scholarly journals On the Significance of the Higher-Order Stress in Riser Vortex-Induced Vibrations Responses

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Jie Wu ◽  
Decao Yin ◽  
Halvor Lie ◽  
Carl M. Larsen ◽  
Rolf J. Baarholm ◽  
...  
Keyword(s):  
Fatigue Damage ◽  
Flexible Pipe ◽  
Third Order ◽  
Higher Harmonics ◽  
The Third ◽  
Flexible Pipes ◽  
Vortex Induced Vibrations ◽  
Vortex Shedding Frequency ◽  
Order Stress ◽  
The Impact

Vortex-induced vibrations (VIV) can lead to fast accumulation of fatigue damage and increased drag loads for slender marine structures. VIV responses mainly occur at the vortex shedding frequency, while higher harmonics can also be excited. Recent VIV model tests with flexible pipes have shown that higher harmonics in the crossflow (CF) direction can contribute to the fatigue damage significantly due to its higher frequency. Rigid cylinder experiments show that the CF third-order harmonics are more pronounced when the motion orbit is close to a “figure 8” shape and the cylinder is moving against the flow at its largest CF motion. However, there is still lack of understanding of when and where higher harmonics occur for a flexible pipe. Therefore, significant uncertainty remains on how to account for fatigue damage due to higher harmonics in VIV prediction. In the present paper, representative VIV data from various riser model test campaigns are carefully studied and analyzed. The key parameters that influence the magnitude of the third-order harmonic stress are found to be the bending stiffness, the reduced velocity, and the orbit stability. The experimental data are analyzed in order to assess the impact of each parameter on the third-order harmonic stress. A preliminary empirical response model to estimate the maximum CF third-order harmonic stress based on these identified structural and hydrodynamic parameters has been proposed. The results of this study will contribute to reduce the uncertainty and unnecessary conservatism in VIV prediction.

Fatigue Damage From High Mode Number Vortex-Induced Vibration

2006 ◽  
Author(s):  
J. Kim Vandiver ◽  
Susan B. Swithenbank ◽  
Vivek Jaiswal ◽  
Vikas Jhingran
Keyword(s):  
Fatigue Damage ◽  
Field Experiments ◽  
Higher Harmonics ◽  
Vortex Induced Vibration ◽  
Third Harmonic ◽  
The Third ◽  
Damage Rate ◽  
Surface Vessels ◽  
Vortex Shedding Frequency ◽  
First Time

This paper presents results from two field experiments using long flexible cylinders, suspended vertically from surface vessels. The experiments were designed to investigate vortex-induced vibration (VIV) at higher than tenth mode in uniform and sheared flows. The results of both experiments revealed significant vibration energy at the expected Strouhal frequency (referred to in this paper as the fundamental frequency) and also at two and three times the Strouhal frequency. Although higher harmonics have been reported before, this was the first time that the contribution to fatigue damage, resulting from the third harmonic, could be estimated with some certainty. This was enabled by the direct measurement of closely spaced strain gauges in one of the experiments. In some circumstances the largest RMS stress and fatigue damage due to VIV are caused by these higher harmonics. The total fatigue damage rate including the third harmonic is shown to be up to forty times greater than the damage rate due to the vibration at the fundamental vortex-shedding frequency alone. This dramatic increase in damage rate due to the third harmonic appears to be associated with a narrow range of reduced velocities in regions of the pipe associated with significant flow-induced excitation.

