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. When simulating a wind turbine, the lowest eigenmodes of the rotor blades areusually used to describe their elastic deformation in the frame of amulti-body system. In this paper, a finite element beam model for the rotorblades is proposed which is based on the transfer matrix method. Both staticand kinetic field matrices for the 3-D Timoshenko beam element are derived bythe numerical integration of the differential equations of motion using aRunge–Kutta fourth-order procedure. In the general case, the beam referenceaxis is at an arbitrary location in the cross section. The inertia term inthe motion differential equation is expressed using appropriate shapefunctions for the Timoshenko beam. The kinetic field matrix is built bynumerical integration applied on the approximated inertia term. The beamelement stiffness and mass matrices are calculated by simple matrixoperations from both field matrices. The system stiffness and mass matricesof the rotor blade model are assembled in the usual finite element manner ina global coordinate system accounting for the structural twist angle andpossible pre-bending. The program developed for the above-mentionedcalculations and the final solution of the eigenvalue problem is accomplishedusing MuPAD, a symbolic math toolbox inMATLAB®. The natural frequencies calculatedusing generic rotor blade data are compared with the results proposed fromthe FAST and ADAMS software.

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