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Статті в журналах з теми "Wake-oscillator model"

Автор: Grafiati

Опубліковано: 10 березня 2023

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1

Hagiwara, Tsuyoshi. "A Comparison between Wake Oscillator Model and Fluids Force Coefficients." Proceedings of the Fluids engineering conference 2000 (2000): 76. http://dx.doi.org/10.1299/jsmefed.2000.76.

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2

M, Muthaiah, Ragul Senthilkumar, and Varunkumar S. "Numerical investigation of thermo-acoustic instability in a model afterburner with a simplified model for observed lock-in Phenomena." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, no. 3 (February 1, 2023): 4088–99. http://dx.doi.org/10.3397/in_2022_0585.

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Thermoacoustic oscillations in a gas turbine afterburner are numerically investigated using CFD. A simplified 2-dimensional axisymmetric afterburner with bluff-body stabilized flame is considered in the investigation. Occurrences of both low and high-frequency thermo-acoustic oscillations in the afterburner chamber are observed at specific fuel flow rates. The flow field from the CFD shows the bluff-body vortex shedding frequency to lock-in with the acoustics of the chamber during the thermo-acoustic oscillations. The synchronization and lock-in of bluff-body wake with chamber acoustics happen with increase in fuel injection rates resulting in thermoacoustic coupling. The Proper Orthogonal Decomposition of the flow field revealed the presence of chamber acoustics in the pressure field confirming the coupling. Then a simplified mathematical model based on the van-der Pol oscillator is attempted to reproduce the observed lock-in behavior of the bluff-body wake. The chamber acoustic field is considered as the forcing term for the simplified oscillator. The oscillator model qualitatively captures the synchronization of the flame-holder wake oscillations with the chamber acoustics. This model could be extended to combustors with bluff-body wake in predicting the thermo-acoustic oscillations.

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3

Kurushina, Victoria, and Ekaterina Pavlovskaia. "Fluid nonlinearities effect on wake oscillator model performance." MATEC Web of Conferences 148 (2018): 04002. http://dx.doi.org/10.1051/matecconf/201814804002.

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Vortex-induced vibrations (VIV) need to be accounted for in the design of marine structures such as risers and umbilicals. If a resonance state of the slender structure develops due to its interaction with the surrounding fluid flow, the consequences can be severe resulting in the accelerated fatigue and structural damage. Wake oscillator models allow to estimate the fluid force acting on the structure without complex and time consuming CFD analysis of the fluid domain. However, contemporary models contain a number of empirical coeffcients which are required to be tuned using experimental data. This is often left for the future work with the opened question on how to calibrate a model for a wide range of cases and find out what is working and is not. The current research is focused on the problem of the best choice of the fluid nonlinearities for the base wake oscillator model [1] in order to improve the accuracy of prediction for the cases with mass ratios around 6.0. The paper investigates six nonlinear damping types for two fluid equations of the base model. The calibration is conducted using the data by Stappenbelt and Lalji [2] for 2 degrees-of-freedom rigid structure for mass ratio 6.54. The conducted analysis shows that predicted in-line and cross-flow displacements are more accurate if modelled separately using different damping types than using only one version of the model. The borders of application for each found option in terms of mass ratio are discussed in this work, and appropriate recommendations are provided.

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4

Poore, Aubrey B., Eusebius J. Doedel, and Jack E. Cermak. "Dynamics of the Iwan-Blevins wake oscillator model." International Journal of Non-Linear Mechanics 21, no. 4 (January 1986): 291–302. http://dx.doi.org/10.1016/0020-7462(86)90036-3.

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5

Zhang, Xiulin, Xu Zhang, Shuni Zhou, Wenzha Yang, Liangbin Xu, Lina Yi, Gengqing Tian, Yong Ma, Yuheng Hao, and Wenchi Ni. "A Modified Wake Oscillator Model for the Cross-Flow Vortex-Induced Vibration of Rigid Cylinders with Low Mass and Damping Ratios." Journal of Marine Science and Engineering 11, no. 2 (January 17, 2023): 235. http://dx.doi.org/10.3390/jmse11020235.

