(L'hôpital's Rule is used to solve the equation as the limit of goes to zero - or some such nonsense.) If m = -10log(2), use the following equation for the area: NOTE - The above equation is invalid if the slope m = -10log(2) because you would be dividing by zero.
In addition, from a practical point of view, we know that it would be physically impossible to achieve unreasonably high sigma values.īelow is presented the method to calculating the root-mean-square acceleration (G rms) response from a random vibration ASD curve. There is no theoretical maximum value for the Gaussian random variable however, we typically design to 3 sigma since it would only be theoretically exceeded 0.3% of the time. 99.7% of the time, the acceleration time history would have peaks that would not exceed the +/- 3 sigma accelerations.95.4% of the time, the acceleration time history would have peaks that would not exceed the +/- 2 sigma accelerations.68.3% of the time, the acceleration time history would have peaks that would not exceed the +/- 1 sigma accelerations.If the accelerometer time history is a stationary Gaussian random time history, the rms acceleration (also called the 1 sigma acceleration) would be related to the statistical properties of the acceleration time history (you may have to refresh your probability and statistics knowledge for this): 707 times the peak value of the sinusoidal acceleration (if just a plain average were used, then the average would be zero). If the accelerometer time history is a pure sinusoid with zero mean value, e.g., a steady-state vibration, the rms acceleration would be. The G rms is the root-mean-square acceleration (or rms acceleration), which is just the square root of the mean square acceleration determined above. Using the mean square value keeps everything positive. That is, if you were to look at a time history of an accelerometer trace and were to square this time history and then determine the average value for this squared acceleration over the length of the time history, that would be the mean square acceleration.
Mean-square acceleration is the average of the square of the acceleration over time. The easiest way to think of the G rms is to first look at the mean square acceleration. But to physically interpret this value we need to look at G rms a different way. It is very easy to describe the G rms (root-mean-square acceleration, sometimes written as GRMS or Grms or grms or g rms) value as just the square root of the area under the ASD vs.