Vibration Analysis Based On Hamilton's Principlefor Vertical Axis Wind Turbines Blade With Cross-section Of NACA0015 Airfoil

In recent years,there is increasing interest in study of vertical axis wind turbines.Commercial potential is expected of vertical axis wind turbines(VAWT)especially in the case of low level and strong winds.In this thesis,the NACA0015 airfoil is chosen as cross-section of the blade of vertical axis wind turbines to study vibration characteristic of blades.Slender blades can be modelled as Euler beams.Hamilton's principle combined with Euler-Bernoulli beam theory is employed to derive the equations of bending-twisting coupled motion of the blade.Vibration modes are solved numerically by central finite difference approximation,and the natural frequencies of blades are obtained for fixed support and simply support,respectively.Compared to modal analysis with ANSYS Workbench,it is shown that the results by the two approaches are close to each other in low frequency modes,but have slightly larger differences in high frequency modes,which proves the accuracy of the method established in this paper.As a consequence,in order to avoid resonance effect with external forces such as wind field which can destroy blade structure,this paper covers,in both fixed support and simply support,the influence of the rotational velocity,blade length cross-section chord length and cross-section shape on the natural frequencies of solid blades,as well as,the differences in natural frequencies for the hollow and solid blades.The results show that firstly natural frequencies of blades decrease with the increase of blade length,secondly natural frequencies decrease with the increase of rotational velocity,thirdly the relationship between cross-section chord length and natural frequencies has approximately linear relationship,lastly there is widely different in natural frequencies for the hollow and solid blades.Meanwhile,this paper analyzes emphatically,in both fixed support and simply support,the influence of the rotational velocity,blade length cross-section chord length and cross-section shape on the natural frequencies of hollow blades.The results show that the influence of the rotational velocity and cross-section shape on the natural frequencies of hollow blades is basically the same with that of solid blades,and the influence of blade length and cross-section chord length on the natural frequencies of hollow blades and solid blades is different but has a similar tendency.The research method and numerical analysis results in this paper can provide certain reference basis for industry design for vertical axis wind turbine.