Structural dynamic analysis of a troposkien shape vertical axis wind turbine using mixed finite element formulation

Abstract

Structural dynamic characteristics of a troposkien-shape Vertical Axis Wind Turbine (VAWT) blade are investigated. The structural equations, which represent the behavior of a three dimensionally linear curved beam, are expressed in a state vector form. This state vector form consists of 12-first order linear ordinary differential equations, based on generalized force and generalized displacement variables. The structural equilibrium equations are then coupled with the dynamic equations, arising from the rotation of the blade, to form a complete set of structural dynamic equations. The aforementioned system of structural dynamic equations is treated numerically in the framework of the Finite Element Method (FEM). Due to the nature of the state vector form, a mixed formulation is established in such a manner that preserves the symmetry of the mass and stiffness matrices. The underlying physics of the problem is discussed in terms of natural frequencies and mode shapes. It is shown how the troposkien geometry prevents the system from the dynamic instability arising from the rotation of the blade. It is also demonstrated how the center of mass offset and Coriolis forces result in coupling between the different degrees of freedom of the system