Sparse Modal Decomposition Method Addressing Underdetermined Vortex-Induced Vibration Reconstruction Problem for Marine Risers

When investigating the vortex-induced vibration(VIV)of marine risers,extrapolating the dynamic response on the entire length based on limited sensor measurements is a crucial step in both laboratory experiments and fatigue monitoring of real risers.The problem is conventionally solved using the modal decomposition method,based on the principle that the response can be approximated by a weighted sum of limited vibration modes.However,the method is not valid when the problem is underdetermined,i.e.,the number of unknown mode weights is more than the number of known measurements.This study proposed a sparse modal decomposition method based on the compressed sensing theory and the Compressive Sampling Matching Pursuit(Co Sa MP)algorithm,exploiting the sparsity of VIV in the modal space.In the validation study based on high-order VIV experiment data,the proposed method successfully reconstructed the response using only seven acceleration measurements when the conventional methods failed.A primary advantage of the proposed method is that it offers a completely data-driven approach for the underdetermined VIV reconstruction problem,which is more favorable than existing model-dependent solutions for many practical applications such as riser structural health monitoring.

Experimental Study on Vortex-Induced Vibration of Rough Risers with Coupling Interference Effect Under Side-by-Side Arrangement

A vortex-induced vibration(VIV)experiment of rough risers with coupling interference effect under a side-by-side arrangement was carried out in a wave-current combined flume.The roughness of the riser was characterized by arranging different specifications of surface attachments on the surface of the riser.Rough risers with three different roughnesses were arranged side by side with smooth risers to explore the VIV response of the riser under the combined action of roughness and interference effect,and to reveal the coupling mechanism between roughness and interference effect.The experimental results show that,compared with that of a smooth riser,the VIV of a rough riser under the coupling interference effect has a wider"lock-in"region,and the displacement decreases more significantly at a high reduced velocity,which is more likely to excite higher-order modes and frequency responses.In addition,the displacement response and frequency response of the smooth riser are not significantly affected by wake interference from the rough riser,which is caused by the decrease of the wake region due to the delay of the boundary layer separation point of the rough riser.

Suppression of Vortex-Induced Vibration Caused by A Terebridae-Inspired Cylinder with Different Helical Angles

Biomimetic design has recently received widespread attention.Inspired by the Terebridae structure,this paper provides a structural form for suppressing vortex-induced vibration(VIV)response.Four different structural forms are shown,including the traditional smooth cylinder(P0),and the Terebridae-inspired cylinder with the helical angle of 30°(P_(30)),60°(P_(60)),and 90°(P_(90)).Computational fluid dynamics(CFD)method is adopted to solve the flow pass the Terebridae-inspired structures,and the vibration equation is solved using the Newmark-βmethod.The results show that for P_(30),P_(60) and P_(90),the VIV responses are effectively suppressed in the lock-in region,and P_(60) showed the best VIV suppression performance.The transverse amplitude and the downstream amplitude can be reduced by 82.67%and 91.43%respectively for P_(60) compared with that for P0,and the peak of the mean-drag coefficient is suppressed by 53.33%.The Q-criterion vortices of P_(30),P_(60),and P_(90) are destroyed,with irregular vortices shedding.It is also found that the boundary layer separation is located on the Terebridae-inspired ribs.The twisted ribs cause the separation point to constantly change along the spanwise direction,resulting in the development of the boundary layer separation being completely destroyed.The strength of the wake flow is significantly weakened for the Terebridae-inspired cylinder.

Experimental Study on Vortex-Induced Vibration of Rough Risers Coupling with Interference Effect in Tandem Arrangement

In order to study the response law of vortex-induced vibration(VIV)of marine risers under the combined action of roughness and interference effects,and to reveal the coupling mechanism of roughness and interference effects on the riser,a VIV experiment of rough risers in tandem arrangement was conducted in a wave−current combined flume.The experiment characterized the risers’roughness by arranging different specifications of attachments on the surface of the risers.Three rough risers with different roughness and smooth risers were arranged in tandem arrangement,with the rough risers arranged downstream.The experimental results indicate that the suppression of the attachments on the downstream risers’vibration are more significant both in the CF and IL directions as the reduced velocity increases.For the downstream riser,the amplitude response of rough riser is more significantly weakened compared with the smooth one at high reduced velocity.For the upstream risers,changes in the roughness and spacing ratio have an impact on their‘lock-in’region.When the roughness of downstream risers is relatively large(0.1300)and the spacing between risers is small(S/D=4.0),the reduced velocity range of‘lock-in’region in the CF direction of upstream risers is obviously expanded,and the displacement in the‘lock-in’region is severer.

