Dynamic coupling modeling and analysis of rotating beams based on the nonlinear Green-Lagrangian strain are introduced in this work.With the reservation of the axial nonlinear strain,there are more coupling terms for ...Dynamic coupling modeling and analysis of rotating beams based on the nonlinear Green-Lagrangian strain are introduced in this work.With the reservation of the axial nonlinear strain,there are more coupling terms for axial and transverse deformations.The discretized dynamic governing equations are obtained by using the finite element method and Lagrange’s equations of the second kind.Time responses are conducted to compare the proposed model with other previous models.The stretching deformation due to rotating motion is observed and calculated by special formulations under dynamic equilibrium.The stretching deformation and the change of the associated equilibrium position are taken into account to analyze the free vibration and frequency response of the rotating beams.Analytical and numerical comparisons show that the proposed model can provide reliable results,while the previous models may lead to imprecise results,especially in high-speed conditions.展开更多
The topic of offshore wind energy is attracting more and more attention as the energy crisis heightens.The blades are the key components of offshore wind turbines,and their dynamic characteristics directly determine t...The topic of offshore wind energy is attracting more and more attention as the energy crisis heightens.The blades are the key components of offshore wind turbines,and their dynamic characteristics directly determine the effectiveness of offshore wind turbines.With different rotating speeds and blade length,the rotating blades generate various centrifugal stiffening effects.To directly analyze the centrifugal stiffening effect of blades,the Rayleigh energy method (REM) was used to derive the natural frequency equation of the blade,including the centrifugal stiffening effect and the axial force calculation formula.The axial force planes and the first to third order natural frequency planes which vary with the rotating speed and length were calculated in three-dimensional coordinates.The centrifugal stiffening coefficient was introduced to quantitatively study the relationship between the centrifugal stiffening degree and the rotating speed,and then the fundamental frequency correction formula was built based on the rotating speed and the blade length.The analysis results show that the calculation results of the fundamental frequency correction formula agree with the theoretical calculation results.The error of calculation results between them is less than 0.5%.展开更多
基金the National Natural Science Foundation of China(Nos.12232012,12202110,12102191,and 12072159)the Fundamental Research Funds for the Central Universities of China(No.30922010314)the Natural Science Foundation of Guangxi Province of China(No.2020GXNSFBA297010)。
文摘Dynamic coupling modeling and analysis of rotating beams based on the nonlinear Green-Lagrangian strain are introduced in this work.With the reservation of the axial nonlinear strain,there are more coupling terms for axial and transverse deformations.The discretized dynamic governing equations are obtained by using the finite element method and Lagrange’s equations of the second kind.Time responses are conducted to compare the proposed model with other previous models.The stretching deformation due to rotating motion is observed and calculated by special formulations under dynamic equilibrium.The stretching deformation and the change of the associated equilibrium position are taken into account to analyze the free vibration and frequency response of the rotating beams.Analytical and numerical comparisons show that the proposed model can provide reliable results,while the previous models may lead to imprecise results,especially in high-speed conditions.
基金Supported by the National Natural Science Foundation of China under Grant No.50708015the foundation of State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology
文摘The topic of offshore wind energy is attracting more and more attention as the energy crisis heightens.The blades are the key components of offshore wind turbines,and their dynamic characteristics directly determine the effectiveness of offshore wind turbines.With different rotating speeds and blade length,the rotating blades generate various centrifugal stiffening effects.To directly analyze the centrifugal stiffening effect of blades,the Rayleigh energy method (REM) was used to derive the natural frequency equation of the blade,including the centrifugal stiffening effect and the axial force calculation formula.The axial force planes and the first to third order natural frequency planes which vary with the rotating speed and length were calculated in three-dimensional coordinates.The centrifugal stiffening coefficient was introduced to quantitatively study the relationship between the centrifugal stiffening degree and the rotating speed,and then the fundamental frequency correction formula was built based on the rotating speed and the blade length.The analysis results show that the calculation results of the fundamental frequency correction formula agree with the theoretical calculation results.The error of calculation results between them is less than 0.5%.
