Nonlinear vibration analysis of horizontal axis wind turbine blades using a modified pseudo arc-length continuation method

•A new dynamic model is developed for vibration analysis of horizontal axis wind turbine blades.•A method based on pseudo arc-length continuation method is introduced for amplitude frequency response (AFR) analysis of multi-DOF systems.•Forced vibration analysis of the blade under operating loads is examined.•The effects of the various terms and loads on the linear and nonlinear AFR curves are investigated using presented method. The horizontal axis wind turbine (HAWT) blades are exposed to parametric and direct excitations of harmonic nature due to the gravity and aerodynamic loads. Hence, the study of the periodic response of the HAWT blades under these operating loads is of great importance in structural design. In this paper, a new computationally efficient dynamic model for the blade is presented including the pre-twist effects. The Rayleigh-Ritz technique is applied to the derived dynamic model and a reduced order model (ROM) is devised in a systematic manner. An efficient method based on the pseudo arc-length continuation method is introduced to find out the edge-wise and flap-wise amplitude-frequency response (AFR) curves of the blade under harmonic wind inflow. Furthermore, the forced vibration of the blade under different operating loads including gravity, centrifugal and aerodynamic loads (due to the uniform and shear wind inflows) is studied separately. Applying the proposed method, the effects of structural damping, nonlinear terms, pre-twist ratio, and cyclic excitation due to the gravity force as well as the centrifugal force on the AFR curves are investigated. Eventually, the dynamic model and the presented method for the frequency analysis are validated with the available data.