Unstable vibrations of a two-blade wind turbine tower are theoretically investigated. The theoretical model is a five-degree-of-freedom (5DOF) system, however, the equations of motion are derived separately for 3DOF subsystem (I) and 2DOF subsystem (II). Parametric excitation due to the asymmetry of the moments of inertia of the blade rotor is included only in subsystem (I). Frequency equations are derived and natural frequency diagrams are calculated to clearly demonstrate both the rotational speeds where unstable regions appear and which type of unstable vibrations may occur. It is found that at most, five unstable regions may appear depending on the values of the system parameters in subsystem (I). Two types of unstable vibrations may occur; single mode including a single frequency and dual mode including two frequencies. The influences of the asymmetry of moments of inertia, tower rigidity, and installation position of the blade rotor on the response of the system are also theoretically investigated. Van der Pol’s method is applied to determine the expressions for the response curves. The influences of the blade rotor unbalances on the translational, inclinational and torsional vibrations of the tower are shown. It is found that the amplitudes of the response curves corresponding to single and dual mode are infinite and finite at their boundaries, respectively. The validity of the theoretical analysis is confirmed by numerical simulations.

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