Semi-analytical solution for dynamic behavior of a fluid-conveying pipe with different boundary conditions

Abstract

This paper analyzes the dynamic behavior of a fluid-conveying pipe with different pipe end boundary conditions. The pipe is considered to be an Euler-Bernoulli beam, and a motion equation for the pipe is derived using Hamilton's principle. A semi-analytical method, which includes the differential quadrature method (DQM) and the Laplace transform and its inverse, is used to obtain a model for the dynamic behavior of the pipe. The use of DQM provides a solution in terms of pipe length whereas use of the Laplace transform and its inverse produce a solution in terms of time. An examination of the results of sampling pipe displacement at different numbers of sample points along the pipe length shows that the method we developed has a fast convergence rate. The frequency and critical velocity of the fluid-conveying pipe derived by DQM are exactly the same as the exact solution. The numerical results given by the model match well with the result obtained using the Galerkin method. The effect on pipe displacement of the pipe end boundary conditions is investigated, and it increases with an increase in the edge degrees of freedom. The results obtained in this paper can serve as benchmark data in further research.

Determination of Natural Frequency and Critical Velocity of Inclined Pipe Conveying Fluid under Thermal Effect by Using Integral Transform Technique

“…[ [26][27] are less than 2.46%. These little differences may be attributed to the using of different models in the two references.…”

“…To validate the analytical calculation method proposed in this work, the fundamental natural frequency is calculated at stationary fluid case (U = 0) and at fluid velocities U = 0.5, U = 1, and U = 1.5, respectively, and compared with those in the work of Ni et al [26] and Liang et al [27]. Table 2 presents the geometry and material properties used in this comparison, and lists the obtained results.…”

Optimization of Hoop Layouts for Reducing Vibration Amplitude of Pipeline System Using the Semi-Analytical Model and Genetic Algorithm

“…Li and Yang [20] adopted He's variational iteration method to analyze the vibration of pipeline conveying fluid with various boundary conditions. Liang et al [21] used Laplace transform and differential quadrature method to analyzed pipeline conveying fluid. Zhang [22] applied the method of multiple scales and the Galerkin's procedure to analyze the dynamics of cantilevered pipe.…”

Axial mechanical experiments of unbonded flexible pipes

“…Both numerical and analytical studies have to make lots of assumptions and put forward a slice of interesting results in the past 40 years (Feret and Bournazel 1987;Witz and Tan 1992;Kebadze 2000;Custódio and Vaz 2002;Pesce et al 2010;Saevik 2011;Ramos et al 2014;Ramos and Kawano 2015;Ebrahimi et al 2018). Although some advances like viscoelastic considered in model (Guedes 2010;Liu and Vaz 2016a;Santos et al 2017, Liang et al 2018, 2019, there is…”