Articles | Volume 4, issue 1
Wind Energ. Sci., 4, 57–69, 2019
Wind Energ. Sci., 4, 57–69, 2019

Research article 28 Jan 2019

Research article | 28 Jan 2019

Determination of natural frequencies and mode shapes of a wind turbine rotor blade using Timoshenko beam elements

Evgueni Stanoev and Sudhanva Kusuma Chandrashekhara

Related subject area

Material science and structural mechanics
A fracture mechanics framework for optimising design and inspection of offshore wind turbine support structures against fatigue failure
Peyman Amirafshari, Feargal Brennan, and Athanasios Kolios
Wind Energ. Sci., 6, 677–699,,, 2021
Short summary
Constructing fast and representative analytical models of wind turbine main bearings
James Stirling, Edward Hart, and Abbas Kazemi Amiri
Wind Energ. Sci., 6, 15–31,,, 2021
Short summary
Development of a numerical model of a novel leading edge protection component for wind turbine blades
William Finnegan, Priya Dasan Keeryadath, Rónán Ó Coistealbha, Tomas Flanagan, Michael Flanagan, and Jamie Goggins
Wind Energ. Sci., 5, 1567–1577,,, 2020
Short summary
Finite element simulations for investigating the strength characteristics of a 5 m composite wind turbine blade
Can Muyan and Demirkan Coker
Wind Energ. Sci., 5, 1339–1358,,, 2020
Short summary
Simplified support structure design for multi-rotor wind turbine systems
Sven Störtenbecker, Peter Dalhoff, Mukunda Tamang, and Rudolf Anselm
Wind Energ. Sci., 5, 1121–1128,,, 2020
Short summary

Cited articles

Andersen, L. and Nielsen, S. R.: Elastic Beams in Three Dimensions, Department of Civil Engineering, Aalborg University, Aalborg, 2008. 
Bazoune, A. and Khulief, Y.: Shape Functions of Three-Dimensional Timoshenko Beam Element, J. Sound Vib., 12, 473–480, 2003. 
Graf, W. and Vassilev, T.: Einführung in computerorientierte Methoden der Baustatik, Verlag Ernst&Sohn, Berlin, 2006. 
Jonkman, J., Butterfield, S., Musial, W., and Scott, G.: Definition of a 5-MW Reference Wind Turbine for Offshore System Development, Technical Report NREL/TP-500-38060, National Renewable Energy Laboratory, Colorado, 2009. 
Jureczko, M., Pawlak, M., and Mezyk, A.: Optimisation of wind turbine blades, J. Mater. Process. Tech., 463–471, 2005. 
Short summary
In the frame of a multi-body simulation of a wind turbine, the lowest rotor blade eigenmodes are used to describe their elastic deformations. In this paper, a finite Timoshenko beam element is proposed based on the transfer matrix method. The element stiffness and mass matrices are derived by numerical integration of the differential equations of motion. A numerical example with generic rotor blade data demonstrates the performance of the method in comparison with FAST/ADAMS software results.