Dynamic Response of a Fluid-Conveying Riser Subject to Vortex-Induced Vibration: Integral Transform Solution

2014 ◽  
Author(s):  
Jijun Gu ◽  
Zhenhua Song ◽  
Kang Zhang ◽  
Liguo Su ◽  
Menglan Duan
Keyword(s):  
Differential Equations ◽  
Dynamic Response ◽  
Integral Transform ◽  
Fluid Velocity ◽  
Critical Evaluation ◽  
Cross Flow ◽  
Coupled System ◽  
Vortex Induced Vibration ◽  
Wake Oscillator ◽  
Line Force

Analysis of dynamic response of a fluid-conveying riser is an important aspect in subsea production system. In the present paper, dynamic response of a pinned-pinned riser subject to external fluid force was solved by the generalized integral transform technique (GITT). A nonlinear wake oscillator models was used to represent the cross-flow and in-line force acting on the riser, leading to a coupled system of second-order Partial Differential Equations (PDEs). 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 numerical and experimental results, allowing a critical evaluation of the technique performance. The influence of conveying fluid velocity and mean top tension were evaluated to show that they should not be negligible in numerical simulation of Vortex-Induced Vibration of a long flexible riser.

Nonlinear Analysis of Vortex Induced Dynamic Response of Marine Riser

2013 ◽  
Vol 353-356 ◽  
pp. 2736-2740
Author(s):  
Lin Lin ◽  
Yan Ying Wang
Keyword(s):  
Dynamic Response ◽  
Cross Flow ◽  
Dynamic Responses ◽  
Marine Riser ◽  
Governing Equations ◽  
Nonlinear Dynamic Response ◽  
Wake Oscillator Model ◽  
Wake Oscillator ◽  
Flow Profiles ◽  
Line Force

Vortex-induced dynamic response is the most important issue influencing marine riser. This paper presents an investigation on the vortex-induced nonlinear dynamic response of marine riser subjected to combined waves,currents and platform movement. The in-line force was solved by Morison equation under combined waves,currents and platform movement while cross-flow force was solved by wake oscillator model. Updated Lagrangianmethod was used to solve the nonlinear problem.The governing equations were discretized by finite element method and solved by Newmark-β method in time domain. Influence of nonlinearity, comparisons of vortex-induced dynamic responses under different boundary conditions and different flow profiles were discussed.

Mathematical Model and Analytical Solution for the Vibration of Inclined Fluid-Transporting Submarine Pipelines

2019 ◽  
Vol 161 (A4) ◽  
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Integral Transform ◽  
Internal Flow ◽  
Equation System ◽  
Theoretical Understanding ◽  
Wake Oscillator ◽  
Lock In ◽  
Irregular Topography ◽  
The Mathematical Model

Due to the complexity of submarine environments, the nature of the dynamic response of free-spanning submarine pipelines, particularly inclined pipelines, is unclear. This paper aims to theoretically analyze the vibration behaviors of inclined fluid-transporting free-spanning submarine pipelines in the deepwater area. The mathematical model for the vibration of inclined fluid-transporting pipelines is established considering the influence of gravity on vibration response, and a non-linear wake oscillator is employed to model the vortex shedding behind the pipeline free span. The partial differential equation system is solved through the generalized integral transform technique (GITT), which is an analytical or semi-analytical method. Parametric analysis are carried out to investigate the effects of the inclination on the dynamic response of fluid-transporting pipelines. It is found that the inclination of the free-spanning pipeline will radically alter the natural frequency of the structure, and consequently the VIV lock-in region. In addition, the slope of the seabed will cause a more significant internal flow effect. The thorough theoretical understanding of inclined fluid-transporting pipelines helps increase the design accuracy for pipelines installed on a seabed with a highly irregular topography.

Passive Suppression Mechanisms in Laminar Vortex-Induced Vibration of a Sprung Cylinder With a Strongly Nonlinear, Dissipative Oscillator

2017 ◽  
Vol 84 (8) ◽  
Author(s):  
Antoine Blanchard ◽  
Lawrence A. Bergman ◽  
Alexander F. Vakakis
Keyword(s):  
Parameter Space ◽  
Stokes Equations ◽  
Density Ratio ◽  
Cross Flow ◽  
Nonlinear Energy Sink ◽  
Spectral Element ◽  
Body Motion ◽  
Vortex Induced Vibration ◽  
Wake Oscillator ◽  
Viv Suppression

