Dynamic Analysis of Offshore Wind Turbine Towers with Fixed Monopile Platform Using the Transfer Matrix Method

Document Type: Research Paper


Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, Iran


In this paper, an analytical method for vibrations analysis of offshore wind turbine towers with fixed monopile platform is presented. For this purpose, various and the most general models including CS, DS and AF models are used for modeling of wind turbine foundation and axial force is modeled as a variable force as well. The required equations for determination of wind turbine tower response excited by the Morrison force are derived based on Airy wave theory. The transfer matrix is derived for each element of the tower using Euler-Bernoulli’s beam differential equation and the global transfer matrix is obtained considering boundary conditions of the tower and constructing the point matrix. The effective wave force is intended in several case studies and Persian Gulf Environmental conditions are examined for the installation of wind farms. Finally, the obtained results by the transfer matrix method are compared with the results of the finite elements method and experimental data which show good agreement in spite of low computational cost.      


[1] Herbert G.M., Iniyan S., Sreevalsan E., Rajapandian S., 2007, A review of wind energy technologies, Renewable and Sustainable Energy 11: 1117-1145.
[2] Manwell J.F., McGowan J.G., Rogers J.G., 2002, Wind Energy Explained (Theory, Design and Application), John Wiley & Sons.
[3] Data sheet offshore wind energy, 2010, European Wind Energy Association, Publishing Physics Web, www.ewea.com.
[4] Mostafaeipour A., 2010, Feasibility study of offshore wind turbine installation in Iran compared with the world, Renewable and Sustainable Energy 14: 1-22.
[5] Samani M., Zadegan H., Saibani M., 2011, Feasibility study of offshore wind turbine installation in the Persian Gulf, Proceedings of the 13th Marine Industries Conference .
[6] Kaljahi A., Lotfollahi M., 2013, Performance analysis of tension leg platform offshore wind turbine in The Caspian Sea, Proceedings of the First New Energy Conference.
[7] Kaljahi A., Lotfollahi M., 2013, Technical feasibility study of using offshore wind turbine in the Iran, Proceedings of the First New Energy Conference.
[8] Breton S.P., Moe G., 2009, Status, plans and technologies for offshore wind turbines in Europe and North America, Renewable Energy 34: 646-654.
[9] Van Bussel G.J.W., Zaaijer M.B., 2001, Reliability, availability and maintenance aspects of large scale offshore wind farms, Proceedings of the MAREC.
[10] Bhattacharya S., Lombardi D., Wood D.M., 2010, Similitude relationships for physical modeling of monopile-supported offshore wind turbines, International Journal of Physical Modeling in Geotechnics 11: 58-68.
[11] Kim K.T., Lee C.W., 2011, Structural vibration analysis of large-scale wind turbines considering periodically time-varying parameters, Proceedings of the 13th World Congress in Mechanism and Machine Science.
[12] Chaoyang F., Nan W., Bol Z., Changzheng C., Dynamic performance investigation for large-scale wind turbine tower, Proceedings of the IEEE.
[13] Bazeos N., Hatzigeorgiou G. D., HondrosI D., Karamaneas H., Karabalis D. L., Beskos D. E., 2002, Static, seismic and stability analyses of a prototype wind turbine steel tower, Engineering Structures 24: 1015-1025.
[14] Salehi S., Pirooz M., Daghigh M., 2009, Aerodynamic and structural analysis of offshore wind turbine tower in The Persian Gulf, Proceedings of the Marine industries conference.
[15] Lavassas G., Nikolaidis G., Zervas P., Efthimiou E., Doudoumis I.N., Baniotopoulos C.C., 2003, Analysis and design of the prototype of a steel 1-MW wind turbine tower, Engineering Structures 25: 1097-1106.
[16] He Z., Jianyuan X., Xiaoyu W., 2009, The dynamic characteristics numerical simulation of the wind turbine generators tower based on the turbulence model, Proceedings of the International Conference on Industrial Electronics and Applications.
[17] Bush E., Manuel L., 2009, Foundation models for offshore wind turbines, Proceedings of the Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition.
[18] Passon P., Kühn1M., Butterfield S., Jonkman J., Camp T., Larsen T.J., 2007, OC3 benchmark exercise of aero-elastic offshore wind turbine codes, Journal of Physics, Conference Series 75: 1-12.
[19] Chen J., Jiang D., 2010, Modal analysis of wind turbine tower, Proceedings of the IEEE.
[20] Murtagh P.J., Basu B., Broderick B.M., 2004, Simple models for natural frequencies and mode shapes of towers supporting utilities, Computers and Structures 84: 1745-1750.
[21] Maalawi Y., 2007, A Model for yawing dynamic optimization of a wind turbine structure, International Journal of Mechanical Sciences 49: 1130-1138.
[22] Wang J., Qin D., Lim T., 2010, Dynamic analysis of horizontal axis wind turbine by thin-walled beam theory, Journal of Sound and Vibration 325: 3565-3586.
[23] Kort D.A., 2003, The transfer matrix method applied to steel sheet pile walls, International Journal for Numerical and Analytical Methods in Geomechanics 27: 453-472.
[24] Dawson B., Davies M., 1974, An improved transfer matrix procedure, International Journal for Numerical Methods in Engineering 8: 111-117.
[25] Tso W.K., Chan P.C.K., 1973, Static analysis of stepped coupled walls by transfer matrix method, Building science 8: 167-177.
