In-plane and out-of-plane dynamics of curved pipes conveying fluid by integral transform method

Abstract

This study presents a new solution for the dynamic behavior of in-plane and out-of-plane motion of a curved pipe conveying fluid, using the generalized integral transform technique (GITT). The system of sixth-and fourth-order partial differential equations governing three-dimensional motion of the curved pipe is integral transformed into three coupled systems of second-order ordinary differential equations, which are solved numerically by using the NDSolve routine of Mathematica. Excellent convergence behavior of the GITT solution is shown by comparing the vibration deflections at different points along the curved pipe centerline obtained with of different truncation orders. The results of natural frequencies and vibration responses compare well with available results in the literature obtained by other methods. Furthermore, we investigate the dynamic behavior of the curved pipe with different axial forces, flow velocities and other vibration parameters. A relationship between boundary conditions and axial forces is provided, and a series of vibration displacement and velocity trajectories is obtained. It is shown that the GITT is a convenient and effective mathematical method for vibration analysis of the curved pipe conveying fluid and can be used for further study of the dynamics of variable-curvature curved pipes. Keywords Curved pipe conveying fluid • Generalized integral transform technique • Dynamic behavior • In-plane and outof-plane vibration • Natural frequency * Chen An

An application of data-driven modeling for hydroelasticity of an elastically supported semi-circular pipe conveying fluid

“…The Galerkin method (Jung and Chung, 2008) and the finite-element method (FEM) (Zhai et al ., 2013) are the two popular solving methods. Recently, some advanced methods were also applied in the theoretical modelings, such as the geometrically-exact method (Tang and Sweetman, 2021), absolute nodal coordinate formulation (Zhou et al ., 2022) and integral transform method (Li et al ., 2019a).…”

Bending of variable thickness rectangular thin plates resting on a double-parameter foundation: integral transform solution

“…Recently, hybrid analytical-numerical approaches, the finite integral transform method and the generalized integral transform technique (GITT) (Cotta and Mikhailov, 1997; Cotta, 1998; An and Su, 2014), has been developed to solve the structural mechanics problems (Li et al. , 2019; Zhang et al.…”

“…Recently, hybrid analytical-numerical approaches, the finite integral transform method and the generalized integral transform technique (GITT) (Cotta and Mikhailov, 1997;Cotta, 1998;An and Su, 2014), has been developed to solve the structural mechanics problems (Li et al, 2019;Zhang et al, 2019a;Ullah et al, 2019;An et al, 2020;Li et al, 2020;He et al, 2021), and heat and fluid problems (An et al, 2013;Fu et al, 2018;Lisboa et al, 2018Lisboa et al, , 2019Machado dos Santos et al, 2022). The GITT method essentially preserves the properties of partial differential equations, which is different from the physics-preserving schemes of the finite difference method and the finite element method (Zhao et al, 2017;Shen et al, 2018;Jiang et al, 2021Jiang et al, , 2022.…”

Nonlinear Analysis of L-shaped Pipe Conveying Fluid with the Aid of Absolute Nodal Coordinate Formulation

“…To solve this problem, several large-deformation-based theoretical models were developed based on the absolute nodal coordinate formulation (ANCF) [14,15] or the geometrically accurate beam model [16,17]. As another kind of pipe commonly used in engineering, the curved fluid-conveying pipe, has also been received extensive attention from scholars [18][19][20][21][22][23][24][25][26][27]. In these studies, three different theories, including the conventional inextensible theory, the extensible theory and the modified inextensible theory, were mainly employed to develop the different theoretical models that could predict the stability and dynamics of a semi-circular pipe conveying fluid with both ends supported.…”