Vibration Analysis Of A Pipe Conveying Pulsating Fluid With Excitation Of Supporting Motion

This paper researches the parametric resonances of pinned-pinned and clamped-clamped pipes conveying pulsating fluid with supporting motion excitation. The effect of parameters, such as the mean fluid velocity, damping, mass ratio, external applied tension, on the parametric instability regions and the nonlinear dynamics of the system is analyzed. In the analysis, theoretical investigations are performed firstly, and then the results that are obtained from the theoretical examination are proved by numerical simulations and calculations.The partial differential governing equation is solved directly by the method of multiple scales (MMS), and the closed-form equations are obtained at order zero and order one. The natural frequencies of the first two modes are determined analytically as function of fluid velocity,mass ratio and external applied tension. When the pulsating frequency is nearly twice as big as a natural frequency,and the frequency of supporting motion nearly equals the natural frequency, the resonance occurs. With the solvability conditions, we can get the response equation of the vibration amplitude and the curves of amplitude response.With the Galerkin method, the governing equation is truncated into a set of ordinary differential equations of order four. The phase plane portrait and time (velocity) history portraits are investigated respectively at different exciting frequency to confirm the theoretical results.