Stability analysis for internal flow-induced vertical cantilevered pipe subject to multiple lumped masses

Abstract

This study investigates the effects of both single and multiple lumped masses attached to a vertical cantilevered pipe conveying internal flow. By introducing delta and Heaviside functions, the governing equation of the vibration of a pipe with lumped masses is newly established based on Hamilton’s principle. The gravitational force of the lumped mass should be considered in the theoretical model but has been essentially ignored in previous research. The harmonic differential quadrature (HDQ) method is applied to solve the governing vibration equation. The newly developed model is validated through a comparison with published data. Numerical results show that the gravity force of the lumped mass plays an important role, and ignoring this force leads to inaccurate results in the investigation of lumped mass effects. The instability of the pipe is analyzed using this new model with various lumped mass weights, positions, and fluid mass ratios. The numerical results showed that lumped masses significantly affect the critical flow velocity, vibration frequency, and modal shapes. The conclusions are expected to supply valuable guidance to reduce pipe vibration using lumped masses in engineering applications.