of
parts and eventual failure. But, if you know the extent of the vibration,
you can properly design the component(s) to live longer than the you
expected to use the component. That is why planes and helicopters have
limited life. There are two types of vibration: free and forced. Free
vibration is when a component vibrates under the action of forces inherent
in the system, specifically mass and stiffness of the material. Every
system has this property and it is called natural frequency. Forced
vibration occurs due to external forces causing vibration of the
system. This is like a helicopter blade rotating and causing vibrations
throughout the whole helicopter. Now if a forced vibration coincides with
the natural frequency of a component, then large oscillations can result,
tearing the component apart. One of the most famous examples of this was
the Tacoma Narrows Bridge. Oscillations started due to the wind (aeolian
harp). These oscillations corresponded to the natural frequency of the
bridge, which led to excessive force on the bridge which caused it to
collapse. I am sure there is video on the web of this disaster. To limit
vibration problems, analysis is done to minimize vibrations occurring
around natural frequencies of components, hence your mention of the
pumps. We can determine the frequency that will be transmitted by the
pumps and do things to mitigate the problem, i.e. dampers, running at
different speeds, etc. Different materials can be used (different mass)
or a different component shape can be used (different stiffness) to also
limit natural frequency problems of the component that may see these
Hopefully this helped. Thanks for using Newton.
Christopher Murphy, P.E.
Basically, all materials are slightly elastic or "springy." It might not
seem like it, but steel beams, pipes, buildings, bridges, and tuning forks
can all be made to vibrate in different ways.
Like a stretched guitar string that makes a certain musical note,
materials and structures tend to vibrate at certain natural frequencies. If
you could push on a building really hard, it might vibrate back and forth at
a frequency of 1 cycle per second, or Hz. That's its natural frequency.
(Actually it is more complicated - the building might vibrate sideways at 1
Hz and up and down at 3 Hz.) A drinking glass might vibrate at 500 Hz if
you hit it with a spoon.
If the item is "driven" by a force at the natural frequency (forced
oscillations), vibrations can keep getting larger and larger. Sort of like
pushing someone on a playground swing. If you push correctly, the person
can swing very high.
Loud sound can shatter a drinking glass if it is at the right frequency.
The right kind of earthquake, if it lasts a long time can topple a building
if it gets into "resonance".
Vibrations are a big problem in machines that rotate. If you speed up a car
engine you may hear buzz and vibrate at different engine speeds as things in
the engine compartment start to vibrate. Sometimes these vibrations can
So, in light of the resonance problem it is reasonable that a hydraulic pump
would have a rotation speed chosen so that it does NOT induce any vibrations
in other parts on the helicopter.
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Update: June 2012