On the Occurrence of Higher Harmonics in the VIV Response

2015 ◽  
Author(s):  
Jie Wu ◽  
Decao Yin ◽  
Halvor Lie ◽  
Carl M. Larsen ◽  
Rolf J. Baarholm ◽  
...  
Keyword(s):  
Fatigue Damage ◽  
Cross Flow ◽  
Transverse Motion ◽  
Flexible Beam ◽  
Flow Profile ◽  
Third Order ◽  
Higher Harmonics ◽  
Sheared Flow ◽  
Vortex Induced Vibrations ◽  
Shedding Frequency

Vortex Induced Vibrations (VIV) can lead to fast accumulation of fatigue damage and increased drag loads on slender marine structures. A cylinder subjected to VIV can vibrate in both in-line (IL) and cross-flow (CF) directions. The CF response is dominated by the primary shedding frequency and the IL response frequency is often two times of the primary CF frequency. In addition, higher harmonics can also be present. The third order harmonics are more pronounced when the motion orbit of the cylinder is close to “figure 8″ shape and cylinder is moving against the flow at its largest transverse motion. Recent studies with flexible beam VIV tests have shown that higher harmonics can have significant contribution to the fatigue damage in addition to the loads at the primary shedding frequency. However, there is a lack of understanding of when and where higher harmonic loads occur. The fatigue damage due to the higher harmonics is not considered in the present VIV prediction tools. In the present paper, the test data of selected cases subjected to linearly sheared flow profile from two test programs, the Shell high mode VIV test[11] and the Hanøytangen test[5] have been studied. The factors that may influence the occurrence of the higher harmonics, such as the bending stiffness, reduced velocity and orbits stability, have been studied. The importance of higher harmonics in VIV fatigue has also been investigated. Finally, a method to include higher harmonics in the fatigue calculation is presented.

scholarly journals Changes in Incisor Third-Order Inclination Resulting from Vertical Variation in Lingual Bracket Placement

2009 ◽  
Vol 79 (4) ◽  
pp. 747-754 ◽  
Author(s):  
Michael Knösel ◽  
Klaus Jung ◽  
Liliam Gripp-Rudolph ◽  
Thomas Attin ◽  
Rengin Attin ◽  
...  
Keyword(s):  
Null Hypothesis ◽  
Interindividual Variation ◽  
Occlusal Plane ◽  
Third Order ◽  
Vertical Variation ◽  
Independent Variables ◽  
The Third ◽  
Dependent Variables ◽  
Incisor Inclination ◽  
The Impact

Abstract Objective: To test the null hypothesis that third-order measurements are not correlated to lingual incisor features seen on radiographs. Material and Methods: The lateral headfilms of 38 untreated, norm-occlusion subjects without incisor abrasions or restorations were used for third-order measurements of upper and lower central incisors and assessment of the inclination of four sites suitable for lingual bracket placement with reference to the occlusal plane perpendicular. Lingual sections were determined by the tangents at the incisal fossa (S1), at the transition plateau between incisal fossa and the cingulum (S2), by a constructed line reaching from the incisal tip to the cingulum (S3), and by a tangent at the cingulum convexity (S4). Third-order angles were also assessed on corresponding dental casts using an incisor inclination gauge. Regression analysis was performed using the third-order measurements of both methods as the dependent variables and the inclination of the lingual enamel sections (S1, S2, S3, S4) as the independent variables. Results: The null hypothesis was rejected. For the most common bracket application sites located on the lingual shovel (S1 and S2), third-order inclination changes of 0.4–0.7 degrees are expected for each degree of change in the inclination of the lingual surface. The impact of bracket placement errors on third-order angulation is similar between sections S1 and S2 and the cingulum convexity (S4). Section S3 proved to be least affected by interindividual variation. Conclusion: The third-order measurements are correlated to lingual incisor features. Accordingly, third-order changes resulting from variation in lingual bracket placement can be individually predicted from radiographic assessments.

Experimental Study on Flexible Bare Pipe Arrays Undergoing Vortex-Induced Vibrations

2018 ◽  
Author(s):  
Y. Liu ◽  
C. Shi ◽  
Z. Liu ◽  
J. Wang ◽  
X. Bao
Keyword(s):  
Fatigue Damage ◽  
Dynamic Responses ◽  
Array Configuration ◽  
Damage Rate ◽  
Flexible Pipes ◽  
Vortex Induced Vibrations ◽  
Helical Strakes ◽  
Preliminary Study ◽  
Single Pipe ◽  
Center Distance