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The classical wake oscillator model is capable of predicting the vortex-induced vibration response of a cylinder at high mass-damping ratios, but it fails to perform satisfactorily at low mass-damping ratios. A modified wake oscillator model is presented in this paper. The modification method involves analyzing the variation law of the add mass coefficient of the cylinder versus reduced velocity and expressing the reference lift coefficient CL0 as a function of the add mass coefficient. The modified wake oscillator model has been demonstrated to have better accuracy in capturing maximum amplitudes and flow velocity at low mass-damping ratios. However, the modified model at present form is unable to accurately predict the vortex-induced vibration response at high damping ratios. The purpose of this paper is to propose a new modification idea. In order to achieve better results when applying this modification idea to particular objects, it may be necessary to first understand the response law of these kinds of objects.

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6

Kurushina, Victoria, Andrey Postnikov, Guilherme Franzini, and Ekaterina Pavlovskaia. "Optimization of the Wake Oscillator for Transversal VIV." Journal of Marine Science and Engineering 10, no. 2 (February 20, 2022): 293. http://dx.doi.org/10.3390/jmse10020293.

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Vibrations of slender structures associated with the external flow present a design challenge for the energy production systems placed in the marine environment. The current study explores the accuracy of the semi-empirical wake oscillator models for vortex-induced vibrations (VIV) based on the optimization of (a) the damping term and (b) empirical coefficients in the fluid equation. This work investigates the effect of ten fluid damping variations, from the classic van der Pol to more sophisticated fifth-order terms, and prediction of the simplified case of the VIV of transversally oscillating rigid structures provides an opportunity for an extended, comprehensive comparison of the performance of tuned models. A constrained nonlinear minimization algorithm in MATLAB is applied to calibrate considered models using the published experimental data, and the weighted objective function is formulated for three different mass ratios. Comparison with several sources of published experimental data for cross-flow oscillations confirms the model accuracy in the mass ratio range. The study indicates the advantageous performance of the models tuned with the medium mass ratio data and highlights some advantages of the Krenk–Nielsen wake oscillator.

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7

KIKITSU, Hitomitsu, Yasuo OKUDA, and Jun KANDA. "NUMERICAL EVALUATION OF INTERACTION PHENOMENON BY USING WAKE OSCILLATOR MODEL." Journal of Structural and Construction Engineering (Transactions of AIJ) 73, no. 624 (2008): 211–18. http://dx.doi.org/10.3130/aijs.73.211.

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8

Postnikov, Andrey, Ekaterina Pavlovskaia, and Marian Wiercigroch. "2DOF CFD calibrated wake oscillator model to investigate vortex-induced vibrations." International Journal of Mechanical Sciences 127 (July 2017): 176–90. http://dx.doi.org/10.1016/j.ijmecsci.2016.05.019.

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9

Alon Tzezana, Gali, and Kenneth S. Breuer. "Thrust, drag and wake structure in flapping compliant membrane wings." Journal of Fluid Mechanics 862 (January 15, 2019): 871–88. http://dx.doi.org/10.1017/jfm.2018.966.

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Анотація:

We present a theoretical framework to characterize the steady and unsteady aeroelastic behaviour of compliant membrane wings under different conditions. We develop an analytic model based on thin airfoil theory coupled with a membrane equation. Adopting a numerical solution to the model equations, we study the effects of wing compliance, inertia and flapping kinematics on aerodynamic performance. The effects of added mass and fluid damping on a flapping membrane are quantified using a simple damped oscillator model. As the flapping frequency is increased, membranes go through a transition from thrust to drag around the resonant frequency, and this transition is earlier for more compliant membranes. The wake also undergoes a transition from a reverse von Kármán wake to a traditional von Kármán wake. The wake transition frequency is predicted to be higher than the thrust–drag transition frequency for highly compliant wings.

