The article studies the parameters of a pulsating fluid flow that lead to vibration in the pipeline. A mathematical model has been developed for the vibration of a viscoelastic pipeline based on the theory of beams when a pulsating fluid flows through it. Using the Bubnov-Galerkin method, based on a polynomial approximation of deflections, the problem is reduced to the study of systems of ordinary integro-differential equations, the solution of which is found by a numerical method. A computational algorithm has been developed for solving the problems of oscillation of composite pipelines with a flowing pulsating fluid. The influence of the singularity in the nuclei of heredity on the vibrations of structures with viscoelastic properties is studied numerically. It is shown that with an increase in the viscosity parameter of the pipeline material, the critical flow rate decreases. It was revealed that an increase in the value of the pulsation frequency of the liquid and the excitation coefficient leads to a decrease in the critical velocity of the liquid flow.
1. Attia EM. Vibrations analysis of ruptured pipe conveying pulsating fluid flow and supported by a magnetorheological damper. Journal of Vibroengineering 2016; 18(5); 3242-3257. https: doi.org/10.21595/jve.2016.16904.
2. Paidoussis MP, Issid NT. Dynamic stability of pipes conveying fluid. Journal of Sound and Vibration 1974; 33(3); Pp 267–294.
3. Hong Bo Zhai, Jian Jun Su, Xiao Min Yan, Wei Liu. Dynamic Response of the Pipe Conveying Fluid with the Pressure Pulsation. Advanced Materials Research 2015; 1094; Pp491-494.
4. Jiantao Li, Hua Deng, Wenjun Jiang. Dynamic response and vibration suppression of a cantilevered pipe conveying fluid under periodic excitation. Journal of Vibration and Control 2019; 25(11); 107754631983778. DOI: 10.1177/1077546319837789
5. Paidoussis MP, Sundararajan C. Parametric and Combination Resonances of a Pipe Conveying Pulsating Fluid. J Appl Mech 1975; 42(4); Pp780-784. doi:10.1115/1.3423705.
6. Liu Long, Xuan Fuzhen. Flow-Induced Vibration Analysis of Supported Pipes Conveying Pulsating Fluid Using Precise Integration Method. Mathematical Problems in Engineering 2010; 2010(12). DOI: 10.1155/2010/806475
7. Daniel G Gorman, Jason M Reese, Zhang YL. Vibration of a Flexible Pipe Conveying Viscous Pulsating Fluid Flow. Journal of Sound and Vibration 2000; 230(2); 379-392. DOI: 10.1006/jsvi.1999.2607
8. Panda LN, Kar RC. Nonlinear dynamics of a pipe conveying pulsating fluid with parametric and internal resonances. Nonlinear Dyn 2007; 49;9-30. https: doi.org/10.1007/s11071-006-9100-6
9. Bamadev Sahoo, Panda LN, Pohit G. Parametric and Internal Resonances of an Axially Moving Beam with Time-Dependent Velocity. Modelling and Simulation in Engineering 2013; 2013; ID 919517. http: dx.doi.org/10.1155/2013/919517
10. Jialin Tian,Changfu Yuan, Lin Yang, Chunming Wu, Gang Liu, Zhi Yang. The vibration analysis model of pipeline under the action of gas pressure pulsation coupling. Engineering Failure Analysis 2016; 66; Pp328-340. https: doi.org/10.1016/j.engfailanal.2016.05.017
11. František Trebuňa, František Šimčák, Róbert Huňady, Miroslav Pástor. Identification of pipes damages on gas compressor stations by modal analysis methods. Engineering Failure Analysis 2013; 27; Pp 213-224. https://doi.org/10.1016/j.engfailanal.2012.08.024
12. Sha Zhou, Tian-Jun Yu, Xiao-Dong Yang, Wei Zhang. Global Dynamics of Pipes Conveying Pulsating Fluid in the Supercritical Regime. International Journal of Applied Mechanics 2017; 09(02); 1750029. https: doi.org/10.1142/S1758825117500296
13. Wang Yikun, Ni Qiao, Wang Lin, Luo Yangyang, Yan Hao. Nonlinear impacting oscillations of pipe conveying pulsating fluid subjected to distributed motion constraints. Journal of Mechanics of Materials and Structures 2017; 12(5); Pp 563-578. DOI: 10.2140/jomms.2017.12.563
14. Mironova TB, Prokofiev AB, Shorin VP. FINITE ELEMENT TECHNIQUES FOR PIPE SYSTEM VIBROACOUSTICAL CHARACTERISTICS MODELLING. Vestnik of Samara University. Aerospace and Mechanical Engineering 2012;1(32); Pp135-140.
