Vibration of Pipes Containing Flowing Fluids

Abstract

A numerical solution to the equation of motion that describes the behavior of an elastically supported pipe of infinite length conveying an ideal pressurized fluid has been developed, and a new interpretation of the effects produced by internal pressure forces is presented. The effects of foundation modulus, flow velocity, and internal pressure on the dynamic stability, frequency response, and wave-propagation characteristics of an undamped system are discussed. The stability of the system is assured if the flow velocity does not exceed a critical value. Internal pressure decreases the observed frequency of the system while the presence of flow produces two effects: one increases and the other decreases the oscillation frequency. The spatial wave form is shown to be asymptotically symmetric with respect to an axis translating downstream at a constant velocity. For large values of the foundation modulus, the behavior of the pipe is represented by a positively traveling wave packet of frequency equal to the natural frequency of the spring-mass system with an envelope which is an unattenuated duplication of the initial disturbance. Graphical examples of the numerical results for a 30-india steel pipe with a 1/4 -in-thick wall are shown.