RESONANCE Vibrational modes

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RESONANCEVibrational modes

• Shashana Williams

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Resonance Defined

• The state of a system in which an abnormally
  large vibration is produced in response to an
  external stimulus, occurring when the frequency
  of the stimulus is the same, or nearly the same,
  as the natural vibration frequency of the system.
• Resonance falls under the broader scope of
  vibrational modes.

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Making The Connection

• Vibrational Modes
• As we learned in class, everything has a natural
  frequency at which it vibrates.
• The natural frequencies are determine by material
  characteristics such as density, molecular
  structure along with design characteristics such
  as size and shape.
• Everyday structures such as buildings, cars,
  bridges, airplanes and Shuttles have an inherent
  natural frequency.
• Any oscillations applied to these systems that
  match their natural frequency causes them to be
  in resonance and can result in extremely high
  amplitudes.

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The Danger

• A system in resonance is in jeopardy of
  destroying itself.
• As previously mentioned, high amplitudes result
  when a system is in resonance.
• Used in this context, amplitude is a measure of
  how displaced from the norm a system is.
• This displacement reduces structural integrity
  and hence makes the system weaker.
• With continued vibration, the already weakened
  structure collapses on itself.

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Some examples of resonance include

• Bridges
• The Marching Band
• The Case of the Singing Wine Glass

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Bridges

• A very famous example of resonance waves
  destroying a bridge is the Tacoma Narrows bridge,
  which fell apart in 1940 in a 40-mph (64-kph)
  wind. The wind that day was at just the right
  speed, and hitting the bridge at just the right
  angle, to start its vibrating. Continued winds
  increased the vibrations until the waves grew so
  large and violent that they broke the bridge
  apart.

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Marching

• When an army marches across a bridge, the
  soldiersare often told to "break step. This is
  to avoid the possibility that their rhythmic
  marching will start resonating throughout the
  bridge. An army that is large enough and
  marchingat the right cadence, could make a
  bridge sway and undulate until it breaks apart.

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The Singing Wine Glass

• In the case of the wine glass, your finger slides
  and sticks along the surface of the glass as you
  rub the rim (a wet fingertip has no oil and makes
  a better contact with the glass).
• The rubbing imparts energy to the glass molecules
  and causes them to resonate.
• The motion of your hand sets up a wave of
  vibration traveling through the glass.
• The vibrating glass causes air molecules to
  vibrate at the same frequency.
• The vibrating air molecules are the sound wave
  that you hear (the frequency or pitch of the
  sound wave is the same as the resonant frequency
  of the glass).

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I Learned

• that all structures have modes of vibration.
• that the most important mode of vibration is
  resonance.
• that resonance is the preferred or natural
  mode of vibration of a structure.
• that if allowed to continue in resonance, a
  structure could destroy itself.
• that resonance is important in the design of
  man-made structures such as buildings, bridges
  and airplanes.
• that there are also benefits of a system in
  resonance such as the singing glass.
• that I could also do the opposite and use a tone
  to break the glass.
• that a 30 or 50 mph wind would likely not have
  destroyed the Tacoma Narrows bridge in this way.
  Hence the resonant condition is specific.
• that marching in unison appears gracious and
  beautiful, but could prove destructive if
  propagated.