Flexible Cylindrical Structures Research Articles

Fatigue damage characteristics of a flexible cylinder under concomitant excitation of time-varying axial tension and VIV

Flexible cylindrical structures are susceptible to the concomitant excitation of vortex-induced vibration (VIV) and time-varying axial tension in offshore engineering. The structural instability caused by the simultaneous excitation can lead to severe fatigue damage, threatening the safe application of cylindrical structures. In this paper, experimental research was conducted on a long flexible cylinder with an aspect ratio of L/D = 350 to investigate its fatigue characteristics under the concomitant excitation. The reduced velocity Vr ranged from 1.34 to 26.71. The axial tension excitation was characterized by three axial tension amplitude ratios Tv/Tc = 0.1–0.3 (where Tv is the tension amplitude and Tc is the constant tension) and six axial tension frequency ratios fv/f1 = 0.5–4.0 (where fv is the tension frequency and f1 is the fundamental frequency of the cylinder). The S–N curve method and the linear accumulative damage theory were employed to estimate the fatigue damage. The effects of reduced velocity, excitation amplitude and excitation frequency on the fatigue damage characteristics were discussed in terms of the fatigue damage distribution and maximum fatigue damage. The effect of the tension excitation on the fatigue damage is more pronounced at low reduced velocities (Vr ≤ 5.34) when the VIV is not excited, since the axial tension can excite the mode vibration. The fatigue damage area and maximum fatigue damage are significantly enhanced with the increase of the tension amplitude ratio and frequency ratio due to the occurrence of higher-order mode vibrations. The effect of axial tension excitation on the fatigue damage of the cylinder is more pronounced in the in-line (IL) direction than in the cross-flow (CF) direction. However, for a small amplitude ratio (Tv/Tc = 0.1), the tension excitation is only noticeable with a large frequency ratio (fv/f1 = 4.0). On the other hand, as the reduced velocity increases, the VIV of the cylinder is excited and dominates the fatigue characteristics. The accumulative fatigue damage distribution is aggravated with the increase of reduced velocity. The time-varying axial tension has a negligible effect on the fatigue damage distribution features and the maximum fatigue damage values of the cylinder. Nevertheless, under certain circumstances, the axial tension excitation can slightly alleviate the fatigue damage in some regions along the cylinder.

PROPOSAL FOR RESEARCH AND DEVELOPMENT OF VERTEBRAL EXOSKELETON TO REDUCE PHYSICAL STRESS IN THE SPINE

He presents work aims to develop a mechanism capable of assisting the physical efforts of the spine. Exoskeletons are currently tools developed by the field of engineering with important work in the medical physiotherapeutic area and in the search for a better performance of the human capacity to lift loads, being that the main focus of the use of such tools in the movement more quickly and efficient. The device in development is composed of low weight and flexible cylindrical structures connected by means of the fastening brackets which provide a modular characteristic to the system. Such a feature allows the exoskeleton to be adapted to aid movement. The performance of the exoskeleton is also modular, and can be performed passively, by means of springs and shock absorbers, or actively through actuators or motors.

Vortex-induced vibration fatigue damage prediction method for flexible cylinders based on RBF neural network

Vortex-induced vibration (VIV) is an important factor resulting in fatigue failure of cylindrical structures in offshore engineering applications (such as risers and cables). The traditional empirical model for VIV prediction often yields unsatisfactory results due to its dependence on the selection of empirical coefficients. Thus, establishing a general approach to VIV damage prediction based on artificial neural networks and engineering experience is of great significance to engineering guidance. In this paper, a VIV damage prediction model of a flexible cylinder was established using a radial basis function neural network (RBFNN) and model test data. Compared with back propagation neural network (BPNN), genetic algorithm-back propagation neural network (GA-BPNN), and generalized regression neural network (GRNN), the RBFNN exhibited excellent performance with high accuracy and the shortest training time in predicting the VIV damage of flexible cylinders. In addition, the VIV fatigue of flexible cylinders fitted with passive control devices (control rods and helical strakes) was predicted. Using three and four control rods, the VIV reduction effect was observed to be better when the attack angle θ was in the range of 30°–45° and 15°–30°, respectively. Further, regarding helical strakes, the damage values of the cylinder were significantly reduced; however, the VIV suppression effect was significantly affected by the yaw angles. The VIV damage prediction model of this paper is expected to serve as important engineering guidance for the preliminary design, installation arrangement, operation, and maintenance of flexible cylindrical structures in offshore engineering applications.