Vortex-induced vibration (VIV) excited by current is a major contributor to the fatigue accumulation of marine risers. For deepwater operations, several risers are often arranged together in an array configuration. In this study, a set of four identical flexible pipes of a rectangular arrangement were tested in a water tunnel. By comparing the dynamic responses of a pipe in an array with that of a single isolated pipe, the effects of the current speed and the center-to-center distance between the up-stream and downstream pipes on their dynamic responses were investigated. Fatigue damages accumulated on each pipe in an array was calculated and a factor, termed “fatigue damage amplification factor”, was defined as a ratio between the fatigue damage rate of pipe in an array and the fatigue damage rate of a single pipe at a same current condition. The results showed that for bare pipes (i.e., without helical strakes), the downstream pipes in an array configuration may have larger dynamic responses and fatigue damage rates than those of a single pipe; and, it is not always conservative to assume that the fatigue damage rate estimated for a single pipe can be used to represent the fatigue damage rates of pipes in an array. This preliminary study provided some meaningful results for the design, analysis and operation of marine riser arrays.

Investigation on Mechanical Properties of Fibreglass Reinforced Flexible Pipes Under Torsion

2018 ◽  
Author(s):  
Pan Fang ◽  
Yuxin Xu ◽  
Shuai Yuan ◽  
Yong Bai ◽  
Peng Cheng
Keyword(s):  
Mechanical Behavior ◽  
Torsion Angle ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Load Condition ◽  
Element Model ◽  
Flexible Pipe ◽  
Torsional Load ◽  
Flexible Pipes ◽  
The Impact

Fibreglass reinforced flexible pipe (FRFP) is regarded as a great alternative to many bonded flexible pipes in the field of oil or gas transportation in shallow water. This paper describes an analysis of the mechanical behavior of FRFP under torsion. The mechanical behavior of FRFP subjected to pure torsion was investigated by experimental, analytical and numerical methods. Firstly, this paper presents experimental studies of three 10-layer FRFP subjected to torsional load. Torque-torsion angle relations were recorded during this test. Then, a theoretical model based on three-dimensional (3D) anisotropic elasticity theory was proposed to study the mechanical behavior of FRFP. In addition, a finite element model (FEM) including reinforced layers and PE layers was used to simulate the torsional load condition in ABAQUS. Torque-torsion angle relations obtained from these three methods agree well with each other, which illustrates the accuracy and reliability of the analytical model and FEM. The impact of fibreglass winding angle, thickness of reinforced layers and radius-thickness ratio were also studied. Conclusions obtained from this research may be of great practicality to manufacturing engineers.

scholarly journals A Theoretical Approach to Predict the Fatigue Life of Flexible Pipes

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
José Renato M. de Sousa ◽  
Fernando J. M. de Sousa ◽  
Marcos Q. de Siqueira ◽  
Luís V. S. Sagrilo ◽  
Carlos Alberto D. de Lemos
Keyword(s):  
Fatigue Life ◽  
Fatigue Damage ◽  
Cross Section ◽  
Time Domain ◽  
Theoretical Approach ◽  
Flexible Pipe ◽  
Stress Effects ◽  
Flexible Pipes ◽  
Counting Methods ◽  
Mean Stresses

This paper focuses on a theoretical approach to access the fatigue life of flexible pipes. This methodology employs functions that convert forces and moments obtained in time-domain global analyses into stresses in their tensile armors. The stresses are then processed by well-known cycle counting methods, andS-Ncurves are used to evaluate the fatigue damage at several points in the pipe’s cross-section. Finally, Palmgren-Miner linear damage hypothesis is assumed in order to calculate the accumulated fatigue damage. A study on the fatigue life of a flexible pipe employing this methodology is presented. The main points addressed in the study are the influence of friction between layers, the effect of the annulus conditions, the importance of evaluating the fatigue life in various points of the pipe’s cross-section, and the effect of mean stresses. The results obtained suggest that the friction between layers and the annulus conditions strongly influences the fatigue life of flexible pipes. Moreover, mean stress effects are also significant, and at least half of the wires in each analyzed section of the pipe must be considered in a typical fatigue analysis.

