Metal Fatigue: What It Is, Why It Matters

Appendix B: Random Load Theory and RMS

Notation

A separate notation is included because many of the symbols listed are used only in this appendix.

a, b

constants in two parameter Weibull distribution

f

frequency

G( f)

power spectral density

H

wave height

H 1 / 3

significant wave height

I

irregularity factor

m 0, m 2, m 4

moments of spectral density function

N

number of cycles, return period

P( H 1 / 3)

exceedance of H 1 / 3

P( S)

exceedance of S

P( S/ ?)

exceedance of S/s

p( S)

probability density of S

p( S/ ?)

probability density of S/ ?

R( ?)

autocorrelation function

S

random process

s

instantaneous value of S

S / ?

expected value of S/ ?

S c / ?

clipping ratio

S m

mean value of S

S o

value of S below which peaks are omitted

T

total time, wave period

t

time

?

Euler s constant = 0 .5772

?

spectral bandwidth

?

standard deviation (random process theory), root mean square (fatigue)

? p

root mean square of peaks

? p , c

root mean square of peaks after clipping of high peaks

? p , o

root mean square of peaks after omission of low peaks

?

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