Wind energy is one of the most promising and growing sources of renewable energy all over the world. As it is being realized across the globe that the utilization of the available wind energy resources is hugely less, there is an urgent need for more wind turbines and with improved technology to provide higher power outputs and efficiency. This requires improved modeling and analysis of the dynamic response of the wind turbine blades to further improve and optimize the structure. The structural analysis of wind turbine systems under wind loads forms the preliminary analysis of the design of a wind turbine. Moreover, the dynamics of rotating blades along with the hub have a decisive influence on the dynamics of the whole system, which in general is complex due to the coupling of bending and twisting deformations. The vibrations of such structures in service are often treacherous, and sometimes even fatal, which has attracted substantial attention in both academic and industrial communities.
Owing to the anti-symmetry of the aerofoil cross-section of wind turbine blades, the center of flexure and the centroid are noncoincident which results in a bending-torsion coupling. Moreover, due to a varying twist along the length of the blade, there also exists bending-bending coupling in the dynamic response of wind turbine blades. The Blade element momentum theory with various corrections, which is widely used for calculating the aerodynamic loads on the blades, calculates the loads at the center of each such element. Moreover, wind turbine blades are often modeled as discontinuous multi-step beams because of the variation in their structural and material properties. Thus, the complete study of the dynamics of wind turbine blades requires a coupled bending-bending-torsion analysis of discontinuous multi-step beams, which is the main objective of this work. The hierarchical functions applied locally using the Ritz method are chosen in the study. As a first step, Bardell’s polynomials and Beslin’s trigonometric functions are chosen as the hierarchical functions as they have been used in the literature for vibration problems. To apply them to the free vibration problem of a general multi-step beam, first the convergence studies of both these sets are performed. A modification in the trigonometric hierarchical set is also performed to improve the accuracy and convergence for both low and very high modes. These hierarchical sets are further applied to a multi-step beam with 13 steps, first studied by Jaworski and Dowell. The results of natural frequencies obtained when using different hierarchical sets are compared and the superiority of the modified trigonometric set is observed. In the next part of the study, the hierarchical sets are applied to the forced vibration problem with the aim to study the vibration of wind turbine blades showing complex bend-bend-twist coupling.