15. Anoshkin AN, Zuyko VYu, Ivanov SG. Calculation of Stress-strain State and Prediction of the Strength of Polymer Reinforced Gas Pipes. Bulletin of the Samara State University. Natural science series 2007; 6; Pp 419-426.
16. Yagubov EZ, Tskhadaya ND, Yagubov ZKh. Multichannel Pipelines for Oil and Gas Transportation and Recovery of Worn out Oil and Gas Pipelines. Scientific papers 2013; 1; Pp 57-63.
17. Yu-Jia Hu, Weidong Zhu. Vibration analysis of a fluid-conveying curved pipe with an arbitrary undeformed configuration. Applied Mathematical Modelling 2018; 64; Pp 624–642. https: doi.org/10.1016/j.apm.2018.06.046
18. Ting Chen, Dynamic Characteristic Analysis for Fluid-Conveying Pipe of TBM Dynamic Characteristic Analysis for Fluid-Conveying Pipe of TBM. IOP Conf. Series: Earth and Environmental Science 2019; 252; 052120. doi:10.1088/1755-1315/252/5/052120
19. Dahmane M, Boutchicha D, Adjlout L. One-way fluid structure interaction of pipe under flow with different boundary conditions. MECHANIKA 2016; 22(6). Pp 495-503. http: dx.doi.org/10.5755/j01.mech.22.6.13189.
20. Jialin Tian, Changfu Yuan, Lin Yang, Chunming Wu, Gang Liu, Zhi Yang. The vibration analysis model of pipeline under the action of gas pressure pulsation coupling. Engineering Failure Analysis 2016; 66; Pp 328-340. https: doi.org/10.1016/j.engfailanal.2016.05.017
21. Zeming Fan, Xiaojun Yu, Qiang Zhang, Sifan He, Gansu Chen, Junye Du, Yifei Wen. Fatigue life estimation for simply-supported pipeline of robots under hybrid excitation. International Journal of Fatigue 2018;108; Pp 127-139. https: doi.org/10.1016/j. ijfatigue.2017.11.00 2
22. Colum M Holtam, David P Baxter, Ian A Ashcroft, Rachel C Thomson. Effect of crack depth on fatigue crack growth rates for a C–Mn pipeline steel in a sour environment. International Journal of Fatigue. 2010; 32(2); Pp 288-296. https: doi.org/10.1016/j. ijfatigue.2009.06.013
23. Hemat Ali Esmaeili, Mehran Khaki, Morteza Abbasi. Structural Engineering and Mechanics 2018; 67(1); Pp 21-31. http: dx.doi. org/10.12989/sem.2018.67.1.021.
