Dynamic Response of Pipe Conveying Fluid with Lateral Moving Supports

Baohui Li,Zhengzhong Wang,Lina Jing

doi:10.1155/2018/3295787

Baohui Li, Zhengzhong Wang + Show 1 more

Open Access

https://doi.org/10.1155/2018/3295787

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Abstract

The Galerkin method is proposed to reveal the dynamic response of pipe conveying fluid (PCF), with lateral moving supports on both ends of the pipe. Firstly, the dynamic equation is derived by the Newtonian method after calculating the acceleration of the fluid element via the dynamics approach. Secondly, the discrete form of the dynamic equation is formulated by the Galerkin method. Thirdly, the numerical analysis of the system is carried out through the fourth-order Runge–Kutta method, and the effectiveness of the proposed method is validated by comparison with the analytical results obtained by the mode superposition method. In the example analysis, the responses of the lateral deflection and bending moment are investigated for the pinned-pinned, clamped-pinned, and clamped-clamped PCF. The effects of fluid velocity and the moving frequencies of supports are discussed. Especially, the deflection responses are analyzed under extreme condition; i.e., the moving frequency of a support is identical to the natural frequency of PCF.

Highlights

Transportation pipes are widely used in various industry fields, such as oil exploitation, aviation fuel piping, and nuclear plant cooling systems. e flow-induced vibration, seriously threatens the safe operation of the systems.Each year, the vibration-induced leakage and failure cause huge losses in the economy worldwide
The researchers have already reached a consensus on the classic dynamic model of pipe, such as the linear free vibration model for PCF, which can be described by the following equation [2]: EI
Concluding Remarks e dynamic responses of three types of fluid-conveying pipes with lateral moving supports are investigated in this paper. e dynamic equations are deduced after obtaining the acceleration of fluid. e Galerkin method and fourthorder Runge–Kutta method are adopted in the numerical analysis. e responses with respect to deflection and bending moment are obtained considering different fluid

Summary

Introduction

Transportation pipes are widely used in various industry fields, such as oil exploitation, aviation fuel piping, and nuclear plant cooling systems. e flow-induced vibration, seriously threatens the safe operation of the systems. The characteristics of dynamic response of PCF are investigated with consideration of both coupling effect between fluid and pipe and the external moving supports. E acceleration of the fluid element, shown, is essential for derivation of the dynamic equation of PCF by the Newtonian method. We introduce another moving reference frame x′o′y′ with unit vectors i′ and j′, which is attached to the pipe element. Kij 􏽚 􏼔φ′′i ′′(ξ) +􏼐u2 + P􏼑φ′′i (ξ)􏼕φj(ξ) dξ, Fj 􏽚 cω sin ωτφj(ξ) dξ, where ()′ z()/zx. e fourth-order Runge–Kutta method is employed to solve Equation (14) by changing the equation into the following form: Y_ (τ) AY(τ) + P(τ),

Dimensionless deflection η Dimensionless deflection η

Dimensionless moment M