The Mathematical Analysis of Problems Describing the Dynamics of Pipes Conveying Fluids

Abstract

In this Masters thesis, the dynamics of pipes conveying pulsating flow are investigated. The initial-boundary value problem associated with the linear beam equations of motions governing the pipe system is derived using the principles of Lagrangian mechanics. In this thesis, the fluid flow is assumed to have a small velocity with harmonic time dependence $V(t)=\varepsilon(V_0+ V_1 \sin(\Omega t))$, which allows us to investigate the effects of different pulsation frequencies on the pipe system. For certain $\Omega$ frequencies, the pipe system is observed to be exposed to more complex dynamical behaviours. By using the multiple time scale perturbation method, comprehensive insights into the stability and the dynamic behaviour of pipe systems are achieved.

The study focuses on investigating the primary resonance frequencies and understanding how pulsation frequencies near those resonance frequencies impact the stability of the system. Furthermore, we elaborate on special resonance cases where multiple oscillatory modes interact leading to even more complicated dynamics.

By building upon existing literature this research enhances our understanding of stability and dynamic behaviors under various flow pulsation frequencies. This study makes an important contribution to the present literature by exploring scenarios where multiple resonant modes interact, due to coinciding primary resonance frequencies, which has not been extensively discussed in the literature. Our findings suggests scepticism on the relevance of the existing solution methods and results in the literature for certain parameter values.