# The Great Amplitude Format Debate

Shock and vibration test specifications for avionics and military equipment have almost always been specified in terms of acceleration. The main reason is that acceleration can easily be measured by accelerometers.

Velocity sensors are also available but are less common.

Gaberson, Chamblers et al, claim that pseudo velocity bests represents the damage potential of a shock or vibration event.  Pseudo velocity is the relative displacement multiplied by the natural frequency (rad/sec).  This assertion has merit.  I have written a paper on this subject at: sv_velocity.pdf

On the other hand, Steinberg gives empirical formulas for the fatigue potential for both shock and vibration for circuit boards in terms of relative displacement.  The formulas are given in Steinberg’s Book.

The shock response spectrum can be plotted in tripartite format, showing each of the three amplitude metrics as a function of natural frequency.  A good engineering practice is to review all three response parameters in this format for thoroughness.

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There are two pseudo velocity metrics.

Let omega be the natural frequency in (rad/sec)

The pseudo velocity shock spectrum (PVSS) is calculated by multiplying the relative displacement SRS value by omega.

The acceleration pseudo velocity shock spectrum (APVSS) is obtained by dividing each acceleration SRS value by omega.

Dr. Howard Gaberson has generated some examples which show that the PVSS and APVSS are nearly equal except at very low natural frequencies where the APVSS tends to be higher.

In addition, the true relative velocity can be calculated using the method in:  ramp_invariant_base.pdf

The two pseudo velocity metrics and the true relative velocity metric can be used somewhat loosely and interchangeably in regard to damage potential estimation.  Further experiments and research are needed to refine these concepts.

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Dr. Howard Gaberson’s Papers

SRS Tripartite

Stress-Velocity Relationship

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– Tom Irvine

## 3 thoughts on “The Great Amplitude Format Debate”

1. Hi,

You’ve written a very interesting pedagogical paper.

So stress is related to velocity in many cases.

In my humble opinion, this relationship is quite applicable until we consider a point located on the structure far enough from boundary conditions or driving sources. Because, in these cases, the near field or evanescent waves have no influence. In general, the presence of the near field tends to modify this relationship.

Lionel