Coupled Cross-Flow/in-Line Vortex-Induced Vibration Responses of a Catenary-Type Riser Subjected to Uniform Flows

A three-dimensional numerical scheme was developed to investigate the vortex-induced vibration(VIV)of a catenary-type riser(CTR)in the in-line(IL)and cross-flow(CF)directions.By using the vector form intrinsic finite element method,the CTR was discretized into a finite number of spatial particles whose motions satisfy Newton’s second law.The Van der Pol oscillator was used to simulate the effect of vortex shedding.The coupling equations of structural vibration and wake oscillator were solved using an explicit central differential algorithm.The numerical model was verified with the published results.The VIV characteristics of the CTR subjected to uniform flows,including displacement,frequency,standing wave,traveling wave,motion trajectory,and energy transfer,were studied comprehensively.The numerical results revealed that the multimode property occurs in the CF-and IL-direction VIV responses of the CTR.An increase in the flow velocity has slight effects on the maximum VIV displacement.Due to structural nonlin-earity,the double-frequency relationship in the CF and IL directions is rarely captured.Therefore,the vibration trajectories display the shape of an inclined elliptical orbit.Moreover,the negative energy region is inconspicuous under the excitation of the uniform flow.

Dynamic Response of Two-Degree-of-Freedom Riserless Drill String for Vortex-Induced Vibration Suppression and Enhancement

The mechanical behavior,dynamic evolution,and flow-field distribution of a two-degree-of-freedom riserless drill string were simulated numerically by using FLUENT fluid simulation software with the user-defined function embedded.The rotation angular velocities before and after the critical rotation angular velocity were used as independent variables,and the reduced velocity range was 3-14.Fluid-structure coupling was realized based on the dynamic overset grid and the SST k-ωturbulence model.Results reveal that the dynamic response of the riserless drill string was considerably affected by rotation and flow velocity,which are coupled with each other.The cross-flow average dimensionless displacement increased with the rotation angular velocity,and rotation considerably enhanced the in-line maximum average dimensionless displacement.However,the cross-flow amplitude caused by vortex-induced vibration was suppressed when the rotation angular velocity reached a certain value.The in-line and cross-flow frequencies were the same,thereby causing the trajectory to deviate from the standard'figure-eight'shape and become a closed circle shape.The vortex did not fall behind the cylinder at low reduced velocity with high-rotation angular velocity,and the structure of the near-wake vortex remained U-shaped.The wake of the cylinder was deflected along the cross-flow direction,thereby leading to vibration asymmetry and resulting in increased vibration instability and disordered vibration trajectories,especially at high-rotation angular velocities.

Experimental Investigation of Multi-Mode Vortex-Induced Vibration of Flexible Risers with Different Mass Ratios

Experiments were conducted on risers with different mass ratios to study the effect of mode conversion and spanwise correlation. The slenderness ratio of the riser model was set as 169, and the Reynolds numbers are 1600-14400. The dynamic responses of riser models versus reduced velocity were analyzed, and the spanwise displacement, frequency,and trajectory of the mode conversion from the lower to the higher mode were explored. The results revealed that the riser model with a higher mass ratio excites a higher number of modes. The conversion region of multi-mode competition exists and narrows with the increasing mass ratio. Mode conversion is continuous and manifests as the transmission of peaks and troughs in mode shape: the peaks and troughs of mode shape move up in the mode stable development region and move down in the mode conversion region. The single-mode dominating vibration exhibits a standing wave feature, and the traveling wave feature is significant in the mode conversion region. Furthermore, the frequency jump is always transmitted from the trough to the peak of the mode shape, and finally, all the axial positions vibrate at the same frequency. The trajectory in the mode conversion region deviates from the 8-shape and recovers the standard8-shape at the middle and late stages of the mode stable development region.