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10

Hussin, W. N. W., F. N. Harun, M. H. Mohd, and M. A. A. Rahman. "Analytical modelling prediction by using wake oscillator model for vortex-induced vibrations." JOURNAL OF MECHANICAL ENGINEERING AND SCIENCES 11, no. 4 (December 30, 2017): 3116–28. http://dx.doi.org/10.15282/jmes.11.4.2017.14.0280.

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11

Xu, Wan-Hai, Xiao-Hui Zeng, and Ying-Xiang Wu. "High aspect ratio (L/D) riser VIV prediction using wake oscillator model." Ocean Engineering 35, no. 17-18 (December 2008): 1769–74. http://dx.doi.org/10.1016/j.oceaneng.2008.08.015.

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12

Fujiwara, Toshifumi. "VIM Time-domain Simulation on a Semi-submersible Floater Using Wake Oscillator Model." Journal of the Japan Society of Naval Architects and Ocean Engineers 27 (2018): 49–55. http://dx.doi.org/10.2534/jjasnaoe.27.49.

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13

Mathelin, L., and E. de Langre. "Vortex-induced vibrations and waves under shear flow with a wake oscillator model." European Journal of Mechanics - B/Fluids 24, no. 4 (July 2005): 478–90. http://dx.doi.org/10.1016/j.euromechflu.2004.12.005.

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14

Ge, Fei, Wei Lu, Lei Wang, and You-Shi Hong. "Shear flow induced vibrations of long slender cylinders with a wake oscillator model." Acta Mechanica Sinica 27, no. 3 (June 2011): 330–38. http://dx.doi.org/10.1007/s10409-011-0460-x.

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15

Farshidianfar, A., and N. Dolatabadi. "Modified higher-order wake oscillator model for vortex-induced vibration of circular cylinders." Acta Mechanica 224, no. 7 (February 12, 2013): 1441–56. http://dx.doi.org/10.1007/s00707-013-0819-0.

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16

KOBAYASHI, Yukinori, Eisuke KAMIDE, and Yohei HOSHINO. "Disturbance Cancellation Control and Coupling Vibration of an Elastic Supported Cylinder and Wake Oscillator (Improvement of Control Simulation by Using van der Pol Wake Oscillator Model)." Transactions of the Japan Society of Mechanical Engineers Series C 72, no. 716 (2006): 1109–14. http://dx.doi.org/10.1299/kikaic.72.1109.

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17

Su, Zhi Bin, and Sheng Nan Sun. "Vortex-Induced Dynamic Response of Submerged Floating Tunnel Tether Based on Wake Oscillator Model." Advanced Materials Research 919-921 (April 2014): 1262–65. http://dx.doi.org/10.4028/www.scientific.net/amr.919-921.1262.

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To study the vibration response of submerged floating tunnel tether under the combined action of vortex-induced vibration and parametric vibration, a non-linear vibration equation based on wake oscillator model is set up taking the geometric nonlinearity of tether into account, in which effect of tube on tether is simplified as axial excitation. An approximate numerical solution of planning submerged floating tunnel tether is obtained by applying Galerkin method and Runge-kutta method. The variation degree of mid-span displacement response and axial force of tether is analyzed when the vortex-induced resonance and parametric resonance occur. The results show that, when vortex-induced resonance and parametric resonance occur simultaneously, the mid-span displacement and axial force of tether increase dramatically; the tether sag effect results in the asymmetry of tether mid-span vibration amplitude.

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18

A Rahman, Mohd Asamudin, Wan Norazam Wan Hussin, Mohd Hairil Mohd, Fatimah Noor Harun, Lee Kee Quen, and Jeom Kee Paik. "Modified wake oscillator model for vortex-induced motion prediction of low aspect ratio structures." Ships and Offshore Structures 14, sup1 (March 20, 2019): 335–43. http://dx.doi.org/10.1080/17445302.2019.1593308.