We study cross-flow vortex-induced vibration (VIV) of a linearly sprung circular cylinder equipped with a dissipative oscillator with cubic stiffness nonlinearity, restrained to move in the direction of travel of the cylinder. The dissipative, essentially nonlinear coupling between the cylinder and the oscillator allows for targeted energy transfer (TET) from the former to the latter, whereby the oscillator acts as a nonlinear energy sink (NES) capable of passively suppressing cylinder oscillations. For fixed values of the Reynolds number (Re = 48, slightly above the fixed-cylinder Hopf bifurcation), cylinder-to-fluid density ratio, and dimensionless cylinder spring constant, spectral-element simulations of the Navier–Stokes equations coupled to the rigid-body motion show that different combinations of NES parameters lead to different long-time attractors of the dynamics. We identify four such attractors which do not coexist at any given point in the parameter space, three of which lead to at least partial VIV suppression. We construct a reduced-order model (ROM) of the fluid–structure interaction (FSI) based on a wake oscillator to analytically study those four mechanisms seen in the high-fidelity simulations and determine their respective regions of existence in the parameter space. Asymptotic analysis of the ROM relies on complexification-averaging (CX-A) and slow–fast partition of the transient dynamics and predicts the existence of complete and partial VIV-suppression mechanisms, relaxation cycles, and Hopf and Shilnikov bifurcations. These outcomes are confirmed by numerical integration of the ROM and comparisons with spectral-element simulations of the full system.

scholarly journals Vortex-Induced Vibration of a Cable-Stayed Bridge

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
M. T. Song ◽  
D. Q. Cao ◽  
W. D. Zhu
Keyword(s):  
Differential Equations ◽  
Dynamic Response ◽  
Galerkin Method ◽  
Vortex Shedding ◽  
Rectangular Cross Section ◽  
Mode Shapes ◽  
Vortex Induced Vibration ◽  
Cable Stayed Bridge ◽  
Geometric Nonlinear ◽  
Bridge Model

The dynamic response of a cable-stayed bridge that consists of a simply supported four-cable-stayed deck beam and two rigid towers, subjected to a distributed vortex shedding force on the deck beam with a uniform rectangular cross section, is studied in this work. The cable-stayed bridge is modeled as a continuous system, and the distributed vortex shedding force on the deck beam is modeled using Ehsan-Scanlan’s model. Orthogonality conditions of exact mode shapes of the linearized undamped cable-stayed bridge model are employed to convert coupled governing partial differential equations of the original cable-stayed bridge model with damping to a set of ordinary differential equations by using Galerkin method. The dynamic response of the cable-stayed bridge is calculated using Runge-Kutta-Felhberg method in MATLAB for two cases with and without geometric nonlinear terms. Convergence of the dynamic response from Galerkin method is investigated. Numerical results show that the geometric nonlinearities of stay cables have significant influence on vortex-induced vibration of the cable-stayed bridge. There are different limit cycles in the case of neglecting the geometric nonlinear terms, and there are only one limit cycle and chaotic responses in the case of considering the geometric nonlinear terms.

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

2020 ◽  
Vol 27 (2) ◽  
pp. 48-57
Author(s):  
Guanghai Gao ◽  
Yunjing Cui ◽  
Xingqi Qiu
Keyword(s):  
Prediction Model ◽  
Deep Sea ◽  
Nonlinear Partial Differential Equations ◽  
Solution Process ◽  
Cross Flow ◽  
Vortex Induced Vibration ◽  
Sheared Flow ◽  
Wake Oscillator ◽  
Real Size ◽  
Heave Motion

AbstractIt is widely accepted that vortex-induced vibration (VIV) is a major concern in the design of deep sea top-tensioned risers, especially when the riser is subjected to axial parametric excitations. An improved time domain prediction model was proposed in this paper. The prediction model was based on classical van der Pol wake oscillator models, and the impacts of the riser in-line vibration and vessel heave motion were considered. The finite element, Newmark-β and Newton‒Raphson methods were adopted to solve the coupled nonlinear partial differential equations. The entire numerical solution process was realised by a self-developed program based on MATLAB. Comparisons between the numerical calculation and the published experimental test were conducted in this paper. The in-line and cross-flow VIV responses of a real size top-tensioned riser in linear sheared flow were analysed. The effects of the vessel heave amplitude and frequency on the riser VIV were also studied. The results show that the vibration displacements of the riser are larger than the case without vessel heave motion. The vibration modes and frequencies of the riser are also changed due to the vessel heave motion

scholarly journals On Numerical Analysis of Carreau–Yasuda Nanofluid Flow over a Non-Linearly Stretching Sheet under Viscous Dissipation and Chemical Reaction Effects