Vortex-Induced Vibration Response Features of A Submarine Multi-Span Pipeline via Towing Tank Experimental Tests

In offshore engineering, the phenomenon of free span often occurs, and the pipeline may have multiple free spans adjacent to each other, forming a multi-span pipeline. The interaction of different spans makes the structural vibration characteristics more complex, which may change the fatigue characteristics of the pipeline and affect the safety of the structure. In this paper, model tests were designed to explore the vortex-induced vibration(VIV) characteristics of multi-span pipelines and investigate the multi-span interaction mechanism. The experimental study mainly focused on the dynamic response of double-span pipelines, and further extended to triple-span pipelines, hoping that the results can be applied to more complex environment. The effects of span-length ratio, buried depth and axial force on VIV of the pipeline were investigated and discussed. The dynamic response of the pipeline varied with the span length. There was obvious interaction between different spans of multi-span pipelines, and the pipe-sediment interaction obviously affected the vibration characteristics of pipeline. The differences of pipeline burial depth and axial force changed the structural stiffness. With the increase of buried depth, the response amplitude presented a downward trend. The spanwise evolutions were asymmetric caused by the pipe-sediment interaction and multi-span interaction. The results can help to identify multi-span pipelines in engineering, and realize the prevention and control of free spans.

Experimental Study on Vortex-Induced Vibration of Marine Riser Model with Coupling Interference Effect Under Combined Internal and External Flow

A partition model of interference efficiency was constructed to study the coupling interference effect under combined internal and external flow.The concept of“internal flow efficiency”,“velocity ratio”and“interference efficiency”were introduced to quantify the effect of internal flow and interference,and reveal the coupling mechanism among internal flow,external flow and interference effect.The results showed that the dynamic response of risers under variable angles was significantly different after considering the effect of internal flow.When the external flow velocity was smaller than 0.25 m/s,the vibration of risers was promoted by the internal flow.With the increase of external flow velocity,the effect of internal flow was weakened and the dynamic response of riser mainly depended on the external flow and interference effect.Under the effect of different internal flow,the interference efficiency had similar change trend.The interference effect amplified the complex secondary flow effect inside the riser,making the dynamic response of riser complex and random.In this paper,the overlap area and subdivision criterion of interference effect were constructed within the range of experimental velocity ratio,and the change curve of interference efficiency was obtained with an average meaning,which may have important practical meaning.

Global Dynamic Characteristic of Nonlinear Torsional Vibration System under Harmonically Excitation

Torsional vibration generally causes serious instability and damage problems in many rotating machinery parts. The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonlinear friction force is investigated. On the basis of the generalized dissipation Lagrange＇s equation, the dynamics equation of nonlinear torsional vibration system is deduced. The bifurcation and chaotic motion in the system subjected to an external harmonic excitation is studied by theoretical analysis and numerical simulation. The stability of unperturbed system is analyzed by using the stability theory of equilibrium positions of Hamiltonian systems. The criterion of existence of chaos phenomena under a periodic perturbation is given by means of Melnikov＇s method. It is shown that the existence of homoclinic and heteroclinic orbits in the unperturbed system implies chaos arising from breaking of homoclinic or heteroclinic orbits under perturbation. The validity of the result is checked numerically. Periodic doubling bifurcation route to chaos, quasi-periodic route to chaos, intermittency route to chaos are found to occur due to the amplitude varying in some range. The evolution of system dynamic responses is demonstrated in detail by Poincare maps and bifurcation diagrams when the system undergoes a sequence of periodic doubling or quasi-periodic bifurcations to chaos. The conclusion can provide reference for deeply researching the dynamic behavior of mechanical drive systems.

Torsional vibration of a pipe pile in transversely isotropic saturated soil

This study considers the torsional vibration of a pipe pile in a transversely isotropic saturated soil layer. Based on Biot＇s poroelastic theory and the constitutive relations of the transversely isotropic medium, the dynamic governing equations of the outer and inner transversely isotropic saturated soil layers are derived. The Laplace transform is used to solve the governing equations of the outer and inner soil layers. The dynamic torsional response of the pipe pile in the frequency domain is derived utilizing 1D elastic theory and the continuous conditions at the interfaces between the pipe pile and the soils. The time domain solution is obtained by Fourier inverse transform. A parametric study is conducted to demonstrate the influence of the anisotropies of the outer and inner soil on the torsional dynamic response of the pipe pile.

