This technical note investigates some formulae used for estimating the variance of fatigue damage in Gaussian narrowband random loadings. A simple approximation is proposed and compared with the exact closed-form solution based on the Gaussian hypergeometric function. The approximation estimates the coefficient of variation with an error that is about 2% for an S-N inverse slope of $m$ = 4 and below 10% for $m$ = 6.

中文翻译：

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窄带高斯随机载荷中疲劳损伤的方差：精确解和近似值

本技术说明研究了一些用于估计高斯窄带随机载荷中疲劳损伤方差的公式。提出了一个简单的近似，并与基于高斯超几何函数的精确闭式解进行比较。对于 SN 反斜率，近似估计变异系数的误差约为 2%$米$ = 4 及以下 10% $米$ = 6。