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.
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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MIL-STD-810E states that it is based on unpublished observations that military-quality equipment does not tend to exhibit shock failures below a shock response spectrum velocity of 100 inches/sec (254 cm/sec).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.
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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.
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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)
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Stress-velocity examples for beam bending are given in: stress_velocity_examples.pdf
The base acceleration input used in the paper is: avs.txt
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– Tom Irvine