Analysis Of The Self-vibration Of Pipe Conveying Fluid

The question of self-vibration of pipes conveying fluid is a significant research subject in the areas of pipeline fluid mechanics and linear dynamics for late fifty years. Pipes are extensively used in aeronautic and aerospace engineering, petrochemical industry, nuclear plants and so on. They play an important role in industry, agriculture and our daily life. But because of the complexity of the problem, the researches are focused on numerical process and analysis.When fluid flows in the pipe, it will vibrate and will lead to the pipe's vibration. And this will change the fluid field movement inversely. So a coupled system composed of structure and fluid is formed in a finite area. In this paper, the self-vibration character of the pipe conveying fluid has been investigated, and the emphasis is put on the influence of the fluid speed on the self-vibration.First, based on the three-dimensional theory of elasticity and the linear Euler equations, a finite element formulation is derived to calculate and analyze the vibration of pipe conveying fluid. The influence of fluid on the pipe is converted to additional mass matrices, additional damping matrices and additional stiffness matrices on the Structure-Fluid interface, which are added to original matrices correspondingly. And the finite element expressions considered the added mass matrices, added damping matrices and added stiffness matrices are obtained, where the added damping matrix and the added stiffness matrix are relative with the fluid velocity. The vibration equation of the structure in the structure-fluid coupled system is changed into the common elastic vibration equation which can be solved easily.Then to testify the accuracy of finite element derivation and Matlab programs, two computations are done in this paper. A comparison is between the natural frequencies from the program in computing the simply supported rectangle plate and that from the analytic solution. It can be seen that the finite element derivation is correct. Then the model of pipe is divided into the quadrilateral elements. The self-vibration character of pipe obtained from the program under no fluid is compared with that from the analytic solution. The former are closer to the latter. So the Matlab program is feasible.At last, the fluid is divided into eight-node brick elements. The self-vibration character of pipe conveying fluid is computed by the finite element program. Then the influence of fluid velocity on pipes is discussed. The self-vibration frequencies of the pipe decrease as fluid velocity increase. The faster fluid speed is, the faster self-vibration frequency decreases. The higher vibration frequency is influenced more greatly.