An efficient method to predict steady state vibration of three dimensional piping system conveying a pulsating fluid

The dynamic equations of motion for a three dimensional piping system conveying a harmonically pulsating fluid contain time varying terms attributable to the fluid pulsating in the pipe. In this study, finite element formulation for this three-dimensional piping system was performed. The stiffness and damping matrices in the finite element modeling vary according to time because of the effects of the harmonically pulsating fluid. The frequency-domain method based on eigenvalue analysis cannot be used in this kind of problem. Conventional numerical time domain methods require substantial computational efforts. An efficient numerical method to predict the steady state time response of the piping system was presented. In this method, simultaneous equations were constructed by comparing the coefficients of a Taylor series expansion instead of directly solving the problem in the time domain. The accuracy and efficiency of this method were validated by comparison with a conventional numerical integration method