What Does Double Amplitude (D.A.) Mean in Sine Vibration?

When you input your frequency and acceleration data into a sine vibration frequency response NASTRAN deck, you may run into that cryptic notation, 0.32 inch D.A. from 10-20Hz. This is what is known as a vibrational amplitude. But since NASTRAN does not know what D.A. is, and you probably don't either, you need to convert that value into something everyone understands, such as a vibrational acceleration, which could be measured in g's or in/sec2 or m/s2. Fortunately, this conversion is not difficult to do.

Start with the fact that acceleration is the second time derivative of length:
  x = (xo)(sine((omega)(t))
  x dot = (xo)(omega)(cosine((omega)(t))
  x double dot = -(xo)(omega)^2(sine((omega)(t))

At maximum amplitude (ignore the minus sign):
  sine((omega)(t)) = 1

Therefore:
  x double dot max = (xo)(omega)^2

By definition xo is the single amplitude:
  xo = DA/2

Also, we know:
  omega = (2pi)(f)

Finally we get the acceleration in terms of the length you are using (length/sec2):
  x double dot = (DA/2)(2pi)^2(f)^2
  x double dot = (19.74)(f)^2(DA)

If you are working in an inch/pound system and you want your answer in g, here is the final equation:
  x double dot = (0.0511)(f)^2(DA)

Back to the Sine Vibe page

Ryan Simmons
August 2002


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