Free Vibration Analysis and Numerical Simulation of Slightly Curved Pipe Conveying Fluid Based on Timoshenko Beam Theory

Author:

Yuan Jia-Rui1,Fan Xin2,Shu Song3,Ding Hu1ORCID,Chen Li-Qun1

Affiliation:

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, 99 Shangda Road, Shanghai 200444, P. R. China

2. University of Science and Technology of China, Anhui 230026, P. R. China

3. State-Owned Machinery Factory in Wuhu, Wuhu 241007, P. R. China

Abstract

The modeling of a slightly curved pipe conveying fluid usually adopts the Euler–Bernoulli beam theory. In this paper, a dynamic model of the slightly curved pipe conveying fluid based on the Timoshenko beam theory is established for the first time. The complex mode method is used to obtain the frequencies, the modes, and the first critical velocity of the slightly curved pipe. Two kinds of initial configurations of the pipe with fixed–fixed boundary conditions are studied. Based on the Galerkin truncation method, the natural frequencies of the slightly curved pipe are also obtained with the generalized eigenvalue method. Moreover, the Coriolis force caused by the fluid is equivalent to the damping matrix. Therefore, a novel finite element model of the curved pipe considering fluid influence is developed. The numerical simulation method is extended to calculate the mode and frequency of the slightly curved pipe. Numerical results show that all the three methods have high accuracy when calculating the natural frequencies of the transverse vibration of the slightly curved pipe conveying fluid. However, the developed finite element method does not show the effect of flow velocity when determining the modes. Moreover, the initial bending cannot be ignored when analyzing the vibration characteristics of the slightly curved pipe conveying fluid.

Funder

China National Funds for Distinguished Young Scientists

Key Disciplines Construction Project of Shanghai Municipal

Publisher

World Scientific Pub Co Pte Ltd

Subject

Mechanical Engineering,Mechanics of Materials,General Materials Science

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