Hydrodynamic characteristics of two side-by-side flexible cylinders with different diameters experiencing flow-induced vibration

Slender flexible cylindrical structures, such as marine risers and the tendons of tension leg platforms, have been widely used in offshore engineering. This paper mainly investigates the hydrodynamic characteristics of two flexible cylinders with unequal diameters in a side-by-side arrangement subjected to flow-induced vibration (FIV). A series of model tests are carried out in a towing tank. The aspect ratios and mass ratios of the two flexible cylinders are 350/181 and 1.90/1.47, respectively. A diameter ratio of 0.5 and a centre-to-centre spacing ratio of 6.0 are selected for the experimental tests. The experimental results of two cases, namely, those of an unequal-diameter cylinder system and an equal-diameter cylinder system, are compared and discussed. With the comparison of the hydrodynamic coefficients of large cylinder #1 and small cylinder #2 in the unequal-diameter cylinder system and small cylinder #3 in the equal-diameter cylinder system, the FIV features of two side-by-side unequal-diameter cylinders are systematically explored. The in-line (IL) and cross-flow (CF) vibration responses and hydrodynamic characteristics are specifically investigated. The wake effect caused by the vibration of the cylinders is more obvious and important for small cylinder #2 in the unequal-cylinder system. The lift coefficient CLy and fluctuating force coefficient CCF_rms of small cylinder #2 in the CF direction are obviously higher than those of the isolated cylinder in the larger reduced velocity range (Vrs = 7.52–17.54). The added mass coefficient Cax, varying drag coefficient CDx and fluctuating force coefficient CIL_rms in the IL direction decrease significantly when reduced velocity Vrs increases from 22.54 to 25.05. Compared with the two side-by-side cylinders in the equal-diameter cylinder system, the two cylinders in the unequal-diameter cylinder system exhibit a stronger interaction under the initial spacing ratio (S/d = 6.0).

The effect of time-varying axial tension on VIV suppression for a flexible cylinder attached with helical strakes

Flexible cylindrical structures, such as top-tensioned risers (TTRs) and tethers of tension leg platforms (TLPs), usually vibrate under the combined excitation of vortex shedding and time-varying axial tension. Helical strakes are widely used to suppress vortex-induced vibration (VIV). The VIV suppression effectiveness of helical strakes for a flexible cylinder under axial tension excitation is still unknown. Model tests were conducted to investigate the effect of time-varying axial tension on VIV suppression for a flexible cylinder fitted with helical strakes. Three tension amplitude ratios (Tv/Tc = 0.1, 0.2 and 0.3, where Tv is the amplitude of the varying tension and Tc is the constant axial tension) and four tension frequency ratios (fv/f1 = 0.5, 1.0, 2.0 and 4.0, where fv is the frequency of the varying tension and f1 is the fundamental natural structural frequency) were considered. The vibration displacements were reconstructed using the measured strains by the modal analysis method. The dominant mode, response frequency and displacement amplitude were determined to show the influence of axial excitation on the dynamic characteristics of the flexible cylinder attached with helical strakes. When the reduced velocity is low, the second-order mode vibrations of the straked cylinder with axial excitation are excited. Due to the axial excitation, the straked cylinder has large cross-flow (CF) and in-line (IL) displacements at low reduced velocities. The displacement contours in the case of fv/f1 = 1.0 are remarkably different from those in other cases. When the reduced velocity increases, the effect of vortex shedding is enhanced. Both fv induced by axial excitation and the fn induced by vortex shedding are prominent, meaning that both vortex shedding and axial excitation affect the vibration of the straked cylinder. Under axial excitation, the IL displacements of the straked cylinder are enlarged, especially in the case of fv/f1 = 1.0. Axial excitation can reduce the VIV suppression efficiency of helical strakes.

