Modeling Nonlinear Free Vibrations of Wind Turbine Tower

The goal of this paper is to study the large amplitude free vibration of wind turbine tower which modeled as a variable cross-section beam with eccentric mass. The effects of variable axial force due to gravity is also taken into account. The nonlinear governing equations of motion and the corresponding boundary conditions of the system are obtained using the Hamilton's principle as well as Euler-Bernoulli’s assumptions. Then a numerical finite difference scheme is utilized to find the natural frequencies and the mode shapes of the system. Using Galerkin method, the partial differential equations governing dynamic of the system are reduced to ordinary differential equations in terms of the end displacements which are coupled due to the presence of the transverse eccentricity. These temporal coupled ODEs are then solved analytically using the multiple time scales perturbation technique. The obtained analytical results are compared with the numerical ones and excellent agreement is observed. The results of this research can be used to study the effect of the eccentric tip mass, variable cross-section and gravity on the large amplitude vibration of wind turbine tower for improved dynamic performance.