| New energy is the important foundation of promoting the sustainable development of global economy and ecology.Wind energy,as a new energy with the best development and utilization prospect,is favored by people.Wind turbine is the equipment that converts wind energy into electric energy.Its main structure includes tower,blade,nacelle and hub,with the large-scale development trend of wind turbine,the vibration problem of tower and blade becomes increasingly prominent.The basic form of wind turbine tower vibration is bending and torsional vibration.The separation of mass center from its centroid in cross section will lead to coupled bending and torsional vibration of the wind turbine tower.The basic forms of wind turbine blade vibration are edgewise,flapwise,torsional and longitudinal vibration.Under certain conditions,the edgewise,flapwise,torsional and longitudinal vibration of the blade also appear coupling.Vibration will cause fatigue damage to the wind turbine,thus affecting the life of the wind turbine,serious vibration will lead to the collapse of the wind turbine,resulting in huge economic losses and even casualties.Therefore,the research on the vibration characteristics of bending-torsion coupling tower and edgewise-flapwise-torsional-longitudinal coupling blade has theoretical value and practical engineering significance.The main research work of this paper is as follows:(1)The coupled bending-torsional free vibration characteristics of the inhomogeneous tower with variable-section are studied.The dynamic model of the inhomogeneous tower with variable-section on the elastic foundation is proposed.Based on the Euler-Bernoulli beam theory and D’Alembert principle,the three variable coefficient differential equations of motion are derived for the inhomogeneous tower with variable-section.Considering the installation and operation factors of the wind turbine,the dimensionless natural frequencies and mode shapes of the tower under multiple constraint conditions are obtained by the extended differential quadrature method.The effect of foundation stiffness,wall thickness,eccentricity etc.on the dimensionless natural frequencies and mode shapes of tower are analyzed.The frequency veering problem for the coupled bending and torsional vibration of tower is discussed.(2)The coupled bending-torsional bucklling characteristics of the inhomogeneous tower with variable-section are studied.The mechanical model of the inhomogeneous tower with variable-section subjected to eccentric compression on elastic foundation is established.Based on the principle of minimum potential energy and the Euler-Bernoulli beam(column)theory,the three variable coefficient differential equations of coupled bending and torsional buckling of the tower are derived.The elastic and rigid constraints are taken into account in the boundary conditions of the tower bottom.The installation process of the wind turbine is taken into account in the boundary conditions of the tower top.The dimensionless critical load of coupled bending-torsional buckling of the inhomogeneous tower with variable cross-section under multiple boundary conditions is obtained.The effects of warping stiffness,wall thickness,foundation stiffness,cross-section size and eccentricity on the dimensionless critical loads of the coupled bending-torsional buckling of the tower are analyzed.(3)The coupled edgewise-flapwise-torsional-longitudinal free vibration characteristics of the rotating balde are studied.Taking into account the effect of installation angle and cone angle of the actual connection mode between the blade and hub,a dynamic model of rotating blade with installation angle and cone angle is proposed.Based on Timoshenko beam theory,the expressions for the strain and velocity components at any point on the rotating blade cross section are given,and the nonlinear expressions for the strain energy and kinetic energy of the rotating blade are derived under modetately large deformation conditions.Six variable coefficient differential equations of the coupled edgewise-flapwise-torsional-longitudinal vibration for the rotating blade are derived by using the Hamilton’s principle.The dimensionless natural frequencies and mode shapes of the six kinds of coupled vibration of the rotating blade are solved.The effect of parameters such as eccentricity,rotational speed,cross-section variation coefficient,Coriolis force on the coupled vibration mode of the rotating blade is analyzed.The subject of blade instability caused by overspeed of the wind rotor is analyzed.The effect of eccentricity,section variation coefficient,installation angle and cone angle on the critical rotational speed of blade instability is analyzed.(4)The coupled edgewise-torsional and flap wise-torsional free vibration characteristics of the pre-curved balde with inhomogeneous and variable-section are studied.Based on the Timoshenko beam theory and D’Alembert’s principle,the three variable coefficient differential equations of the coupled edgewise-torsional vibration of a variable-curvature blade with inhomogeneous and variable-section are derived.The effects of elastic restraint stiffness,cross section geometry and other factors on the dimensionless natural frequency and mode shape of coupled flapewise-torsional vibration of blade are analyzed.Considering the effect of shear deformation and moment of inertia,the variable coefficient differential equations of coupled edgewise-torsional vibration of a constant-curvature inhomogeneous blade with variable section are derived.The effects of warping stiffness,elastic restraint stiffness,and cross-section variation coefficient on the dimensionless natural frequency and mode shape of coupled flap wise-torsional vibration of the blade are studied.The frequency steering phenomenon of the blade caused by the cross-section variation coefficient is discussed. |
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