Prediction of Vortex-Induced Vibration of Long Flexible Cylinders Modeled by a Coupled Nonlinear Oscillator: Integral Transform Solution

Abstract

The Generalized Integral Transform Technique (GITT) was applied to predict dynamic response of Vortex-Induced Vibration (VIV) of a long flexible cylinder. A nonlinear wake oscillator model was used to represent the cross-flow force acting on the cylinder, leading to a coupled system of second-order Partial Differential Equations (PDEs) in temporal variable. The GITT approach was used to transform the system of PDEs to a system of Ordinary Differential Equations (ODEs), which was numerically solved by using the Adams-Moulton and Gear method (DIVPAG) developed by the International Mathematics and Statistics Library (IMSL). Numerical results were presented for comparison to those given by the finite difference method and experimental results, allowing a critical evaluation of the technique performance. The influence of variation of mean axial tension induced by elongation of flexible cylinder was evaluated, which was shown to be not negligible in numerical simulation of VIV of a long flexible cylinder.

Dynamic behavior of pipes conveying gas–liquid two-phase flow

“…In this study, the dynamic behavior of pipes conveying gas-liquid two-phase flow is analytically and numerically investigated on the basis of the generalized integral transform technique (GITT), which has been successfully developed in heat and fluid flow applications (Cotta, 1993(Cotta, , 1998Cotta and Mikhailov, 1997) and further applied in solving the dynamic response of axially moving beams (An and Su, 2011), axially moving Timoshenko beams (An and Su, 2014b), axially moving orthotropic plates (An and Su, 2014a), damaged Euler-Bernoulli beams (Matt, 2013a), cantilever beams with an eccentric tip mass (Matt, 2013b), fluidconveying pipes (Gu et al, 2013), the wind-induced vibration of overhead conductors (Matt, 2009) and the vortex-induced vibration of long flexible cylinders (Gu et al, 2012). The most interesting feature in this technique is the automatic and straightforward global error control procedure, which makes it particularly suitable for benchmarking purposes, and the only mild increase in overall computational effort with increasing number of independent variables.…”

Generalized integral transform solution for free vibration of orthotropic rectangular plates with free edges

“…The infinite systems of linear algebraic equations are truncated to a sufficiently large finite order NW in both directions, for computational purposes. The truncated equations (24), (26) and (28) can be written in matrix form as follows:…”

“…The boundary conditions at free edges of the rectangular plate were treated exactly by carrying out integral transform of the boundary conditions along the free edge direction. Generalized integral transform technique is a hybrid analytical-numerical method that has been applied successfully in a wide range of flow and heat transfer problems [17][18][19][20], as well as in static and dynamic structural analyses [21][22][23][24][25][26][27][28][29][30][31][32][33][34]. In this work, the free vibration of orthotropic thin rectangular plates with a pair of opposite edges clamped and one or two free edges (CSCF, CCCF, CFCF) is studied analytically by using generalized integral transform technique.…”

Prediction of Vortex-Induced Vibration Response of Deep Sea Top-Tensioned Riser in Sheared Flow Considering Parametric Excitations

“…So far, many researchers have focused their attention on the study of the coupled in-line and cross-flow VIV response of different riser models [6][7][8][9][10][11]. However, the axial parametric excitations have not been considered in these studies.…”