Dynamic Response Analysis Of Large Floating Offshore Wind Turbine Blades Considering Nonlinear Geometric Stiffness

As a kind of renewable and clean energy,wind energy has attracted widespread attention at home and abroad.With the technological advance and increasing demand for electricity,the wind turbine has been developed with a larger capacity and longer blades.The length of a single wind turbine blade even reaches more than 100 meters.To solve the problem of weight increase caused by the longer blade,many new composite materials are used in the production and manufacturing of wind turbine blades.Large wind turbine blades are slender structures with flexibility.The use of composite materials will cause coupling between the deformation of blade sections in different directions,such as extension-twist coupling,bend-twist coupling,etc.,which makes the nonlinear characteristics of the blade’s dynamic response more significant.Besides,the offshore floating wind turbine is permanently moored in the working sea area,and the environmental conditions encountered by floating wind turbines are always severe.Under the action of wind,wave and current,the dynamic responses of blades are very complex.Considering the interaction between the structure of blades and the marine environment,the analysis and evaluation of blade internal loads,especially the loads at blade root,is very important to the safe production and operation of the wind turbine.At present,only the linear stiffness is considered for the numerical model of floating wind turbine blades.The influence of nonlinear geometric stiffness caused by large deformation on the blade vibration is ignored.It is impossible to accurately predict the nonlinear dynamic response of large floating wind turbine blades based on these models.There is a lack of systematic and in-depth research on the analysis of vibration response for large floating wind turbine blades considering the effect of nonlinear geometric stiffness.Based on the interaction between the structure of floating offshore wind turbine blades and the marine environment,the nonlinear dynamic response characteristics of floating offshore wind turbine blades are deeply analyzed,where the coupling terms of blade sections’ linear stiffness and the nonlinear geometric stiffness were both considered.This project is one of the important sections of the National Natural Science Fundation of China,‘Study on the dynamics characteristics for wind power system of floating foundation based on coupled multi-body’.The main research content and key conclusions are as follows:1.Research on analysis method and structural modeling of wind turbine blades.The analysis methods and numerical models of wind turbine blade structures were fully investigated at home and abroad.And the differences between calculation methods and structural models were compared and analyzed.There are two widely used wind turbine blade structure models.The one is the Euler-Bernoulli beam model based on the linear modal superposition method that only considers bending deformation.The other one is the geometrically exact beam model considering the extension-twist coupling nonlinear geometric stiffness,but the nonlinear stiffness is calculated according to the empirical formula.In this study,considering the influence of higher-order strain terms,the constitutive equation of the one-dimensional beam model was derived using the variational asymptotic method.The one-dimensional beam model considering fully coupled nonlinear geometric stiffness was established.A calculation program called BDRQX(Beam Dynamic Response QX)was developed based on this model.The accuracy of the program was verified by simulating the tensile test of composite laminates.2.Analysis of stiffness coupling characteristics and comparative study of static deformation for wind turbine blades.The blades of the DTU 10 MW reference wind turbine were studied.The variational asymptotic method was used to calculate the twodimensional cross-section linear stiffness and nonlinear geometric stiffness of the blades.The coupling characteristics of blade section stiffness were analyzed.Based on the calculation program BDRQX,the natural characteristics and static deformation of wind turbine blades were calculated.The results obtained by BDRQX,the EulerBernoulli beam model and the structural model considering the extension-twist coupling nonlinear geometric stiffness were compared with the results of threedimensional finite element models.The research shows that with the increase of blade deformation,the effect of nonlinear geometric stiffness becomes more and more significant.The one-dimensional beam model established in this paper considering the fully coupled nonlinear geometric stiffness is the closest to the results of the threedimensional finite element model,which proves that the model in this paper is more reasonable and reliable.3.Analysis of the coupled dynamic response of floating wind turbine blades based on different structural models.The 10 MW floating wind turbine was studied in this work.The one-dimensional beam model considering the fully coupled nonlinear geometric stiffness established in this paper,the Euler-Bernoulli beam model and the structural model considering the extension-twist coupling nonlinear geometric stiffness were used to simulate wind turbine blades.A fully coupled nonlinear numerical analysis model was established for the floating wind turbine system.The nonlinear dynamic responses of blades under the action of marine environment were calculated.The influence of nonlinear geometric stiffness on blade dynamic response was studied.The results show that the Euler-Bernoulli beam model based on linear modal method can not consider the coupling between different deformations,and ignores the influence of torsional deformation.The calculation results of the Euler-Bernoulli beam model are quite different from the results of the structural model developed in this study.The calculation accuracy of the Euler-Bernoulli beam model is lower.The results of the model developed in this study is compared with the structure model considering the extension-twist coupling nonlinear geometric stiffness.It is shown that the fully coupled nonlinear geometric stiffness has little effect on the blade root flapwise and edgewise moment,but mainly affects the blade root torsional moment.The deformations at blade tip are large,thus the influence of fully coupled nonlinear geometric stiffness on the tip section edgewise and torsional moment is very significant.4.Analysis of the short-term extreme value of floating wind turbine blades based on different structural models.Based on the mean up-crossing rate of the blade root bending moment time history under different load levels,an efficient and accurate extrapolation method was used to calculate the short-term extreme values of the blade root bending moments.A program was also compiled to calculate the extreme value of the blade root bending moments.Compared with the results of the model developed in this paper,the short-term extreme values of blade root flapwise bending moment are larger under different working conditions,while the short-term extreme values of blade root edgewise bending and torsional moment are relatively small calculated by the Euler-Bernoulli beam model based on the linear modal method.The short-term extreme value of the blade root torsional moment calculated by the structure model considering the extension-twist coupling nonlinear geometric stiffness is 6.9% smaller than the model developed in this paper near the rated wind speed.In order to improve the accuracy of predicting the extreme load of wind turbine blades and ensuring the safe operation of wind turbines,it is necessary to consider the effect of fully coupled nonlinear geometric stiffness.5.Analysis of dynamic responses for floating wind turbine blades under the condition of the freak wave.The traditional random phase modulation method was improved to generate freak wave elevation,and the efficiency of this method was verified.Using the blade structural model established in this study which considers the fully coupled nonlinear geometric stiffness,the transient responses of a 10 MW wind turbine and its blades under the action of freak waves were calculated for rated operating and extreme parked load conditions.The results were analyzed to study the nonlinear dynamic response characteristics of blades under the action of freak waves.The results show that the shock load effect of the freak wave has a significant impact on the transient response of the wind turbine floating foundation and the blade root flapwise moment under operating conditions.The research results of this work are of great significance for promoting the development and utilization of offshore wind energy in China and ensuring the sustainable development of the economy.This research has important theoretical meaning and engineering value for the design,production and maintenance of largescale floating wind turbine blades.