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RMS displacements in Linear Dynamic Analysis

Question asked by Kirby Meyer on Apr 1, 2009
Latest reply on Dec 10, 2009 by 1-L5M1MV
Hello All

This is the first time posting here. I've had a good amount of exposure to Random Vibration and Shock (Modal Time Response) analyses performed in Simulation and its predecessor.

The displacement results of a R.V. or Hamonic Response analysis can either be stated as RMS or through spectral response (PSD). (I think this is also true with Modal Time Response, but I can't remember.) This is the displacement in Length^2/frequency over the frequency band. For the PSD, one can elect to use sensor data and export the data to spreadsheet. For the RMS, one can just look at the contours in Simulation.

Parseval's Theorem implies that the Drms is simply the integral of the PSD curve, taken to the 1/2 power. This is no different than the area of the curve used to obtain the Grms for a random vibration input spectrum.

My concern is that, when I calculate the area under the curve of the sensor's spreadsheet data (using Trapezoidal Rule), I get factors of 3 to 4 less than the Drms expressed through the RMS contours in Simulation. Does anyone know how Simulation interpolates and obtains the RMS displacement?

As an aside, I have done some hand calculations under Random Vibration for critically damped components and found that the PSD's RMS jives very closely to estimates under random vibration, so I wondering if the RMS calculator in Simulation has something in it.

Kirby M