Photo‐controlled alignment and helical organization in main‐chain liquid crystalline alternating polymers

AbstractMaterials with highly ordered nanoscale structures can translate molecular processes to macroscopic function. Here we report on the photo‐controlled organization of achiral alternating copolymers composed of discrete length blocks showing well‐defined sub‐10 nm morphologies. These alternating copolymers consist of main‐chain azobenzene building blocks alternating with discrete oDMS blocks of various precise lengths. Remarkably, we demonstrate the imprinting of a stable helical molecular arrangement in spin‐casted thin films by irradiation with circularly polarized light, without chiral dopant or plasticizer required. By following the out‐of‐equilibrium photo‐switching process over irradiation time, the mechanism of molecular reorganization is unraveled and rationalized with the nature of the morphology. Linear photo‐organization is preferentially reached with flexible and symmetric cylindrical structures while helical photo‐organization is most easily obtained with robust but rotatable lamella structures. These findings suggest that precision in the synthesis and assembly of alternating copolymers can lead to complete control over molecular organization and main‐chain motion.

Modelling of coupled cross-flow and in-line vortex-induced vibrations of flexible cylindrical structures. Part I: model description and validation

This paper is first of the two papers dealing with the nonlinear modelling and investigation of coupled cross-flow and in-line vortex-induced vibrations (VIVs) of flexible cylindrical structures. As a continuation of the previous work (Qu and Metrikine in Ocean Eng 196:106732, 2020) where a new single wake oscillator model was proposed and studied for VIVs of rigid cylinders, the present paper focuses on applying it to flexible cylinders. In this paper, the structure is modelled as an extensible Euler–Bernoulli beam and its 3D nonlinear coupling motion is described in the absolute coordinate system. The single van der Pol wake oscillator model with nonlinear coupling to the in-line motion of the structure, in addition to the classic linear cross-flow motion coupling, is uniformly distributed along the structure to model the hydrodynamic force acting on it. The finite element method has been applied to solve the dynamics of the coupled system, and the experiments of the VIV of a top-tensioned straight riser subjected to a step flow have been taken for the validation of the model. The model has been shown to be able to capture most features of VIVs of flexible cylinders, and a good agreement between the simulation results and the experimental measurements has been observed with regard to the amplitude, frequency and excited mode of both cross-flow and in-line vibrations, as well as the mean in-line deflection due to the amplified in-line force. While it is conventionally expected that the VIV of a flexible cylinder subjected to a uniform flow is dominated by a single frequency, a multi-frequency response is observed in the simulation results over the range of flow velocities through which the transition of the dominant mode of vibration occurs.

Modelling of coupled cross-flow and in-line vortex-induced vibrations of flexible cylindrical structures. Part II: on the importance of in-line coupling

To illustrate the influence of the in-line coupling on the prediction of vortex-induced vibration (VIV), the simulation results of the coupled cross-flow and in-line VIVs of flexible cylinders- obtained with three different wake oscillator models with and without the in-line coupling- are compared and studied in this paper. Both the cases of uniform and linearly sheared flow are analysed and the simulation results of the three models are compared with each other from the viewpoints of response pattern, fluid force, energy transfer and fatigue damage. The differences between the simulation results from the three models highlight the importance of the in-line coupling on the prediction of coupled cross-flow and in-line VIVs of flexible cylindrical structures.

Flow-induced vibrations of three and four long flexible cylinders in tandem arrangement: An experimental study

Multiple flexible cylindrical structures arranged in tandem are commonly used in various fields of engineering. Up to now, limited information is available about the flow-induced vibrations (FIVs) of more than two tandem flexible cylinders. Although some FIV characteristics of multiple tandem flexible cylinders can be studied by considering a tandem flexible cylinder pair, there are other characteristics remain unrevealed which require further investigations. This paper presents an experimental study on the FIVs of three and four flexible cylinders in tandem arrangement. The flexible cylinder models are identical with a mass ratio of 1.9 and a length-to-diameter ratio of 350. The centre-to-centre spacings between the cylinders are kept constant as 6D. The towing speed ranges from 0.05 m/s to 1 m/s and the corresponding Reynolds number lies in the range of 800–16 000. It is found that the presence and vibrations of the downstream cylinders have almost negligible effects on the responses of the most upstream cylinder. Wake-induced vibration (WIV) type responses are observed at high reduced velocities for the downstream cylinders. Due to the shielding effects of the upstream cylinder/cylinders and the influence of the second WIV regime, the transitions between adjacent frequency synchronisation regions and neighbouring vibration modes of the downstream cylinders are delayed to higher reduced velocities. Most of the cylinder responses are dual resonant except for the most downstream cylinder in the three-cylinder system which has identical dominant frequencies in the in-line and cross-flow directions. Combined standing wave and travelling wave responses and standing wave dominated responses are identified for three and four tandem flexible cylinders undergoing FIVs.

