An energy-based ecological footprint model was set up to monitor the sustainable development status of a specific marine system. This model used unit energy value and energy density to convert the consumption into eco...An energy-based ecological footprint model was set up to monitor the sustainable development status of a specific marine system. This model used unit energy value and energy density to convert the consumption into ecological productive areas. It can reflect the utilization degree of resources in the regional development. Then, the quantitative analysis of sustainable development was done by comparing the size of the areas. We defined the concept of energy-based ecological footprint of marine and built energy-based ecological footprint model of marine. Then we applied this model to marine ecological system of Shandong province to evaluate its sustainable development statue. The results showed that the energy-based marine ecological footprint of the marine ecological system in Shandong province was 1.74 × 106 hm^2 in 2010, and the energy-based ecological carrying capacity of this area was 1.60×107 hm^2 per capita. Thus, the marine ecological system of Shandong province has strong sustainability.展开更多
The coupled dynamic characteristics of the conical electromagnetic bearing are presented and their definitions are given. On the basis of the analyses of the characteristics, the dynamic model of five degrees of freed...The coupled dynamic characteristics of the conical electromagnetic bearing are presented and their definitions are given. On the basis of the analyses of the characteristics, the dynamic model of five degrees of freedom (five-DOF) rotor-conical electromagnetic bearing system is made, and the influence of the coupled characteristics on the system optimal controller is analyzed.展开更多
Based on the slip-line field theory, a two-dimensional slip failure mechanism with mesh-like rigid block system was constructed to analyze the ultimate bearing capacity problems of rough foundation within the framewor...Based on the slip-line field theory, a two-dimensional slip failure mechanism with mesh-like rigid block system was constructed to analyze the ultimate bearing capacity problems of rough foundation within the framework of the upper bound limit analysis theorem. In the velocity discontinuities in transition area, the velocity changes in radial and tangent directions are allowed. The objective functions of the stability problems of geotechnical structures are obtained by equating the work rate of external force to internal dissipation along the velocity discontinuities, and then the objective functions are transformed as an upper-bound mathematic optimization model. The upper bound solutions for the objective functions are obtained by use of the nonlinear sequential quadratic programming and interior point method. From the numerical results and comparative analysis, it can be seen that the method presented in this work gives better calculation results than existing upper bound methods and can be used to establish the more accurate plastic collapse load for the ultimate bearing capacity of rough foundation.展开更多
Vibrations of a rotor-bearing system(RBS)can be affected by the frictional forces between the components of the inherent bearings.Thus,an in-depth investigation of the influences of the frictional moments of the beari...Vibrations of a rotor-bearing system(RBS)can be affected by the frictional forces between the components of the inherent bearings.Thus,an in-depth investigation of the influences of the frictional moments of the bearings on the vibrations of the RBS can be helpful for understanding the vibration mechanisms in the rotating machinery.In this study,an improved dynamic model of a RBS considering different frictional force models is presented.A comparative investigation on the influences of the empirical and analytical frictional force models on the vibration characteristics of the RBS is proposed.The empirical frictional force models include Palmgren’s and SKF’s models.The analytical frictional force model considers the rolling friction caused by the radial elastic material hysteresis,slipping friction between the ball and races,viscosity friction caused by the lubricating oil,and contact friction between the ball and cage.The influences of the external load and rotational speed on the vibrations of the RBS are analyzed.The comparative results show that the analytical frictional force model can give a more reasonable method for formulating the effects of the friction forces in the bearings on the vibrations of the RBS.The results also demonstrate that the friction forces in the bearings can significantly affect the vibrations of the RBSs.展开更多
Studying the carrying capacity of resources and environment of city clusters in the central China has important practical guidance significance for promoting the healthy, sustainable and stable development of this reg...Studying the carrying capacity of resources and environment of city clusters in the central China has important practical guidance significance for promoting the healthy, sustainable and stable development of this region. According to their influencing factors and reciprocity mechanism, using system dynamics approaches, this paper built a SD model for measuring the carrying capacity of resources and environment of the city clusters in the central China, and through setting different development models, the comprehensive measurement analysis on the carrying capacity was carried out. The results show that the model of promoting socio-economic development under the protection of resources and environment is the optimal model for promoting the harmony development of resources, environment, society and economy in the city clusters. According to this model, the optimum population scale of the city clusters in 2020 is 42.80×106 persons, and the moderate economic development scale is 22.055×1012 yuan (RMB). In 1996-2020, the carrying capacity of resources and environment in the city clusters took on obvious phase-change characteristics. During the studied period, it is basically at the initial development stage, and will come through the development process from slow development to speedup development.展开更多