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19

Xu, Wan-hai, Ying-xiang Wu, Xiao-hui Zeng, Xing-fu Zhong, and Jian-xing Yu. "A New Wake Oscillator Model for Predicting Vortex Induced Vibration of a Circular Cylinder." Journal of Hydrodynamics 22, no. 3 (June 2010): 381–86. http://dx.doi.org/10.1016/s1001-6058(09)60068-8.

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20

Low, Ying Min, and Narakorn Srinil. "VIV fatigue reliability analysis of marine risers with uncertainties in the wake oscillator model." Engineering Structures 106 (January 2016): 96–108. http://dx.doi.org/10.1016/j.engstruct.2015.10.004.

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21

Gao, Yun, Zhuangzhuang Zhang, Ganghui Pan, Geng Peng, Lei Liu, and Wei Wang. "Three-dimensional vortex-induced vibrations of a circular cylinder predicted using a wake oscillator model." Marine Structures 80 (November 2021): 103078. http://dx.doi.org/10.1016/j.marstruc.2021.103078.

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22

Nakao, Mitsuyuki, Keisuke Yamamoto, Kazuhiro Nakamura, Norihiro Katayama, and Mitsuaki Yamamoto. "A circadian system model with feedback of cross-correlation between sleep-wake rhythm and oscillator." Psychiatry and Clinical Neurosciences 55, no. 3 (June 2001): 295–97. http://dx.doi.org/10.1046/j.1440-1819.2001.00865.x.

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23

Xu, Kun, Yaojun Ge, and Dongchang Zhang. "Wake oscillator model for assessment of vortex-induced vibration of flexible structures under wind action." Journal of Wind Engineering and Industrial Aerodynamics 136 (January 2015): 192–200. http://dx.doi.org/10.1016/j.jweia.2014.11.002.

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24

Mi, L., and O. Gottlieb. "Asymptotic model-based estimation of a wake oscillator for a tethered sphere in uniform flow." Journal of Fluids and Structures 54 (April 2015): 361–89. http://dx.doi.org/10.1016/j.jfluidstructs.2014.11.012.

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25

Mannini, Claudio. "Incorporation of turbulence in a nonlinear wake-oscillator model for the prediction of unsteady galloping response." Journal of Wind Engineering and Industrial Aerodynamics 200 (May 2020): 104141. http://dx.doi.org/10.1016/j.jweia.2020.104141.

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26

Gao, Yun, Zhi Zong, Li Zou, and Shu Takagi. "Vortex-induced vibrations and waves of a long circular cylinder predicted using a wake oscillator model." Ocean Engineering 156 (May 2018): 294–305. http://dx.doi.org/10.1016/j.oceaneng.2018.03.034.

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27

Qu, Yang, Piguang Wang, Shixiao Fu, and Mi Zhao. "Numerical study on vortex-induced vibrations of a flexible cylinder subjected to multi-directional flows." Physics of Fluids 35, no. 3 (March 2023): 037104. http://dx.doi.org/10.1063/5.0138063.

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Анотація:

Vortex-induced vibrations (VIVs) of a flexible cylinder subjected to multi-directional flows have been studied based on a wake oscillator model. The multi-directional flow comprises two slabs of flows in different directions, with each slab having a uniform uni-directional profile. The dynamics of the flexible cylinder is described based on the linear Euler–Bernoulli beam theory, and a wake oscillator model is uniformly distributed along the cylinder to model the hydrodynamic force acting on it. The dynamics of the coupled system has been solved numerically using the finite element method, and simulations have been conducted with the cylinder subjected to multi-directional flows with different angles between the two slabs. A large number of different initial conditions have been applied, and more than one steady-state response has been captured. The steady-state responses exhibit two different patterns: one is characterized by two waves traveling in opposite directions, while the other is dominated by a single traveling wave. The cross-flow VIV primarily occurs in the local cross-flow direction, and a transition of its vibrating direction happens at the interface of the two flows. Such transition is not observed in the inline VIV, and significant vibrations at the double frequency appear in both local cross-flow and inline directions. Energy analysis shows that this transition is boosted by a specific energy transfer pattern between the structure and the flow, which excites the vibration of the cylinder in some directions while damps it in others.