Numerical analysis of rubber dams using fluid–structure interactions

Rubber dams are flexible cylindrical inflatable structures attached to a rigid base and inflated by air and/or water. Due to elasticity of the structure and continuous variation of its shape during operation, a rubber dam structural and hydraulic analysis is more complicated than a rigid dam.This paper deals with numerical analysis of the rubber dams for solving the flow based problem and static and dynamic structural analysis, simultaneously. The three dimensional fluid–structure interactions are analyzed both under the stationary hydrostatic and overflow conditions, based on different internal pressures, and upstream and downstream water depths. The water free-surface was obtained based on two-phase air–water flow interface. The flow separation downstream of the dam was modeled using shear stress transport turbulence model. The results describing height, cross-sectional profile and cross-sectional area of the dams were compared with these of former studies and good agreement was obtained. Altogether, the fluid–structure interaction analysis provides two new correlations to predict the equilibrium height of the rubber dam and its discharge coefficient based on the dam equilibrium height and the total upstream head. It was found that the rubber dam equilibrium height is a function of its thickness, modulus of elasticity, internal pressure and foot width.

A systematic approach to riser VIV response reconstruction

Vortex-induced vibration (VIV) of long flexible cylindrical structures (e.g. risers, pipelines, tendons, mooring lines) enduring ocean currents is ubiquitous in the offshore industry. Though significant effort has gone into understanding this complicated fluid–structure interaction problem, major challenges remain in modeling and predicting the response of such structures (for example a riser). The work presented in this paper provides a systematic approach to estimate and analyze the vortex-induced motions of a marine riser. A systematic framework is developed, which allows reconstruction of the riser motion from a limited number of sensors placed along its length. A full reconstruction criterion is developed, which classifies when the measurements from the sensors contain all information pertinent to riser VIV response, and when they do not, in which case additional, analytical methods must be employed. Reconstruction methods for both scenarios are developed and applied to experimental data. Finally, a systematic study on the error during the reconstruction is also undertaken. The methods developed in this paper can be applied to: improve understanding of the vortex shedding mechanisms, including the presence of traveling waves and higher-harmonic forces; develop tools for in-situ estimation of fatigue damage on marine risers; and estimate the vortex-induced forces on marine risers.

Vibration frequency and lock-in bandwidth of tensioned, flexible cylinders experiencing vortex shedding

In-water vortex-induced vibration (VIV) tests of top-tensioned, flexible cylindrical structures were conducted at Shell Westhollow Technology Center current tank. These tests revealed that the top tension and structural stiffness (both lateral and axial) can have a significant impact on vibration frequencies. During lock-in between the vortex-shedding frequency and the structure's natural frequency, the increase of the vibration frequency with flow speeds is strongly related to the rise of the axial tension. After an initial abrupt rise, the vibration frequency of a bending-stiffness-dominated structure only increased slightly during lock-in. Alternative explanations are provided on why the vibration frequency does not rise significantly but there can still exist a broad lock-in band, and why a more massive structure has a narrower lock-in bandwidth.