Experi mental Study on Vortex-Induced Vibrations of Submarine Pipeline near Seabed Boundary in Ocean Currents

Unlike most previous studies on vortex-induced vibrations of a cylinder far from a boundary, this paper focuses on the influences of close proximity of a submarine pipeline to a rigid seabed boundary upon the dynamic responses of the pipeline in ocean currents. The effects of gap-to-diameter ratio and those of the stability parameter on the amplitude and frequency responses of a pipeline are investigated experimentally with a novel hydro-elastic facility. A comparison is made between the present experimental results of the amplitude and frequency responses for the pipes with seabed boundary effects and those for wall-free cylinders given by Govardhan and Williamson （2000） and Anand （1985）. The comparison shows that the close proximity of a pipeline to seabed has much influence on the vortex-induced vibrations of the pipeline. Both the width of the lock-in ranges in terms of Vr and the dimensionless amplitude ratio Amax/D become larger with the decrease of the gap-to-diameter ratio e/D, Moreover, the vibration of the pipeline becomes easier to occur and its amplitude response becomes more intensive with the decrease of the stability parameter, while tire pipeline frequency responses are affected slightly by the stability parameter.

Experimental Study on Coupled Cross-Flow and in-Line Vortex-Induced Vibration of Flexible Risers

In this work, we study the coupled cross-flow and in-line vortex-induced vibration （VIV） of a fixedly mounted flexible pipe, which is free to move in cross-flow （ Y- ） and in-line （ X- ） direction in a fluid flow where the mass and natural frequencies are precisely the same in both X- and Y-direction. The fluid speed varies from low to high with the corresponding vortex shedding frequency varying from below the first natural frequency to above the second natural frequency of the flexible pipe. Particular emphasis was placed on the investigation of the relationship between in-line and cross-flow vibration. The experimental results analyzed by using these measurements exhibits several valuable features.

The Effect of Internal Fluid on the Response of Vortex-Induced Vibration of Marine Risers

Based on Iwan′s wake oscillator model developed with the classical van der Pol equation, the differential equation for the response of the vortex-induced vibration (VIV) of the riser considering the effect of the internal flowing fluid and the external marine environmental condition is derived. The effect of the internal flowing fluid on the response of VIV of the riser is studied by means of the Finite Element Method. The results show that the effect of the internal fluid velocity on the VIV of the riser is strong when the natural frequency of the riser is close to the vortex shedding frequency. In addition, the increase of the top tension can decrease the sensitivity of the riser to the internal fluid velocity.

Effect of Internal Flow on Vortex-Induced Vibration of Submarine Free Spanning Pipelines

At present, most researches on the vortex-induced vibration of submarine free spanning pipelines ignore the effect of internal flowing fluid; furthermore, there are no research reports considering the coupling effect of internal and external fluid with the free span. In this paper, combining Iwan's wake oscillator model with the differential equation derived for the dynamic response of submarine free spanning pipelines with inclusion of internal flow, the pipe-fluid coupling equations are developed to investigate the effect of internal flow on the vortex-induced vibration of the free spans. The finite element approximation is implemented to derive the matrix equations of equilibrium. The Newmark method combined with simple iteration is used to solve the system of equations. The results indicate that the internal fluid flow may cause the shift of resonance band to the lower frequency and a slight decrease in the peak value; the effect will be more pronounced with the increase of the span length and can be weakened in the presence of the axial tension.

Numerical and Physical Investigation on Vortex-Induced Vibrations of Marine Risers

As a project supported by the National Natural Science Fotmdation of China, a model experiment on the vortex-induced vibration of practical risers transporting tluid in currents was conducted in the Physical Oceanography laboratory of ocean University of China in 2005. Because most of the offshore oil fields in China are in shallow water, the experiment was focused on the risers in shallow water. The similarity theory was used in the experiment to derive the experimental model from the practical model. Considering the internal flowing fluid and external marine environment, the dynamic response of the marine riser was measured. Corresponding numerical simulation was performed with the finite element method. Ccnaparisons were made between the results from the experiment and numerical simulation.