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28

Armin, Milad, Sandy Day, Madjid Karimirad, and Mahdi Khorasanchi. "On the development of a nonlinear time-domain numerical method for describing vortex-induced vibration and wake interference of two cylinders using experimental results." Nonlinear Dynamics 104, no. 4 (June 2021): 3517–31. http://dx.doi.org/10.1007/s11071-021-06527-8.

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AbstractA nonlinear mathematical model is developed in the time domain to simulate the behaviour of two identical flexibly mounted cylinders in tandem while undergoing vortex-induced vibration (VIV). Subsequently, the model is validated and modified against experimental results. Placing an array of bluff bodies in proximity frequently happens in different engineering fields. Chimney stacks, power transmission lines and oil production risers are few engineering structures that may be impacted by VIV. The coinciding of the vibration frequency with the structure natural frequency could have destructive consequences. The main objective of this study is to provide a symplectic and reliable model capable of capturing the wake interference phenomenon. This study shows the influence of the leading cylinder on the trailing body and attempts to capture the change in added mass and damping coefficients due to the upstream wake. The model is using two coupled equations to simulate the structural response and hydrodynamic force in each of cross-flow and stream-wise directions. Thus, four equations describe the fluid–structure interaction of each cylinder. A Duffing equation describes the structural motion, and the van der Pol wake oscillator defines the hydrodynamic force. The system of equations is solved analytically. Two modification terms are added to the excitation side of the Duffing equation to adjust the hydrodynamic force and incorporate the effect of upstream wake on the trailing cylinder. Both terms are functions of upstream shedding frequency (Strouhal number). Additionally, the added mass modification coefficient is a function of structural acceleration and the damping modification coefficient is a function of velocity. The modification coefficients values are determined by curve fitting to the difference between upstream and downstream wake forces, obtained from experiments. The damping modification coefficient is determined by optimizing the model against the same set of experiments. Values of the coefficients at seven different spacings are used to define a universal function of spacing for each modification coefficient so that they can be obtained for any given distance between two cylinders. The model is capable of capturing lock-in range and maximum amplitude.

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29

Lin, Heng, Yiqiang Xiang, Yunshen Yang, and Chaoqi Gao. "Fluid–Vehicle–Tunnel Coupled Vibration Analysis of a Submerged Floating Tunnel Based on a Wake Oscillator Model." Journal of Waterway, Port, Coastal, and Ocean Engineering 148, no. 1 (January 2022): 04021037. http://dx.doi.org/10.1061/(asce)ww.1943-5460.0000677.

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30

Fontecave Jallon, Julie, Enas Abdulhay, Pascale Calabrese, Pierre Baconnier, and Pierre-Yves Gumery. "A model of mechanical interactions between heart and lungs." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367, no. 1908 (December 13, 2009): 4741–57. http://dx.doi.org/10.1098/rsta.2009.0137.

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To study the mechanical interactions between heart, lungs and thorax, we propose a mathematical model combining a ventilatory neuromuscular model and a model of the cardiovascular system, as described by Smith et al. (Smith, Chase, Nokes, Shaw & Wake 2004 Med. Eng. Phys. 26 , 131–139. ( doi:10.1016/j.medengphy.2003.10.001 )). The respiratory model has been adapted from Thibault et al . (Thibault, Heyer, Benchetrit & Baconnier 2002 Acta Biotheor . 50 , 269–279. ( doi:10.1023/A:1022616701863 )); using a Liénard oscillator, it allows the activity of the respiratory centres, the respiratory muscles and rib cage internal mechanics to be simulated. The minimal haemodynamic system model of Smith includes the heart, as well as the pulmonary and systemic circulation systems. These two modules interact mechanically by means of the pleural pressure, calculated in the mechanical respiratory system, and the intrathoracic blood volume, calculated in the cardiovascular model. The simulation by the proposed model provides results, first, close to experimental data, second, in agreement with the literature results and, finally, highlighting the presence of mechanical cardiorespiratory interactions.