Optimal lift force coefficient databases from riser experiments

Significant past effort has gone into understanding the complicated flow–structure interaction problem of vortex-induced vibration (VIV) of long flexible cylindrical structures (e.g., risers, mooring lines, tendons, conductors) in the ocean environment. However, major challenges persist with regard to riser VIV modeling and response prediction. The existing prediction schemes are based on a number of hypotheses, experimental facts and data like strip theory, energy balance, correlation length and, most importantly, the use of lift force coefficient databases. Recent advances in observing the VIV motions on experimental risers with high confidence shows that some of these assumptions may not be valid. One important source of the discrepancies between theoretical estimates and experimental observations arise from the use of experimentally obtained lift coefficient databases. These databases were obtained under the laboratory conditions of limited Reynolds number , and under the assumption that the cross-flow motions are not influenced by restraining the in-line motions. In this paper we develop a method to improve the modeling capability of riser VIV by extracting empirical lift coefficient databases from field riser VIV measurements. The existing laboratory-based lift coefficient databases are represented in a flexible parameterized form using a set of carefully chosen parameters. Extraction of the lift coefficient parameters is posed as an optimization problem, where the objective is to minimize the error between the prediction using a theoretical model and the experimental data. Application of the method to data from the Norwegian Deepwater Programme experiments shows that the new optimal databases significantly reduce the error in estimating the riser VIV cross-flow response.

THE FINITE ELEMENT METHOD FOR HYDROELASTIC INSTABILITY OF UNDERWATER TOWED CYLINDRICAL STRUCTURES

The dynamics of underwater towing of flexible cylindrical structures belongs to the class of fluid–structure interaction problems commonly referred to as “cylinders in axial flow”. The serious concern in such towing operations is the various types of hydroelastic instabilities exhibited by the structure at certain critical tow speeds. In practice, reliable prediction of tow configurations and stability characteristics of such towed systems can lead to optimum deployment of cable scope and control of tow speed. The present investigation is concerned with the development of a comprehensive linear finite element method for the dynamics of the flexible towed cylinder with focus on the stability behaviour. The finite element approximation is derived from a variational statement of the problem based on Hamilton's principle. The various structure- and fluid-related matrices as well as matrices resulting from boundary terms have been derived, resulting in a complex unsymmetric eigenvalue problem. Exhaustive validation and convergence studies show that the comparisons between finite element and analytical results are almost exact. Using the finite element code, the hydroelastic instability of a ship-towed array system has been analyzed. The effect of cable scope and shape of the downstream end on stability have been examined.

A NEW TWIST ON AN OLD MODEL FOR VORTEX-EXCITED VIBRATIONS

A new twist on an old model for predicting the vortex-excited vibrations of flexible cylindrical structures is developed. A van der Pol equation, driven by the local transverse motion of the cylinder, is taken as the governing equation for one component of the fluctuating lift force on the cylinder. The second component of the lift force is represented by a stall term which is linearly proportional to the local transverse velocity of the cylinder. In previous models, the van der Pol equation has been employed as the governing equation for the entire fluctuating lift force on the cylinder. The new model preserves the modal scaling principle for the structural response, as initially predicted by the previous models and since verified experimentally. The empirical parameters in the model are related to the physical mass and damping parameters that define the structural properties so that the maximum structural response and the reduced velocity at which it occurs agree with experimental observations. Because of the stall term, the new model provides for an asymptotic, self-limiting structural response at zero structural damping. This asymptotic, self-limiting behavior was not captured by the previous models.

Wind‐Induced Vibration of Two Flexible Cylindrical Structures

This paper presents a simple mathematical model that can be used to predict the vortex‐excited resonant response of two flexible cylindrical structures in line with the wind direction. A modified van der Pol equation is employed to account for the effect of fluctuating lift forces on the cylinders, and normal mode technique is used for treating the flexibility of the cylinders. The governing equations are nonlinear in nature, and the solutions of these equations are assumed to be in the form of sinusoidal functions. Results obtained are in good agreement with the experimental data.

On a theory for the vortex-excited oscillations of flexible cylindrical structures

The periodic shedding of vortices that accompanies the cross-flow past a bluff cylindrical body can excite the body into resonant transverse oscillations when the vortex shedding frequency and a body natural frequency are sufficiently close to one another. In this paper, a mathematical model that enables one to predict the vortex-excited resonant response of bluff elastic cylinders is developed. Based on some previous work by the authors, a modified van der Pol equation is employed as the governing equation for the fluctuating lift on the cylinder and is coupled to the equation of motion of the cylinder. With previously developed relations between the empirical parameters in the model and the physical mass and damping parameters that appear in the equation of motion of the elastic cylinder, the model is used to predict the resonant response of taut strings and circular cylindrical beams with differing end conditions. These predictions are compared with available experimental results for taut strings, pivoted rods and flexible, cantilevered cylinders. Quite good agreement is obtained.