Three-dimensional dynamics of a novel triply-gyroscopic fluid-conveying pipe system

Abstract

Gyroscopic characteristics extensively exist in motional components, which can lead to coupling of motions along different directions. However, the vibration and stability mechanism of complicated gyroscopic structures still remains unclear. This paper proposes a novel class of triply-gyroscopic system — fluid-conveying pipes conducting simultaneous rotating and spinning motions. Based on a Rayleigh beam model, the coupled differential equations governing in-plane and out-of-plane flexural vibrations and axial vibration are deduced, which fully account for the rotating gyroscopic force, spinning gyroscopic force and fluid gyroscopic force. The Galerkin technique is applied to discretize the governing equations, and the characteristic frequency method is further utilized for solution. Via an in-depth dimensionless analysis, the resonant frequency and stability evolution with the three motions is drawn, and its dependence on the triple gyroscopic and centrifugal effects is revealed. The impacts of significant geometrical and physical properties are also discussed. Three-dimensional (3D) backward and forward whirling shapes of the pipe are simulated, where the rotating motion is involved as novelty. Nonplanar configurations and ‘traveling wave’ vibrations are observed as a result of gyroscopic effects. The study will contribute to in-depth understanding of gyroscopic dynamics, and provide theoretical and designing base for the engineering gyroscopic structures.