DYNAMIC STABILITY OF PIPELINE WITH CONCENTRATED DAMPERS

The article indicates that pipes with a liquid fl owing through them are one of the most common elements in various fields of industry. Pipelines in oil and gas and a number of other industries have valves and connections that can be modeled as concentrated masses. It is very important to consider their impact when investigating the dynamic behavior of pipelines. Developing fluctuations are the subject of research by many scientists. The article investigates a pipe with a static scheme of a beam freely lying on the supports with concentrated dampers. The stability of the system consisting of a pipe with concentrated dampers and a liquid fl owing through it is investigated. The spectral Galerkin method is used to determine the critical fl uid velocity. On the basis of theoretical studies, it has been established that a pipeline system with dampers loses its stability at 1.26 times lower fl uid fl ow rate (Vav = 122. 67, m/s) than in the case without dampers (Vav = 155 m/s).

A STUDY OF PSEUDO SPECTRAL GALERKIN METHOD FOR SOLVING DIFFERENTIAL EQUATIONS

Differential equations have a remarkable potential to exhibit real life phenomenon. Many methods have been developed to solve these differential equations, though only a few stands with time. This paper presents a comparison of Pseudo Spectral Galerkin Method for solving ordinary differential equations with many other global methods. Results shows the high accuracy and rapid convergence of said method. Graphical comparison and error tables have been provided for better understanding of results.