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1148
Author(s):  
Stanford Shateyi ◽  
Hillary Muzara
Keyword(s):  
Differential Equations ◽  
Skin Friction ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Fluid Velocity ◽  
Coupled System ◽  
Linear Differential Equations ◽  
Nanofluid Flow ◽  
Linear Differential

This work reports the Carreau–Yasuda nanofluid flow over a non-linearly stretching sheet viscous dissipation and chemical reaction effects. The coupled system of non-linear partial differential equations are changed into a system of linear differential equations employing similarity equations. The spectral quasi-linearization method was used to solve the linear differential equations numerically. Error norms were used to authenticate the accuracy and convergence of the numerical method. The effects of some thermophysical parameters of interest in this current study on the non-dimensional fluid velocity, concentration and temperature, the skin friction, local Nusselt and Sherwood numbers are presented graphically. Tables were used to depict the effects of selected parameters on the skin friction and the Nusselt number.

Cross-Flow Vortex-Induced Vibration Simulation of Flexible Risers Employing Structural Systems of Different Nonlinearities With a Wake Oscillator

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Shuai Meng ◽  
Xuefeng Wang
Keyword(s):  
Structural Model ◽  
Cross Flow ◽  
Linear Structure ◽  
Structural Systems ◽  
Axial Deformation ◽  
Vortex Induced Vibration ◽  
Wake Oscillator ◽  
Structural Nonlinearities ◽  
Flexible Risers ◽  
Vibration Simulation

To achieve a reliable structural model for vortex-induced vibration (VIV) the prediction of flexible risers, this paper employs structural systems with different geometrical nonlinearities (including a linear structure, a nonlinear one, a coupled cross-flow, and axial nonlinear one) and a classical oscillator to simulate cross-flow VIV. By comparing the experimental and simulation results, it is found that when the drag coefficient is assumed to be a fixed constant along the cylinder (i.e., the damping model is linear function of current velocity), it can affect the vibration amplitude considerably and may alter the dominant modes. When the excited mode of VIV is bending-stiffness dominant, the cross-flow structural nonlinearities can have a profound stiffening effect on vibration response. Although the introduction of axial deformation can reduce this function, the coupled cross-flow and axial nonlinearities still have the effect of decreasing the VIV amplitude.

MATHEMATICAL MODEL AND ANALYTICAL SOLUTION FOR THE VIBRATION OF INCLINED FLUID-TRANSPORTING SUBMARINE PIPELINES

2021 ◽  
Vol 161 (A4) ◽  
Author(s):  
C An ◽  
T T Li ◽  
M L Duan ◽  
H B Huang
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Integral Transform ◽  
Internal Flow ◽  
Equation System ◽  
Theoretical Understanding ◽  
Wake Oscillator ◽  
Lock In ◽  
Irregular Topography ◽  
The Mathematical Model

Due to the complexity of submarine environments, the nature of the dynamic response of free-spanning submarine pipelines, particularly inclined pipelines, is unclear. This paper aims to theoretically analyze the vibration behaviors of inclined fluid-transporting free-spanning submarine pipelines in the deepwater area. The mathematical model for the vibration of inclined fluid-transporting pipelines is established considering the influence of gravity on vibration response, and a non-linear wake oscillator is employed to model the vortex shedding behind the pipeline free span. The partial differential equation system is solved through the generalized integral transform technique (GITT), which is an analytical or semi-analytical method. Parametric analysis are carried out to investigate the effects of the inclination on the dynamic response of fluid-transporting pipelines. It is found that the inclination of the free- spanning pipeline will radically alter the natural frequency of the structure, and consequently the VIV lock-in region. In addition, the slope of the seabed will cause a more significant internal flow effect. The thorough theoretical understanding of inclined fluid-transporting pipelines helps increase the design accuracy for pipelines installed on a seabed with a highly irregular topography.

scholarly journals On a Riemann–Liouville Type Implicit Coupled System via Generalized Boundary Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1205
Author(s):  
Usman Riaz ◽  
Akbar Zada ◽  
Zeeshan Ali ◽  
Ioan-Lucian Popa ◽  
Shahram Rezapour ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Coupled System ◽  
Initial Boundary ◽  
Liouville Type ◽  
Liouville Derivative ◽  
Banach Contraction ◽  
Generalized Boundary Conditions

We study a coupled system of implicit differential equations with fractional-order differential boundary conditions and the Riemann–Liouville derivative. The existence, uniqueness, and at least one solution are established by applying the Banach contraction and Leray–Schauder fixed point theorem. Furthermore, Hyers–Ulam type stabilities are discussed. An example is presented to illustrate our main result. The suggested system is the generalization of fourth-order ordinary differential equations with anti-periodic, classical, and initial boundary conditions.

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