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31

Lin, Lin, and Yan Ying Wang. "Nonlinear Analysis of Vortex Induced Dynamic Response of Marine Riser." Applied Mechanics and Materials 353-356 (August 2013): 2736–40. http://dx.doi.org/10.4028/www.scientific.net/amm.353-356.2736.

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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.

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32

Gander, P. H., R. E. Kronauer, and R. C. Graeber. "Phase shifting two coupled circadian pacemakers: implications for jet lag." American Journal of Physiology-Regulatory, Integrative and Comparative Physiology 249, no. 6 (December 1, 1985): R704—R719. http://dx.doi.org/10.1152/ajpregu.1985.249.6.r704.

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Flights across time zones produce an abrupt displacement of the environmental time cues (zeitgebers), and the endogenous circadian timing system resynchronizes only gradually to the new schedule. A coupled two-oscillator model can simulate the human circadian system in temporal isolation and in artificial zeitgeber cycles. The model is here shown to explain the major features of resynchronization of circadian rhythms after time zone shifts, i.e., the rate of adjustment depends on the rhythm being measured, the number of time zones crossed, the flight direction (eastward or westward), and the strength of the zeitgebers in the new time zone. Investigations of the contribution of different model parameters to system performances suggest that intersubject differences in pacemaker periods may be a major factor in the observed variability in the effects of time zone shifts on circadian rhythms. With individualized period estimate the models can simulate case studies in which four subjects recorded their sleep-wake and core body temperature rhythms throughout simple and complex patterns of transmeridian flights.

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33

Qu, Yang, and Andrei V. Metrikine. "A single van der pol wake oscillator model for coupled cross-flow and in-line vortex-induced vibrations." Ocean Engineering 196 (January 2020): 106732. http://dx.doi.org/10.1016/j.oceaneng.2019.106732.

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34

Violette, R., E. de Langre, and J. Szydlowski. "Computation of vortex-induced vibrations of long structures using a wake oscillator model: Comparison with DNS and experiments." Computers & Structures 85, no. 11-14 (June 2007): 1134–41. http://dx.doi.org/10.1016/j.compstruc.2006.08.005.

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35

Gao, Xi-feng, Wu-de Xie, Wan-hai Xu, Yu-chuan Bai, and Hai-tao Zhu. "A Novel Wake Oscillator Model for Vortex-Induced Vibrations Prediction of A Cylinder Considering the Influence of Reynolds Number." China Ocean Engineering 32, no. 2 (April 2018): 132–43. http://dx.doi.org/10.1007/s13344-018-0015-z.

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36

Mathai, Varghese, Laura A. W. M. Loeffen, Timothy T. K. Chan, and Sander Wildeman. "Dynamics of heavy and buoyant underwater pendulums." Journal of Fluid Mechanics 862 (January 16, 2019): 348–63. http://dx.doi.org/10.1017/jfm.2018.867.

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The humble pendulum is often invoked as the archetype of a simple, gravity driven, oscillator. Under ideal circumstances, the oscillation frequency of the pendulum is independent of its mass and swing amplitude. However, in most real-world situations, the dynamics of pendulums is not quite so simple, particularly with additional interactions between the pendulum and a surrounding fluid. Here we extend the realm of pendulum studies to include large amplitude oscillations of heavy and buoyant pendulums in a fluid. We performed experiments with massive and hollow cylindrical pendulums in water, and constructed a simple model that takes the buoyancy, added mass, fluid (nonlinear) drag and bearing friction into account. To first order, the model predicts the oscillation frequencies, peak decelerations and damping rate well. An interesting effect of the nonlinear drag captured well by the model is that, for heavy pendulums, the damping time shows a non-monotonic dependence on pendulum mass, reaching a minimum when the pendulum mass density is nearly twice that of the fluid. Small deviations from the model’s predictions are seen, particularly in the second and subsequent maxima of oscillations. Using time-resolved particle image velocimetry (TR-PIV), we reveal that these deviations likely arise due to the disturbed flow created by the pendulum at earlier times. The mean wake velocity obtained from PIV is used to model an extra drag term due to incoming wake flow. The revised model significantly improves the predictions for the second and subsequent oscillations.

