Analysis of Natural Frequencies and Vibrations in Pipes Under Fluid Flow Using Theoretical Modeling

Abstract

Pipes applications are important and widely used applications in all industrial fields because pipes are used in many fields such as water, oil, gas, etc.   Therefore, it was necessary to highlight the study of the pipes and the problems faced by them. These important and complex problems Which cause failures in many pipe networks are the problem of vibrations.  Where researchers have dealt with the past years the subject in many respects, but the problem has not ended so far. Therefore, in this research, the problem of controlling the vibration resulting from the flow of fluids inside the pipes was shed light on, in addition to the study of vibration reduction for these pipes, where the research included studying the natural frequency of pipes of various types.  Fixation to the pipe at a constant speed and different pressure for two types of fluids (water and oil) at a certain length and diameter, and observing the effect of this addition on the amount of vibration in addition to the natural frequency of the pipe. This study was done by deriving differential equations for pipes for different types of fixations (Pinned-Pinned, Clamped-Pinned, Clamped-Clamped) and the application of boundary conditions for each equation.

Where the equations for the natural frequency of the tubes were reached by the theoretical method (analytically) by deriving the differential equations of motion and dealing with them for the purpose of arriving at the general equation so that it is easy to convert it with changing the inputs and outputs and using the Matlab 2018 program, where the final equations were graphed and the results for the tubes were measured.