When setting up the input ASD of a Random Response Analysis, I set up the ASD function in G^2/Hz as is typical; however, when applying the acceleration load to the base node should the scaling factor be (if working in the metric system) 9.81 or 9.81^2 to ensure results are in correct units (m, Pa, m/s, ect)?
For random response analysis, the loading is a unit acceleration( 1g) applied in the frequency response portion of the solution. If you want all of the response quantities(accel,force,stress etc) to have proper units, then this would 9.81m/sec^2
This means after scaling by the ASD, your acceleration results are actually (m/sec^2)^2, which may not be so handy to look at(since your input ASD is g^2/hz). But with Femap charting, you then scale the acceleration results back into g^2/hz by dividing by (9.81m/sec^2)^2
A good check to make is to always request accel response for your base drive node, it should match your input ASD if you are consistent with units.
Entering the PSD in G's will cause all the output to be in G, including stress. Most analyst prefer their stresses in psi or Pa.
If you have -for example- a white-noise vibration with a PSD input of 0.2G from 10 to 2000 Hz, for output to be in Pa you need to scale the PSD function to be in consistent units, instead of G. You will have to enter a value of 0.20*(9.81)^2 = 19.247 G^2/Hz. Since the input is now in (m/s^2)^2/Hz, all your output will be in meters, Pa, and m/s^2.
You can scale the acceleration load, or the acceleration load curve, the result is the same, but is more generally accepted to scale the PSD curve.
Thank you Joe and Blas for your responses.
Blas, to confirm, are you suggesting scaling the original PSD function and defining that as the input PSD in FEMAP then applying a unit (1G) accleration loading to the base node? If this is the case how would you best handle a variable PSD? Moreover, how does does the factor (lets say 9.81 m/s^2 in this case) applied to the unit acceleration scale the values of the PSD?
My assumption is that it must then scale by the factor squared (e.g 9.81^2). i.e resulting in new PSD values of: input_PSD_value*(scaling_factor)^2/Hz. This, as Blas suggests, results in a scaling of the PSD by the factor^2 and results in metric stress units (Pa), as preferred, yet while applying an acceleration load to the base node of 9.81, as Joe suggests. I agree then that acceleration PSD results need to be divided by (9.81m/s^2)^2 to be directly comparable to the input.
As an aside, if I am correct, stress values of the following two cases should be equal?
1.) Scaling flat PSD by 9.81^2 as an input, then applying unit acceleration loading to base node.
2.) Original flat PSD input with 9.81 acceleration loading applied to base node.
This is my best attempt to reconcile your answers, which I think answers the question slightly differently. I hope I have made myself sufficiently clear. Do you both agree?