Wind and Structures

  • 제32권1호
  • /
  • Pages.11-17
  • /
  • 2021
  • /
  • 1226-6116(pISSN)
  • /
  • 1598-6225(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Application of differential transformation method for free vibration analysis of wind turbine

  • Bozdogan, Kanat Burak (Canakkale Onsekiz Mart University, Engineering Faculty, Civil Engineering Department) ;
  • Maleki, Farshid Khosravi (Bartin University, Faculty of Engineering, Architecture and Design, Mechanical Engineering Department)
  • 투고 : 2020.03.03
  • 심사 : 2020.12.22
  • 발행 : 2021.01.25
⟨ 이전 논문 다음 논문 ⟩

초록

In recent years, there has been a tendency towards renewable energy sources considering the damages caused by non-renewable energy resources to nature and humans. One of the renewable energy sources is wind and energy is obtained with the help of wind turbines. To determine the behavior of wind turbines under earthquake loads, dynamic characteristics are required. In this study, the differential transformation method is proposed to determine the free vibration analysis of wind turbines with a variable cross-section. The wind turbine is modeled as an equivalent variable continuous flexural beam and blade weight is considered as a point mass at the top of the structures. The differential equation representing the free vibration of the wind turbine is transformed into an algebraic equation with the help of differential transformation method and the angular frequencies and the mode shapes of the wind turbine are obtained by the help of the differential transformation method. In the study, a sample taken from the literature was solved with the presented method and the suitability of the method was investigated. The same wind turbine example also modeled by finite element modelling software, ABAQUS. Results of the finite element model and differential transformation method are compared with each other and the results are in good agreement.