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37

Chen, Jie, and Qiu-Sheng Li. "Nonlinear Dynamics of a Fluid–Structure Coupling Model for Vortex-Induced Vibration." International Journal of Structural Stability and Dynamics 19, no. 07 (June 26, 2019): 1950071. http://dx.doi.org/10.1142/s0219455419500718.

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Анотація:

This paper presents a fluid–structure coupling model to investigate the vortex-induced vibration of a circular cylinder subjected to a uniform cross-flow. A modified van der Pol nonlinear equation is employed to represent the fluctuating nature of vortex shedding. The wake oscillator is coupled with the motion equation of the cylinder by applying coupling terms in modeling the fluid–structure interaction. The transient responses of the fluid–structure coupled model are presented and discussed by numerical simulations. The results demonstrate the main features of the vortex-induced vibration, such as lock-in phenomenon, i.e. resonant oscillation of the cylinder occurs when the vortex shedding frequency is near to the natural frequency of the cylinder. The resonant responses of the fluid–structure coupled model in the lock-in region are determined by the multiple scales method. The accuracy of the asymptotic solution by the multiple scales method is verified by comparing with the numerical solution from the motion equation. The effects of different parameters on the steady state amplitude of oscillation are investigated for a given set of parameters. Frequency–response curves obtained from the modulation equation demonstrate the existence of jump phenomena.

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Qu, Yang, Shixiao Fu, Zhenhui Liu, Yuwang Xu, and Jiayang Sun. "Numerical study on the characteristics of vortex-induced vibrations of a small-scale subsea jumper using a wake oscillator model." Ocean Engineering 243 (January 2022): 110028. http://dx.doi.org/10.1016/j.oceaneng.2021.110028.

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39

Prethiv Kumar, R., and S. Nallayarasu. "VIV response of risers with large aspect ratio and low rigidity using a numerical scheme based on wake oscillator model." Applied Ocean Research 118 (January 2022): 103011. http://dx.doi.org/10.1016/j.apor.2021.103011.

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40

Fehér, Rafael, and Juan Julca Avila. "Vortex-induced vibrations model with 2 degrees of freedom of rigid cylinders near a plane boundary based on wake oscillator." Ocean Engineering 234 (August 2021): 108938. http://dx.doi.org/10.1016/j.oceaneng.2021.108938.

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41

Qu, Yang, Shixiao Fu, Yuwang Xu, and Jun Huang. "Application of a modified wake oscillator model to vortex-induced vibration of a free-hanging riser subjected to vessel motion." Ocean Engineering 253 (June 2022): 111165. http://dx.doi.org/10.1016/j.oceaneng.2022.111165.

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42

Xu, Wan-Hai, Jie Du, Jian-Xing Yu, and Jing-Cheng Li. "Wake Oscillator Model Proposed for the Stream-Wise Vortex-Induced Vibration of a Circular Cylinder in the Second Excitation Region." Chinese Physics Letters 28, no. 12 (December 2011): 124704. http://dx.doi.org/10.1088/0256-307x/28/12/124704.

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43

Farshidianfar, A., and H. Zanganeh. "A modified wake oscillator model for vortex-induced vibration of circular cylinders for a wide range of mass-damping ratio." Journal of Fluids and Structures 26, no. 3 (April 2010): 430–41. http://dx.doi.org/10.1016/j.jfluidstructs.2009.11.005.

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44

Song, Wen, Chenshi Yang, Xiaoyi Zhang, and Yongdong Li. "Mathematical Modelling and Dynamic Analysis of a Direct-Acting Relief Valve Based on Fluid-Structure Coupling Analysis." Shock and Vibration 2021 (April 10, 2021): 1–11. http://dx.doi.org/10.1155/2021/5581684.