A Theoretical Method to Estimate the Fatigue Life of Tensile Armors of Flexible Pipes

2018 ◽  
Author(s):  
Kaien Jiang ◽  
Yutian Lu ◽  
Yong Bai
Keyword(s):  
Fatigue Life ◽  
Fatigue Damage ◽  
Theoretical Method ◽  
Mean Stress ◽  
Flexible Pipe ◽  
Friction Coefficients ◽  
Flexible Pipes ◽  
Damage Theory ◽  
Rainflow Counting

This paper mainly focuses on a theoretical methodology to calculate the fatigue life of tensile armor of flexible pipes. This approach employs the local model of flexible pipe that converts forces and moments obtained in time-domain global analyses into stresses in the spiral tendons of tensile armor layer. The stresses are then processed by rainflow counting methods, and S-N curves are adopted to evaluate the fatigue damage of tensile armors. Finally, Miner linear cumulative damage theory is used in order to calculate the accumulated fatigue damage. A case study on the fatigue life of a flexible pipe employing this methodology is presented, and the fatigue life of flexible pipe is obtained. The main points addressed in the study are the effect of mean stress and friction coefficients. The results indicate that the inner tensile armor at suspension point is the most prone to fatigue damage, in addition, mean stress correction and friction coefficients strongly influence the fatigue life of flexible pipes.

Incorporating the Higher Harmonics in VIV Fatigue Predictions

2007 ◽  
Author(s):  
Vikas Jhingran ◽  
J. Kim Vandiver
Keyword(s):  
Fatigue Damage ◽  
Strain Energy ◽  
Oil And Gas ◽  
Oil And Gas Industry ◽  
Dynamic Strain ◽  
Higher Harmonics ◽  
Gas Industry ◽  
Ongoing Research ◽  
Fatigue Design ◽  
Vortex Induced Vibrations

Vortex-Induced Vibrations (VIV) are an important source of fatigue damage for risers in the Oil and Gas industry. Results from resent VIV experiments by Vandiver et al. [1] indicate significant dynamic strain energy at not only the Strouhal frequency, but also its harmonics. In certain regions of the pipe, these higher harmonics accounted for more that half of the measured RMS strain and increased fatigue damage by a factor exceeding twenty. However, the state-of-the-art in VIV prediction only accounts for the vibrations at the Strouhal frequency. Preliminary results from a second set of experiments, described in this paper, confirm the importance of the higher harmonics in fatigue life estimates of pipes. Further, the authors formulate an approach to incorporate the higher harmonics in VIV related fatigue design. Finally, the authors identify the estimation of the higher harmonics, in both location and magnitude, as an important area of ongoing research, the results of which will be required to implement this proposed method.

Magnetic Linear Birefringence in Rare Earth Systems. II. Third-Order Approach

2004 ◽  
Vol 69 (1) ◽  
pp. 34-46
Author(s):  
Lidia Smentek
Keyword(s):  
Rare Earth ◽  
Field Potential ◽  
Second Order ◽  
Rare Earth Ions ◽  
Lanthanide Ions ◽  
Linear Birefringence ◽  
Third Order ◽  
The Third ◽  
The Impact ◽  
Effective Operators

The theory of linear magnetic birefringence of rare earth ions in crystals is extended here by the contributions that represent a direct perturbing influence of the crystal field potential surrounding the central ion. The basic assumptions of the theoretical model are the same as in the previous analysis of second-order terms. The third-order contributions introduced here break the free ionic system approximation, and they represent the impact due to configuration interaction. The effective operators include the perturbing influence of the excitations from the 4f shell to one-electron states of the same parity (as previously at the second order), and in addition, the excitations to states of opposite parity. All contributing terms are expressed by the effective operators that are defined within the perturbed function approach. The tensorial structure of these operators is discussed, and special attention is directed to newly defined radial integrals. The values of all radial integrals that are necessary for the third-order numerical analysis are presented in the case of all lanthanide ions.

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