Parametric study of flapwise and edgewise vibration of horizontal axis wind turbine blades

In this paper, flapwise and edgewise vibrations of a horizontal axis wind turbine (HAWT) blade are studied. Rayleigh-Ritz method is used in which; orthogonal mode functions of the Euler-Bernoulli beam having fixed-free boundary are introduced into the Lagrange function and then the dynamic equations are derived. Effect of gravity, pitch angle, centrifugal stiffening, and rotary inertia are considered. Nondimensional equations are obtained by defining nondimensional parameters like; natural frequency, blade rotation, slenderness ratio, and simple pendulum frequency. The stiffness term of the natural frequency has two speed dependent elements and it is shown that, for small pitch angles, flapwise natural frequencies of the blade are increased by the increasing blade speed while the edgewise natural frequencies of the blade are decreased with the increasing blade speed. Pitch angle values ranging from 0° to 15° has negligible effect on the nondimensional natural frequencies of the blade up to the nondimensional blade speed of 4. Since the natural frequencies are the function of the blade speed, rotor critical speeds should be calculated with Campbell diagrams. Vibrational response of the blade tip to the gravity is dominant and much greater than that of the wind speed in the edgewise and flapwise vibration.