If the response PSD (RPSD) curve after a random vibration analysis describes the RMS (1-sigma) response, how can I get the RPSD that describes the 3-sigma response?
It is the integral of the RPSD curve wrt frequency that gives you the *square* of the RMS value (where RMS = 1 sigma). To get 1 sigma, you integrate RPSD and take the square root, so for 3 sigma:
int RPSD dFreq = 1 sigma^2
3 sqrt (int RPSD dFreq) = 3 sigma
sqrt (int 9 RPSD dFreq) = 3 sigma
In summary, to get the 3-sigma response, you would need 9 times the RPSD.