Here is a survey question.
NASA-HDBK-7005(2001) gives the Franken method as a semi-empirical method for predicting the vibration response of a cylindrical skin to an acoustic pressure field, via extrapolation.
Franken originally published this method in 1962 based on rocket engine static test fire data.
There is some anecdotal flight data that the Franken method has some inaccuracy. For example, the peak vibration response often occurs at a frequency somewhat below the cylinder’s ring frequency.
Please let me know if you have any improved extrapolation methods, or if you can refer me to a paper.
Furthermore, Franken’s method is intended for liftoff. So please let me know if there is a more suitable method for flow-induced vibration at transonic and max-Q.