Richard BealeI found these articles on the internet that may help answer your question.
http://turbolab.tamu.edu/proc/turboproc … 19-134.pdf
http://turbolab.tamu.edu/proc/turboproc … l28019.pdf
I’m most certainly no expert in these matters, but I do have some thoughts, so take the following as only the thoughts of someone who has been involved in piping design for many years and continue to seek expert advice.
It seems to me that there is a big difference between a natural frequency or harmonic vibration that occurs in piping connected to such as a reciprocating compressor and the violent and sudden vibration encountered by the piping ahead of such as a slug catcher; the former being uniform, constant and predictable, and the latter being non uniform and varying in frequency and intensity. I think you’ll find that the design considerations for the two scenarios are quite different.
In short, I believe that you will find that your initial question about natural frequency can’t be correlated to your subsequent example of condensate water hammer in a steam line during start-up.
Keep in mind that I’m speculating to generate further thought. We all live and learn, so please share your findings with us.