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The Variance in Palmgren-Miner Damage Due to Random Vibration

Report Number: AFOSR 1999
Author: Crandall, Stephen H.
Author: Mark, William D.
Author: Khabbaz, Ghassan R.
Corporate Author: Massachusetts Institute of Technology
Laboratory: Air Force Office of Scientific Research
Date of Publication: 1962-01
Pages: 28
Contract: AF 49(638)-564
Project: None Given
AD Number: AD0271151

A random stress-history which is proportional to the stationary response of a single-degree-offreedom vibratory system to wide-band Gaussian excitation is assigned a damage based on the Palmgren-Miner hypothesis and an idealized S-N law. The damage accumulated in time T is a random variable because of the randomness in the number of cycles and the randomness in the amplitudes of the cycles. The mean and variance of the damage are obtained by two procedures: one which accounts for both sources of randomness and one which neglects the randomness in the number of cycles contained in the interval. The two procedures give the same asymptotic result when the bandwidth shrinks to zero. The Theoretical results are illustrated by curves computed for a particular example.

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