Stress Analysis

The simplest and most accurate approach is to model your complex system into CAESAR-II and perform a modal analysis

to find the first natural frequency of a structure you can take the deflection in mm under dead load (or for pipes the dead plus live load) and do the following:

18/sqrt(delta)

it works for steel, concrete and timber for small deflections.

i'd be interested to know if it works for pipes.

The methed like u indicated will work for simple configeration like the boundry conditions can be find easily (simply supported, fixed catilever ,etc) .But in piping system with many branches and Nozzle connections , we cannot assume any of these boundry conditions 100 percent.

Caesr modelling is ofcourse Iam accepting but ,how can we cross check the Caeser natural frequecy.

amazingly, it does work for complex systems. it is because the equation has similar relative rigidities for the type of static systems that we use. you really should try it.