Numerical Prediction of Vortex-Induced Vibrations on Top Tensioned Riser in Consideration of Internal Flow

In consideration of the effect of the internal flowing fluid and the external marine environmental condition on the vortex-induced vibration （VIV） of top tensioned riser （Till）, the differential equation is derived based on work-energy principles and the riser near wake dynamics is modeled by Facchinetti＇ s wake oscillator model. Then Galerkin＇ s finite element approximation is implemented to derive the nonlinear matrix equation of the coupled equations and file corresponding numerical programs are compiled which solve the coupled equations directly in the time domain. The comparison of the predicted results with the recent experimental results and the prediction of SHEAR7 is performed. The results show the validity of the proposed method on the prediction of VIV of deep water risers. The effect of internal flow on the dynamic characteristics and dynmnic response of the riser is analyzed and several valuable conelusions are drawn.

The prediction on in-line vortex-induced vibration of slender marine structures

The in-line （IL） vortex-induced vibration （VIV） that occurs frequently in ocean engineering may cause severe fatigue damage in slender marine structures. To the best knowledge of the authors, in existing literatures, there is no efficient analytical model for predicting pure IL VIV. In this paper, a wake oscillator model capable of analyzing the IL VIV of slender marine structures has been developed. Two different kinds of van der Pol equations are used to describe the near wake dynamics related to the fluctuating nature of symmetric vortex shedding in the first excitation region and alternate vortex shedding in the second one. Some comparisons are carried out between the present model results and experimental data. It is found that many phenomena observed in experiments could be reproduced by the present wake oscillator model.

Non-linear Torsional Vibration Characteristics of an Internal Combustion Engine Crankshaft Assembly

Crankshaft assembly failure is one of the main factors that affects the reliability and service life of engines.The linear lumped mass method,which has been universally applied to the dynamic modeling of engine crankshaft assembly,reveals obvious simulation errors.The nonlinear dynamic characteristics of a crankshaft assembly are instructionally significant to the improvement of modeling correctness.In this paper,a general expression for the non-constant inertia of a crankshaft assembly is derived based on the instantaneous kinetic energy equivalence method.The nonlinear dynamic equations of a multi-cylinder crankshaft assembly are established using the Lagrange rule considering nonlinear factors such as the non-constant inertia of reciprocating components and the structural damping of shaft segments.The natural frequency and mode shapes of a crankshaft assembly are investigated employing the eigenvector method.The forced vibration response of a diesel engine crankshaft assembly taking into account the non-constant inertia is studied using the numerical integral method.The simulation results are compared with a lumped mass model and a detailed model using the system matrix method.Results of non-linear torsional vibration analysis indicate that the additional excitation torque created by non-constant inertia activates the 2nd order rolling vibration,and the additional damping torque resulting from the non-constant inertia is the main nonlinear factor.The increased torsional angular displacement evoked by the high order excitation torque relates to the non-constant inertia.This research project is aimed at improving nonlinear dynamics theory,and the confirmed nonlinear parameters can be used for the structure design of a crankshaft assembly.

A Simplified Nonlinear Model of Vertical Vortex-Induced Force on Box Decks for Predicting Stable Amplitudes of Vortex-Induced Vibrations

Wind-tunnel tests of a large-scale sectional model with synchronous measurements of force and vibration responses were carried out to investigate the nonlinear behaviors of vertical vortex-induced forces （VIFs） on three typical box decks （i.e., fully closed box, centrally slotted box, and semi-closed box）. The mechanisms of the onset, development, and self-limiting phenomenon of the vertical vortex-induced vibration （VlV） were also explored by analyzing the energy evolution of different vertical VIF components and their contributions to the vertical VIV responses. The results show that the nonlinear components of the vertical VIF often differ from deck to deck; the most important components of the vertical VIF, governing the stable amplitudes of the vertical VIV responses, are the linear and cubic components of velocity contained in the self-excited aerodynamic damping forces. The former provides a constant negative damping ratio to the vibration system and is thus the essential power driving the development of the VIV amplitude, while the latter provides a positive damping ratio proportional to the square of the vibration velocity and is actually the inherent factor making the VIV amplitude self-limiting. On these bases, a universal simplified nonlinear mathematical model of the vertical VIF on box decks of bridges is presented and verified in this paper; it can be used to predict the stable amplitudes of the vertical VIV of long-span bridges with satisfactory accuracy.