Wind turbines are one of the fastest-growing energy sources. Based on their axis of rotation they fall into two basic categories: horizontal-axis wind turbines (HAWTs) and vertical-axis wind turbines (VAWTs). Darrieus VAWTs exploit aerodynamic lift. This study entails the vibration analysis of large vertical-axis Darrieus wind turbine blades. Very large wind turbines are becoming more abundant due to their ability to harvest greater wind power. VAWTs are less common than HAWTs for large wind applications, but have some favorable characteristics, for example in offshore applications, and so further development of large VAWTs is anticipated. However, VAWTs are known to have vibration issues. VAWT blade vibration is the focus of this work.The straight-bladed H-rotor/Giromill is the simplest type of VAWT. We first derive the equations of motion of a H-rotor blade modeled as a uniform straight elastic Euler-Bernoulli beam under transverse bending and twist deformation. The reduced-order model suggests the existence of periodic damping, periodic stiffness, and direct excitation generated by a cyclic aeroelastic load. The model also indicates spin softening, which could be detrimental as the turbines become large. Periodic damping and stiffness are examples of parametric excitation and are likely to carry over to other types of VAWT blades. Systems with parametric excitation have been studied with various methods. Floquet theory has been classically used to study the stability characteristics of linear systems with periodic coefficients, and has been commonly applied to Mathieu's equation, which represents a vibration system with periodic stiffness. We apply the Floquet theory combined with the harmonic-balance method to a linear vibration system with a periodic damping coefficient. Based on this theory, the approximated solution includes an exponential part, with an unknown exponent, and a periodic part. Our analysis investigates the initial conditions response, the boundaries of instability, and the characteristics of free response solution of the system. The coexistence phenomenon, in which some of the transition curves overlap so that the instability wedges disappear, is recovered in this approach, and is examined closely.An additional case of the parametric excitation is the combination of parametric damping and parametric stiffness. The Floquet-based analysis shows that the combined parametric excitation reshapes the stability characteristics, compared to the system with only parametric damping or stiffness and disrupts the coexistence which is observed in the parametric damping case.The aeroelastic forces encountered by the wind turbines can cause self-excitation in blades, the mechanism of which can be loosely modeled with van-der-Pol-type nonlinearity. We seek to understand the combined effect of parametric excitation and van der Pol nonlinearity, as both can induce instabilities and oscillations. The oscillator is studied under nonresonant conditions and secondary resonances, with and without external excitation. We analyze the system using the method of multiple scales and numerical solutions. For the case without external excitation, the analysis reveals nonresonant phase drift (quasi-periodic responses), and subharmonic resonance with possible phase drift or phase locking (periodic responses). Hard excitation is treated for nonresonant conditions and secondary resonances, and similar phenomena are uncovered.Some Darrieus VAWTs consist of curved blades. We lastly study the modal analysis of curved Darrieus wind-turbine blades and obtain the mode shapes and modal frequencies. The governing equations are derived using the fundamental deformation mechanics, and thin beam approximations are employed to express the strain and kinetic energies. The assumed-modes method is applied to the energies, and the Euler-Lagrange equation is used to discretize the equations of motion. Implementing these equations, mode shapes are calculated and mapped back onto the curved beam for visualization. This analysis is conducted for pinned-pinned and hinged-hinged blades. The results are compared with Finite element analysis using Abaqus and with the literature.
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