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To explain the sudden jump of pressure as the variation of water depth for a direct-acting relief valve used by torpedo pump as the variation of water depth, a 2-DOF fluid-structure coupling dynamic model is developed. A nonlinear differential pressure model at valve port is applied to model the axial vibration of fluid, and a nonlinear wake oscillator model is used to excite the valve element in the vertical direction; meanwhile, the contact nonlinearity between the valve element and valve seat is also taken into consideration. Based on the developed dynamical model, the water depths for the sudden jumps of pressure can be located precisely when compared with the experimental signals, and the corresponding vibration conditions of the valve element in both the axial and vertical directions are explored. Subsequently, in order to eliminate the sudden jumps of pressure, different pump inlet pressure was tested experimentally; when it was decreased to 0.4 MPa, the pressure jumps ever appeared during the dropping and lifting processes were removed, and the numerical simulation based on the developed mathematical model also verified the experimental measurements.

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45

Feng, Y. L., D. Y. Chen, S. W. Li, Q. Xiao, and W. Li. "Vortex-induced vibrations of flexible cylinders predicted by wake oscillator model with random components of mean drag coefficient and lift coefficient." Ocean Engineering 251 (May 2022): 110960. http://dx.doi.org/10.1016/j.oceaneng.2022.110960.

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46

Chen, Cong, Niccolo Wieczorek, Julian Unglaub, and Klaus Thiele. "Extension of wake oscillator model for continuous system and application to the VIV-galloping instability of a bridge during launching phase." Journal of Wind Engineering and Industrial Aerodynamics 218 (November 2021): 104769. http://dx.doi.org/10.1016/j.jweia.2021.104769.

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47

Doan, Viet-Phan, and Yoshiki Nishi. "Modeling of fluid–structure interaction for simulating vortex-induced vibration of flexible riser: finite difference method combined with wake oscillator model." Journal of Marine Science and Technology 20, no. 2 (September 18, 2014): 309–21. http://dx.doi.org/10.1007/s00773-014-0284-z.

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48

Gao, Guanghai, Yunjing Cui, and Xingqi Qiu. "Prediction of Vortex-Induced Vibration Response of Deep Sea Top-Tensioned Riser in Sheared Flow Considering Parametric Excitations." Polish Maritime Research 27, no. 2 (June 1, 2020): 48–57. http://dx.doi.org/10.2478/pomr-2020-0026.

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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

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49

Yang, Wenwu, Xueping Chang, and Ruyi Gou. "Nonlinear vortex-induced vibration dynamics of a flexible pipe conveying two-phase flow." Advances in Mechanical Engineering 11, no. 10 (October 2019): 168781401988192. http://dx.doi.org/10.1177/1687814019881924.

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In this article, a vortex-induced vibration prediction model of a flexible riser conveying two-phase flow, including geometric and hydrodynamic nonlinearity, is established. A van der Pol wake oscillator is utilized to characterize the fluctuating lift forces. The finite element method is chosen to solve the coupled nonlinear fluid–structure interaction equations. The natural frequencies of the flexible riser are calculated to validate the method through comparisons with results from the literature. The modal analyses show that geometric nonlinearity has a significant effect on the natural frequency, and the critical internal velocity is reduced than those in linear analyses. The impacts of the gas volume fraction as functions of cross-flow velocity on the synchronization region, the displacement amplitudes, and the maximum stresses and frequency spectra have been investigated. The results show that an increase in the gas fraction results in the linear increase in natural frequencies and a wider synchronization region, and an increase in liquid flow rate led to the slight decrease in displacement amplitude and maximum stress within a small flow range.

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50

Gao, Yun, Lei Liu, Ganghui Pan, Shixiao Fu, Shenglin Chai, and Chen Shi. "Numerical prediction of vortex-induced vibrations of a long flexible riser with an axially varying tension based on a wake oscillator model." Marine Structures 85 (September 2022): 103265. http://dx.doi.org/10.1016/j.marstruc.2022.103265.

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