24. Amr Shalaby, Hassan El-Gamal, Elarabi M Attia. Vibrations analysis of pipe convoying pulsating fluid flow. International Journal of Science and Research (IJSR) 2019; 8(2); 1696-1709. DOI: 10.21275/ART20195628
25. Urbanowicz K, Firkodnawski M, Zarzycki Z. Modelling water hammer in viscoelastic pipelines: short brief. J Phys: Conf Ser 2016; 760; 012037
26. Mohamed Amine Guidara, Mohamed Ali Bouaziz, Christian Schmitt, Zitouni Azari, Ezzeddine Hadj-Taieb. A semi-empirical model for structural integrity assessment of defected high density polyethylene pipes. Engineering Failure Analysis 2019; 100; Pp 273-287. https: doi.org/10.1016/j.engfailanal.2019.02.045 27. Xiangpeng Luo, Shunli Lu, Jianfeng Shi, Xiang Li, Jinyang Zheng. Numerical simulation of strength failure of buried polyethylene pipe under foundation settlement. Engineering Failure Analysis 2015; 48; Pp 144-152. https: doi.org/10.1016/j. engfailanal.2014.11.014
28. Li Yun-dong, Yang Yi-ren. Vibration analysis of conveying fluid pipe via He’s variational iteration method. Applied Mathematical Modelling 2017; 43; Pp. 409-420. https: doi.org/10.1016/j.apm.2016.11.029
29. Khudayarov BA, Komilova KhM. Vibration and dynamic stability of composite pipelines conveying a two-phase fluid flows. Engineering Failure Analysis 2019;104; 500-512.
30. Khudayarov BA, Turayev FZh. Numerical simulation of nonlinear oscillations of a viscoelastic pipeline with fluid. Vestn Tom gos un-ta. Matematika i mekhanika 2016; 5(43); Pp 90–98. DOI:10.17223/19988621/43/10
31. Khudayarov BA, Turayev FZh. Mathematical Simulation of Nonlinear Oscillations of Viscoelastic Pipelines Conveying Fluid. Applied Mathematical Modelling 2019; 66; Pp 662-679. https: doi.org/10.1016/j.apm.2018.10.008
32. Koltunov MA. Creeping and relaxation. Moscow. 1976.
33. Tao SY, Liu QY, Wang GR, Jiang JC. Influence of the key parameters of suspended structures on the inherent frequency of oil and gas pipelines. Journal of Sound and Vibration 2015; 355; Pp 39–53. http://dx.doi.org/10.1016/j.jsv.2015.06.044
34. Feng Liang, Jiduo Jin, Xiaodong Yang. Static and dynamic stabilities off luid pipes on elastic foundation. Engineering Mechanics 2010; 11; Pp 166-171.
35. Badalov FB, Khudayarov BA, Abdukarimov A. Effect of the hereditary kernel on the solution of linear and nonlinear dynamic problems of hereditary deformable systems. Journal of Machinery Manufacture and Reliability 2007; 36; 328-335.
36. Badalov FB. Methods for Solving Integral and Integro-differential Equations of the Hereditary Theory of Viscoelasticity. Tashkent Mekhnat. 1987.
37. Badalov FB, Eshmatov Kh, Yusupov M. Some Methods of Solution of the Systems of Integro-differential Equations in Problems of Viscoelasticity. Applied Mathematics and Mechanics 1987; 51(5); Pp 867-871.
38. Khudayarov BA, Turayev FZh. Nonlinear supersonic flutter for the viscoelastic orthotropic cylindrical shells in supersonic flow. Aerospace Science and Technology 2019; 84; Pp 120-130. doi: 10.1016/j.ast.2018.08.044
39. Jinzhe Gonga, Aaron Zecchina , Martin Lamberta, Angus Simpson. Study on the frequency response function of viscoelastic pipelines using a multi-element Kevin-Voigt model. Procedia Engineering 2015;119; Pp 226-234. doi: 10.1016/j.proeng.2015.08.880
40. Mirsaidov M. Using linear hereditary theory of viscoelasticity by dynamic calculation of soil structures. Bases, Foundations and Soil Mechanics 2012; 6; Pp 30-34.
41. Mirsaidov M, Sultanov T. Use of linear heredity theory of viscoelasticity for dynamic analysis of earthen structures. Soil Mechanics & Foundation Engineering 2013; 49(6); Pp 250-256.
"NUMERICAL SIMULATION OF VIBRATION VISCOELASTIC PIPELINE,"
Irrigation and Melioration: Vol. 2021
, Article 5.
Available at: https://uzjournals.edu.uz/tiiame/vol2021/iss4/5