[26] Holzer H., 1921, Die Berechnung der Drehschwingungen, Springer.
[27] Myklestad N.O., 1944, New method of calculating natural modes of uncoupled bending vibrations of airplane wings and other types of beams, Aeronaut Science 6: 153-166.
[28] Pestel C., Leckie A., 1963, Matrix Methods in Elastomechanics, McGraw Hill, New York.
[29] Dai H.L., Wang L., Qian Q., Gan J., 2012, Vibration analysis of three-dimensional pipes conveying fluid with consideration of steady combined force by transfer matrix method, Applied Mathematics and Computation 219: 2453-2464.
[30] Orasanu N., Craifaleanu A., 2011, Theoretical and experimental analysis of the vibrations of an elastic beam with four concentrated masses, Proceedings of the SISOM 2011 and Session of the Commission of Acoustics.
[31] Li Q.S., Fang J.Q., Jeary A.P., 2000, Free vibration analysis of cantilevered tall structures under various axial loads, Engineering Structures 22: 525-534.
[32] Rohani A., 2002, Vibration analysis of rotor, bearing and membrane system in a Gas turbine, Msc Thesis, Sharif University of Technology,Tehran.
[33] Uhrig R., 1966, The transfer matrix method seen as one method of structural analysis among others, Journal of Sound and Vibration 4: 136-148.
[34] Fallah A., 1999, Lateral vibration analysis of ship’s rotor, Msc Thesis, Sharif University of Technology, Tehran.
[35] Farshidianfar A., Hoseinzadeh M., Raghebi M., 2008, A novel way for crack detection in rotors using mode shape changes, Journal of Mechanic and Aerospace 8: 23-37.
[36] Bababake M., 2004, Vibration analysis of rotor-bearing system by transfer matrix method, Msc Thesis, Sharif University of Technology, Tehran.
[37] Meng W., Zhangqi W., Huaibi Z., 2009, Analysis of wind turbine steel tower by transfer matrix method, Proceedings of the International Conference on Electrical Engineering.
[38] Meng W., Zhangqi W., 2011, The vibration frequencies of wind turbine steel tower by transfer matrix method, Proceedings of the Third International Conference on Measuring Technology and Mechatronics Automation.
[39] Guidelines for Design of Wind Turbines, 2002, Second Edition, Printed by Jydsk Centraltrykkeri, Denmark.
[40] Andersen L.V., Vahdatirad M.J., Sichani M.T., Sorensen J.D.,2012, Natural frequencies of wind turbines on mono pile foundations in clayey soils-A probabilistic approach, Computers and Geotechnics 43: 1-11.
[41] Petersen B., Pollack M., Connell B., Greeley D., Daivis D., Slavik C., 2010, Evaluate the effect of turbine period of vibration requirements on structural design parameters, Applied Physical Sciences Corp 10-12.
[42] Schaumann P., Boker C., 2011, Support Structures of Wind Energy Converters, Springer, Wien New York.
[43] Sadeghi K., 2002, Coasts, Ports and Offshore Structures Engineering, Press of Water and Power University, First Edition.
[44] Taghipoor M., Qureshi Tayebi A., Lotfollahi yaghin A., 2005, Investigation of hydrodynamic forces on the roughness of the pile and compare it with candles, smooth and rough, Proceedings of the First Congress on Civil Engineering.
[45] Feyzollahzadeh M., Vibration analysis of offshore wind turbine on a monopile support structure, Msc Thesis, Shahid Beheshti University,Tehran.
[46] Bir G., Jonkman J., 2008, Modal dynamics of large wind turbines with different support structures, Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering.
[47] Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms Working Stress Design, 2000, API Recommended Practice, 2A-WSD.
[48] Jonkman J., Butterfield S., Passon P., Larsen T., Camp T., Nichols J., Azcona J., Martinez A., 2008, Offshore code comparison collaboration within IEA wind annex XXIII: phase II results regarding monopile foundation modeling, NREL/CP-500-42471, National Renewable Energy Laboratory.
[49] Han M., Benaroya H., Wei T., 1999, Dynamics of transversely vibrating beams using four engineering theories, Journal of Sound and vibration 5: 935-988.
[50] Wu J., Chen C., 2007, Forced vibration analysis of an offshore tower carrying an eccentric tip mass with rotary Inertia due to support excitation, Ocean Engineering 34: 1235-1244.
[51] Zhang Y., , Liu Y., , Chen P., Murphy K.D., 2011, Buckling loads and eigen frequencies of a branced beam resting on elastic foundation, Acta Mechanica Solida Sinica 24: 510-518.
[52] Parvanova S., 2011, Beams on Elastic Foundation, University of Architecture, Civil Engineering and Geodesy Sofia, 111-125.
[53] Feyzollahzadeh M., Yadavar Nikravesh M., Rahi A., 2013, Dynamic analysis of offshore wind turbine tower using the transfer matrix method, Proceedings of the 9th International Energy Conference.
[54] Jonkman J., Musial W., 2010, Offshore code comparison collaboration (OC3), Final Technical Report, NREL/TP-5000-48191, National Renewable Energy Laboratory.
[55] Passon P., 2006, Memorandum: Derivation and Description of the Soil-Pile-Interaction Models, IOP Publishing Physics, IEA-Annex XXIIII Subtask 2, Stuttgart, Germany.
[56] Devriendt C., Jordaens P., Ingelgem Y. V., Sitter G. D., Guillaume P., 2012, Monitoring of Resonant Frequencies and Damping Values of an Offshore Wind Turbine on a Monopile Foundation, Offshore Wind Infrastructure, IOP Publishing Physics.
[57] General Specification V90 – 3.0 MW Variable Speed Turbine, 2004, Item no. 950010.R1, IOP Publishing Physics.