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I am conducting research to determine vibration limits for cultural heritage objects (e.g. art, small sculpture, ceramics). The vibration source can be, for example, transport, construction in or next to a museum, or rock concerts in or next to a museum. As a former materials scientist and engineer in the aircraft industry working on component lifing, I am fully aware that vibrations are a form of cyclic load, and that such damage is cumulative. The limits have to be based on some form of an S-N (Wöhler) diagram for fatigue life. S is normally given in stress amplitude, but one could also use displacement/strain, which can be converted to stress. However, in the vibration monitoring world, vibrations are given either in velocity or acceleration, and sometimes power density spectra.

For buildings, vibration criteria are generally given in units of velocity, but in transportation, they are often given in g, and sometimes PDS.

I have been using velocity as a measure for S in the S-N diagrams, since that is what building engineers use, and it is the closest I can get to deformation (one derivative). If I give a vibration limit in velocity (and duration) and the frequency range in which it is valid, then I am indirectly giving a deformation, which is what one sees in building codes.

In the transport industry, acceleration (g) appears to be used more often. I assume that this has to do with the fact that the cause of damage is more likely to be shock than continuous vibrations.

So my question: which unit, velocity or acceleration, correlates better to damage due to vibrations, and why?

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The best vibration correlation to damage I have seen is "Fatigue Damage Spectrum". An excellent explanation of this is in the text, Mechanical Vibration and Shock Analysis, Fatigue Damage (Mechanical Vibrations and Shock Analysis) (Volume 4), Christian Lalanne; ISBN 978-1848216471.

Basically, the technique estimates the modal response of a structure to a particular base excitation vibration across a range of natural frequencies and the damage is assumed to be proportional to the maximum displacement of the object.

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Acceleration, since that translates directly to the force on the object. Constant velocity is irrelevant. Imagine some object on a jet plane traveling fast but smoothly. The high velocity itself doesn't cause problems. It's the sudden change in velocity that does, and that's exactly what acceleration is.

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  • $\begingroup$ Agreed. I've always seen vibration measured in "g". $\endgroup$
    – am304
    Oct 12, 2017 at 13:52
  • $\begingroup$ Vibration testing machines (at least the ones I've seen) vibrate the object under test by attaching it eccentrically to a powerful motor. The eccentricity (amplitude) is adjustable, as is the speed of rotation (frequency). Amplitude , Frequency and test duration in all 3 axes are often stated in electronic components' datasheets. G force is also stated in some cases, but this can be derived from the other metrics. Some machines will compensate for the mass of the test object. These machines can be quite spectacular, although I would be careful if you plan to google this topic :) $\endgroup$
    – user6335
    Oct 12, 2017 at 14:18
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In automotive, we typically develop our durability vibration test profiles based on real world acceleration data using equivalent damage.

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