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The half-power bandwidth method obtains the damping ratio from

  • A.the time taken for the motion to die away completely
  • B.the width of the resonance peak at \( 1/\sqrt{2} \) of its height
  • C.the amplitude of the very first peak of a free vibration record
  • D.the static deflection of the structure under its own weight alone

Answer: B

Correct answer: the width of the resonance peak at \( 1/\sqrt{2} \) of its height

The method uses the shape of the frequency response curve. The frequencies either side of resonance at which the amplitude falls to \( 1/\sqrt{2} \) of the peak bound a band whose width gives the damping:

\[ \xi = \frac{f_2 - f_1}{2f_n} \]

Light damping gives a sharp peak and a narrow band, heavy damping a broad one. It requires a forced vibration test with a swept frequency, where the logarithmic decrement needs only a decay record - the two methods suit different experimental means.

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