The troposkien geometry has been invoked in structural modeling of blades belonging to class of vertical axis wind turbines called Darrieus rotors. Although it is free of bending stresses in the equilibrium position determined by a constant angular velocity, tests have indicated that under certain conditions serious vibrations about the original shape may occur.

A new approach is proposed to study the general problem of free vibration of one-dimensional structures and in particular one of a blade initially curved in the troposkien shape. The present scheme links for the first time two already existing ideas:​ the transfer matrices which were first developed in the 50’s and the relatively recent idea of integrating matrices.

Modal superposition is employed to study the flutter problem when the blade is aerodynamically loaded according to two hypothetical experiments. In the first, a vacuum chamber containing the rotating troposkien blade is brought up to the sea level air density. The second experiment consists of placing the rotating blade in the wind tunnel, increasing the velocity of the wind from zero to characteristic values in the operating range of the turbine. Two different analytical treatments are employed in each one of the aforementioned experiments. The root-locus method of tracing complex roots o? the flutter determinant in the frequency-domain is used in the first experiment, whereas the Floquet-Liapunov stability theory is applied to the second.

The stability of the blade as a function of different support conditons, elastic axis location, turbine speed and structural damping is studied in detail.