Steady-state response of pipes conveying pulsating fluid near a 2:1 internal resonance in the supercritical regime

TLDR: In this paper, the steady-state responses of a pipe conveying fluid with a harmonic component of flow speed superposed on a constant mean value in the supercritical regime were investigated.

Abstract: The work investigates steady-state responses of a pipe conveying fluid with a harmonic component of flow speed superposed on a constant mean value in the supercritical regime. If the flow speed exceeds a critical value, the straight configuration of the pipe becomes unstable and bifurcates into two stable curved configurations. The transverse motion measured from each of the curved equilibrium configurations is governed by a nonlinear integro-partial-differential equation. The Galerkin method is employed to discretize the governing equation into a set of coupled nonlinear ordinary differential equations with gyroscopic terms. For the pipes in the supercritical regime, the method of multiple scales is used to determine the steady-state in the vicinity of two-to-one resonance. In the presence of the internal resonance, the subharmonic, the superharmonic and the summation, and the difference resonances exist due to the pulsating fluid. The amplitude–frequency relationships are established with the emphasis on the effects of the viscosity, the pulsating amplitude, the nonlinearity, and the mean flow speed. Some nonlinear phenomena such as the appearance of the peak or jumps pertaining to modal interaction are demonstrated. The numerical integration results are in agreement with the analytical predictions.