Finite element analysis of forced vibration for a pipe conveying harmonically pulsating fluid

It is well known that the natural frequencies of a pipe become lower as uniform internal fluid velocity increases. The pipe becomes unstable if the fluid is faster than the critical velocity. But in the case of a pipe conveying harmonically pulsating fluid, resonances will occur even though the mean velocity of the fluid is below the critical velocity. Therefore, for improved analysis, the effects of pulsating fluid in the pipe should also be taken into consideration. In this study, a finite element formulation for the pipe was carried out while taking into consideration the effects of the fluid pulsating harmonically in the pipe. The damping and stiffness matrices in the finite element equation vary with time. A stability analysis based on the Bolotin method was carried out. And, a method to directly estimate the forced response of the pipe that does not need to solve a time data from time-variant system is presented. Several numerical examples are given in this paper that validate of this method.