키워드

참고문헌

  1. Abualnaja, K.M. (2020), "Numerical treatment of a physical problem in fluid film flow using the differential transformation method", Int. J. Modern Phys. C, 31(05), 87-96. https://doi.org/10.1142/S0129183120500679.
  2. AbuGazia, M., El Damatty, A.A., Dai, K., Lu, W. and Ibrahim, A. (2020), "Numerical model for analysis of wind turbines under tornadoes", Eng., Struct., 223, 54-67. https://doi.org/10.1016/j.engstruct.2020.111157.
  3. Adeleye, D.O.A., Yusuf, M. and Balogun, O. (2020), "Dynamic analysis of viscoelastic circular diaphragm of a MEMS capacitive pressure sensor using modified differential transformation method", Karbala Int. J. Modern Sci., 6(3), 65-78. https://doi.org/10.33640/2405-609X.1706.
  4. Adhikari, S. and Bhattacharya, S. (2012), "Dynamic analysis of wind turbine towers on flexible foundations", Shock Vib., 19(1), 37-56. https://doi.org/10.3233/SAV-2012-0615.
  5. Anup, K., Whale, J., Evans S.P. and Clausen, P.D. (2020), "An investigation of the impact of wind speed and turbulence on small wind turbine operation and fatigue loads", Renew. Energy, 146, 87-98. https://doi.org/10.1016/j.renene.2019.06.124.
  6. Atangana, A. and Araz, S.I. (2020), "New numerical method for ordinary differential equations: Newton polynomial", J. Comput. Appl. Mathem., 372, 112-122. https://doi.org/10.1016/j.cam.2019.112622.
  7. Bekiryazici, Z., Merdan, M. and Kesemen, K. (2020), "Modification of the random differential transformation method and its applications to compartmental models", Communications Statistics-Theory Methods, 1-22. https://doi.org/10.1080/03610926.2020.1713372
  8. Bermudez, A., Gomez, D., Pineiro, M. and Salgado, P. (2020), "A novel numerical method for accelerating the computation of the steady-state in induction machines", Comput. Mathem. Appl., 79(2), 274-292. https://doi.org/10.1016/j.camwa.2019.06.032.
  9. Bervillier, C. (2012), "Status of the differential transformation method", Appl. Mathem. Comput., 218(20), 10158-10170. https://doi.org/10.1016/j.amc.2012.03.094.
  10. Dado, M. and Al-Sadder, S. (2005), "A new technique for large deflection analysis of non-prismatic cantilever beams", Mech. Res. Commun., 32(6), 692-703. https://doi.org/10.1016/j.mechrescom.2005.01.004.
  11. Dong, L., Sun L.X. and Qin, M. (2012), "Applying transfer matrix method in mode analysis of wind turbine", Advan. Mater. Res., 512, 686-689. https://doi.org/10.4028/www.scientific.net/AMR.512-515.686
  12. Feyzollahzadeh, M. and Mahmoodi, M. (2016), "Dynamic analysis of offshore wind turbine towers with fixed monopile platform using the transfer matrix method", J. Solid Mech., 8(1), 130-151.
  13. Feyzollahzadeh, M., Mahmoodi, M. Yadavar-Nikravesh, S.M. and Jamali, J. (2016), "Wind load response of offshore wind turbine towers with fixed monopile platform", J. Wind Eng. Ind. Aerod., 158, 122-138. https://doi.org/10.1016/j.jweia.2016.09.007.
  14. Fryklund, F., Kropinski, M.C.A. and Tornberg, A.K. (2020), "An integral equation-based numerical method for the forced heat equation on complex domains", Advan. Comput. Mathem., 46(5), 1-36. https://doi.org/10.1007/s10444-020-09804-z.
  15. Ghaderi, M., Ghaffarzadeh, H. and Maleki, V.A. (2015), "Investigation of vibration and stability of cracked columns under axial load", Earthq. Struct., 9(6), 1181-1192. http://dx.doi.org/10.12989/eas.2015.9.6.1181.
  16. Gireesha, B. and Sowmya, G. (2020), "Heat transfer analysis of an inclined porous fin using differential transform method", Int. J. Ambient Energy, 89, 1-7. https://doi.org/10.1080/01430750.2020.1818619.
  17. Hamada, Y.M. (2020), "Solution of a new model of fractional telegraph point reactor kinetics using differential transformation method", Appl. Mathem. Modelling, 78, 297-321. https://doi.org/10.1016/j.apm.2019.10.001.
  18. Jahanghiry, R., Yahyazadeh, R., Sharafkhani, N. and Maleki, V.A. (2016), "Stability analysis of FGM microgripper subjected to nonlinear electrostatic and temperature variation loadings", Sci. Eng. Compos. Mater., 23(2), 199-207. https://doi.org/10.1515/secm-2014-0079.
  19. Liu, H., Li, Y., Duan, Z. and Chen, C. (2020), "A review on multi-objective optimization framework in wind energy forecasting techniques and applications", Energy Convers. Management, 224, 11-24. https://doi.org/10.1016/j.enconman.2020.113324.
  20. Makarios, T.K. and Baniotopoulos, C.C. (2014), "Wind energy structures: modal analysis by the continuous model approach", J. Vib. Control, 20(3), 395-405. https://doi.org/10.1177/1077546312463761.
  21. Makarios, T.K. and Baniotopoulos, C.C. (2015), "Modal analysis of wind turbine tower via its continuous model with partially fixed foundation", Int. J. Innov. Res. Advan. Eng., 2(1), 14-25.
  22. Makarios, T.K., Efthymiou, E. and Baniotopoulos, C.C. (2016), "On the torsional-translational response of wind turbine structures", Arab. J. Sci. Eng., 41(4), 1241-1249. https://doi.org/10.1007/s13369-015-1911-7.
  23. Maleki, V.A. and Mohammadi, N. (2017), "Buckling analysis of cracked functionally graded material column with piezoelectric patches", Smart Mater. Struct., 26(3), 035-041. https://doi.org/10.1088/1361-665X/aa5324.
  24. Malz, E.C., Hedenus, F., Goransson, L., Verendel, V. and Gros, S. (2020), "Drag-mode airborne wind energy vs. wind turbines: An analysis of power production, variability and geography", Energy, 193, 116-125. https://doi.org/10.1016/j.energy.2019.116765
  25. Manenti, S. and Petrini, F. (2010), "Dynamic analysis of an offshore wind turbine: wind-waves nonlinear interaction", Earth Space 2010: Eng Sci., Construct. Operat. Challenging Environm., 2014-2026.
  26. Mawphlang, B.R.K.L.L., Ghimire, M.P., Rai, D.P. and Patra, P. K. (2020), "Buckling behavior of nonuniform carbon nanotubes using nonlocal elasticity theory and the differential transformation method", Int. Nano Lett., 43, 56-79. https://doi.org/10.1007/s40089-020-00319-5.
  27. Meng, C., Su, M. and Wang, S. (2013), "An investigation on dynamic characteristics of a gas turbine rotor using an improved transfer matrix method", J. Eng. Gas Turbines Power, 135(12), 78-90. https://doi.org/10.1115/1.4025234.
  28. Mutyalarao, M., Bharathi, D. and Rao, B.N. (2010), "Large deflections of a cantilever beam under an inclined end load," Appl. Mathem. Comput., 217(7), 3607-3613. https://doi.org/10.1016/j.amc.2010.09.021.
  29. Rajasekaran, S. (2009), Structural Dynamics of Earthquake Engneering Theory and Applcation Using Mathematica and Matlab'India, Woodhead Publshing
  30. Rezaei, E., Tabesh, A. and Ebrahimi, M. (2012), "Dynamic model and control of DFIG wind energy systems based on power transfer matrix", IEEE Transactions Power Delivery, 27(3), 1485-1493. https://doi.org/10.1109/TPWRD.2012.2195685.
  31. Rui, X., Wang, G. and Zhang, J. (2018), Transfer Matrix Method for Multibody Systems: Theory and Applications, John Wiley & Sons.
  32. Schaffarczyk, A. (2020), Types of wind turbines. Introduction to Wind Turbine Aerodynamics, Springer: 7-25.
  33. Sobamowo, M.G., Yinusa, A.A., Adeleye, O.A., Alozie, S.I., Salawu, S.A. and Salami, M.O. (2020), "On the efficiency of differential transformation method to the solutions of large amplitude nonlinear oscillation systems", World Scientific News, 139(1), 1-60.
  34. Wang, L. and Ishihara, T. (2020), "A study of the effects of foundation uplift on the seismic loading of wind turbine tower and shallow foundation using a new dynamic Winkler model", Eng. Struct., 219, 110-125. https://doi.org/10.1016/j.engstruct.2020.110745.
  35. Wang, S., Huang, Y., Li, L., Liu, C. and Zhang, D. (2017), "Dynamic analysis of wind turbines including nacelle-tower-foundation interaction for condition of incomplete structural parameters", Advan. Mech. Eng., 9(3), 43-57. https://doi.org/10.1177/1687814017692940.
  36. Yusof, A. and Mohamed, M. (2020), Vertical Axis Wind Turbines: An Overview, InECCE2019, Springer, 821-835.
  37. Zhou, J. (1986), Differential transformation and its applications for electrical circuits, Huazhong University Press, Wuhan, China.