The Vibration of Tubular Beam Conveying Fluid with Variable Cross Section

Mohamed Gaith

doi:10.3311/ppme.17066

Abstract

The dynamics and stability of flow induced vibration of flow conveying in pipes particularly in case of high velocity flow may lead to severe damage. Predicting the circular natural frequencies and critical fluid velocities is an important tool in design and prevent system failures. In this study transverse dynamic response of simply supported pipe with variable tubular cross sectional area carrying fluid with a constant flow rate is investigated. Euler Bernoulli's beam theory is used to model the pipe. Hamilton's principle will be used to produce the governing equation of motion for the system. The resulting partial differential equation is solved using Galerkin's technique. The impact of the flow velocity and non-uniform variable cross section on the natural frequencies of the system, critical flow velocity and system stability is presented.

Highlights

Tubular beams conveying fluid are found in many engineering applications like aircraft engines, jet pumps, heat exchanger, nuclear reactors and human circulation
3 Results and discussion The significant parameters that affect the stability of the system from Eq (15) are the ratio of pipe density to fluid density, β*, the non-dimensional inlet velocity of the fluid, U, and the change of the circular cross section presented in terms of input to output radius ratio b/a, to be designated as the non-uniform cross section ratio, through the spatial coordinate (X )
For pipe conveying a fluid with uniform cross section with supported ends, as the flow velocity increases, the first natural frequency gradually decrease until it vanishes at the first critical velocity, and becomes negative imaginary, leading to divergence instability

Summary

Introduction

Tubular beams conveying fluid are found in many engineering applications like aircraft engines, jet pumps, heat exchanger, nuclear reactors and human circulation. In this study transverse dynamic response of supported pipe with variable tubular cross sectional area carrying fluid with a constant flow rate is investigated. The impact of the flow velocity and non-uniform variable cross section on the natural frequencies of the system, critical flow velocity and system stability is presented.

Results

Conclusion