A Note on an Analytic Solution for an Incompressible Fluid-Conveying Pipeline System

Abstract

This paper presents an integral transform analytic solution to the equations governing a fluid-conveying pipeline segment where a gyroscopic or Coriolis force effect is taken into consideration. The mathematical model idealizes a segment of the pipeline as an elastic beam conveying an incompressible fluid. It is clearly shown that when such a system is supported at both ends and in a free motion, the Coriolis force dissipates no energy (or simply does not work) as it generates conjugate complex vibratory components for all flow velocities. It is demonstrated that the modal natural frequencies can be computed from the algebraic products of the complex frequency pairs. Clearly, the patterns of the characteristics of the system's natural frequencies are seen partly when the real and imaginary components are plotted, as widely seen in the literature. Nonetheless, results from this study revealed that a continuity profile exists to connect the subcritical, critical, and postcritical vibratory behaviours when the absolute values are plotted for any velocity. In the meantime, the efficacy and versatility of this method against the usual assumed spatial or temporal modal solutions are demonstrated by confirming the predictions and validity of results of earlier workers such as Paidoussis, Ziegler, and others where pre- and postdivergence behaviours are exhibited.