Mathematical model for predicting the blade behaviour of horizontal axis wind turbine

A mathematical model using both beam finite element and thin-walled structure theory is developed to predict the natural frequency and blade behaviour of a horizontal axis wind turbine under constant wind speed and turbulence condition. First of all, the deformation pattern of the blade is defined on the basis of thin-walled structure theory and Timoshenko beam theory, and by considering the blade as a rotation cantilever beam, the governing equation is obtained using the principle of virtual work. Then, it is discreted by a beam element. Constraints are applied to define boundary conditions and coupling of flapwise, edgewise, and elongation deformations on the governing equation using the penalty method. Finally, natural frequencies of the blade are analysed. Detailed expressions for centrifugal and Coriolis forces are obtained. The stress on the root and displacement at the tip are also analysed in detail. The blade's deflection in turbulent conditions is simulated and shown to mostly influence flapwise blade deformation.