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Free And Forced Vibrations
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Free And Forced Vibrations

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  • 1. free and forced vibrations
  • 2. Free oscillators
    • Undamped oscillator
    • Natural frequency,  o
    • No external forces
    • e.g. swing
  • 3. Forced oscillators
    • External forces act on oscillator
    • Forced/driven oscillator
    • Resonance: driving  =  o
    • e.g. loudspeaker
    • vibrates in response to oscillating electric signal (driver)
    • Barton's pendulums
  • 4. Problems
    • Resonance driver applies forces that continually supply energy to oscillator  increasing amplitude
    • A increases indefinitely unless energy transferred away
    • Severe case: A limit reached when oscillator destroys itself
    • e.g. wine glass shatters when opera singer reaches particular note
  • 5. Damping
    • Resonant Amplitude limited by damping forces
    • At resonance:
    • rate of energy supply = WD against damping forces
    • Increasing damping reduces sharpness + strength of resonance
  • 6. Types of damping
    • Oscillating masses lose energy  amplitude decreases
    • Light damping: amplitude decreases gradually
    • Critical damping: amplitude decreases can decrease to zero without oscillation. Minimum time = T/4
  • 7. Q-factors
    • Measure of resonance
    • Definition: number free oscillations a free oscillator competes before decaying to zero *
    • Light damping = large Q factor
    • Heavy damping = small Q factor
      • e.g. Car = 1
      • Guitar string = 10 3
      • Watch quartz crystal = 10 5
    • * This is only an approximation. Q-factor does have a complicated precise mathematical definition
  • 8. Resonance and damping
  • 9. Examples
    • Pushing a child on a swing – maximum A when pushing  =  o
    • Tuning a radio – electrical resonance occurs when  o of tuning circuit adjusted to match  of incoming signal
    • Pipe instruments - column of air forced to vibrate. If reed  =  o of column loud sound produced
    • Rotating machinery – e.g. washing machine. An out of balance drum will result in violent vibrations at certain speeds
  • 10.
    • Investigation strength of chemical bonds – EM radiation = oscillating electrical disturbance. When incident on a crystal ions subjected to oscillating electrical force. At correct frequency ions ions oscillated by resonance
    • Energy is absorbed from radiation, the frequency of which can be measured with a spectrometer
  • 11. Unwanted resonance
    • Structures/machinery
    • Results in destruction
    • Damping
    • Changing  o of object by changing its mass
    • Change stiffness of supports (  moving resonant  away from driving  )
  • 12. Model aircraft being tested for resonance in a wind tunnel