Stress-Velocity Relationship

Shock and vibration environments produce dynamic stresses which can cause material failure in structures. The potential failure modes include fatigue, yielding, and ultimate stress limit. F.V. Hunt wrote a seminal paper on this subject, titled “Stress and Stress Limits on the Attainable Velocity in Mechanical Vibration,” published in 1960. This paper gave the relationship between stress and velocity for a number of sample structures.

H. Gaberson continued research on stress and modal velocity with a series of papers and presentations.

The purpose of the paper sv_velocity.pdf  is to explore the work of Hunt, Gaberson, and others.  Derivations are given relating stress and velocity for a number of structures. Some of these examples overlap the work of previous sources. Other examples are original. In addition, this paper presents some unique data samples for shock events, with the corresponding spectra plotted in tripartite format.

* * *

Shock Severity Limit

An empirical rule-of-thumb in MIL-STD-810E states that a shock response spectrum is considered severe only if one of its components exceeds the level

Threshold = [ 0.8 (G/Hz) * Natural Frequency (Hz) ]

For example, the severity threshold at 100 Hz would be 80 G.

This rule is effectively a velocity criterion.

MIL-STD-810E states that it is based on unpublished observations that military-quality equipment does not tend to exhibit shock failures below a shock response spectrum velocity of 100 inches/sec (254 cm/sec).

The above actually corresponds to 50 inches/sec.  It thus has a built-in 6 dB margin of conservatism.

Note that this rule was not included in MIL-STD-810F or G, however.

* * *

SMC-TR-06-11 AEROSPACE REPORT NO. TR-2004(8583)-1 REV. A, Test Requirements for Launch, Upper-Stage, and Space Vehicles, Section 10.2.6 Threshold Response Spectrum for Shock Significance

A response velocity to the shock less than 50 inches/second is judged to be non-damaging.

This is the case if the shock response spectrum value in G is less than 0.8 times the frequency in Hz.

* * *

The 100 ips threshold is defined in part by the observation that the severe velocities which cause yield point stresses in mild steel beams turn out to be about 130 ips.

Mild Steel Yield stress is: 36 ksi

Speed of sound in Steel is: c = 200,000 ips

rho = 0.00075122 lbf sec^2/in^4
khat = sqrt(3) for rectangular cross-section

Vmax = (yield stress)/(khat * rho * c)
= 36,000 lbf/in^2 /( sqrt(3) * 0.00075122 lbf sec^2/in^4 * 200,000 ips)
= 130 ips for beam (rounded slightly downward)

* * *

Stress-velocity examples for beam bending are given in:  stress_velocity_examples.pdf

The base acceleration input used in the paper is:  avs.txt

* * *

See also:

Great Amplitude Format Debate

Gaberson Papers

Shock and Vibration Severity Thresholds for Structures and Equipment

– Tom Irvine

6 thoughts on “Stress-Velocity Relationship

  1. Pingback: The Great Amplitude Format Debate | Vibrationdata

  2. Tom,

    Thanks for the link & material, I am starting to do some of this now, so it will come in handy!

    I was going to do a quick analysis on a well known WWII rifle, the M1 Garand. The en bloc clip, or magazine, has a distinctive audible ‘ping’ when the magazine runs empty. The interesting history of this sound is that for a period of time our troops were attacked immediately after this sound was heard by enemy troops. Shortly after this, US troops began using empty clips to throw on the floor to attract the enemy troops, taking them by surprise with a full magazine in the rifle…

    Anyway, I’ll take a look at the wave file and give you a short writeup on it if you’re interested.

    By the way, I just got our VP to fund all of my accelerometers, and data acquisition system & software to start collecting data and doing tests for model validation! That is quite a feat, considering the cost and the level of comprehension anyone but myself has about vibration and shock testing.



    On Thu, Apr 4, 2013 at 12:51 PM, Vibrationdata

  3. Pingback: Howard Gaberson Papers | Vibrationdata

  4. Pingback: Shock Severity Limits for Electronic Components | Vibrationdata

  5. Pingback: Shock and Vibration Severity Thresholds for Structures and Equipment | Vibrationdata

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