Based on the relationship between water environment system and human society, water environment carrying capacity (WECC) probes into supporting ability of complex water environment system to the human society. Recen...Based on the relationship between water environment system and human society, water environment carrying capacity (WECC) probes into supporting ability of complex water environment system to the human society. Recent years, due to the shortage of water resources and serious water pollution in several watersheds in China, the research of watershed water environment carrying capacity (WWECC) becomes very important. The conception, connotation and method of representation of WWECC are discussed deeply in this paper. It shows that WWECC is a kind of index that instructs whether the water environment system in watershed can continue to support the development of social economy and ecology, it is dimensionless number.展开更多
Thrust bearing is a key component of the propulsion system of a ship. It transfers the propulsive forces from the propeller to the ship's hull, allowing the propeller to push the ship ahead. The performance of a thru...Thrust bearing is a key component of the propulsion system of a ship. It transfers the propulsive forces from the propeller to the ship's hull, allowing the propeller to push the ship ahead. The performance of a thrust bearing pad is critical. When the thrust bearing becomes damaged, it can cause the ship to lose power and can also affect its operational safety. For this paper, the distribution of the pressure field of a thrust pad was calculated with numerical method, applying Reynolds equation. Thrust bearing properties for loads were analyzed, given variations in outlet thickness of the pad and variations between the load and the slope of the pad. It was noticed that the distribution of pressure was uneven. As a result, increases of both the outlet thickness and the slope coefficient of the pad were able to improve load beating capability.展开更多
Classical beat phenomenon has been observed in most combined systems. The focus of this paper is to provide a better understanding of this phenomenon in an offshore pile-supported pipeline system. The beat phenomeon i...Classical beat phenomenon has been observed in most combined systems. The focus of this paper is to provide a better understanding of this phenomenon in an offshore pile-supported pipeline system. The beat phenomeon is caused by the coupling movement of the pipeline and its vertical pile support under certain conditions. It can induce excessive vibration and cause fatigue failure at pipe elbow. However, in some circumstances it does not exist. Numerical results in both frequency and time domains are presented to elucidate this phenomenon in a combined pipeline system. The conclusions of this paper could give constructive guidance to future design of simply supported pipeline systems.展开更多
Remote sensing data from the Terra Moderate-Resolution Imaging Spectroradiometer (MODIS) and geospatial data were used to estimate grass yield and livestock carrying capacity in the Tibetan Autonomous Prefecture of Go...Remote sensing data from the Terra Moderate-Resolution Imaging Spectroradiometer (MODIS) and geospatial data were used to estimate grass yield and livestock carrying capacity in the Tibetan Autonomous Prefecture of Golog, Qing-hai, China. The MODIS-derived normalized difference vegetation index (MODIS-NDVI) data were correlated with the aboveground green biomass (AGGB) data from the aboveground harvest method. Regional regression model between the MODIS-NDVI and the common logarithm (LOG10) of the AGGB was significant (r2 = 0.51, P < 0.001), it was, there-fore, used to calculate the maximum carrying capacity in sheep-unit year per hectare. The maximum livestock carrying capacity was then adjusted to the theoretical livestock carrying capacity by the reduction factors (slope, distance to water, and soil erosion). Results indicated that the grassland conditions became worse, with lower aboveground palatable grass yield, plant height, and cover compared with the results obtained in 1981. At the same time, although the actual livestock numbers decreased, they still exceeded the proper theoretical livestock carrying capacity, and overgrazing rates ranged from 27.27% in Darlag County to 293.99% in Baima County. Integrating remote sensing and geographical information system technologies, the spatial and temporal conditions of the alpine grassland, trend, and projected stocking rates could be forecasted for decision making.展开更多
Based on the short-bearing model, the stability of a rigid Jeffcott rotor system is studied in a relatively wide parameter range by using Poincaré maps and the numerical integration method. The results of the cal...Based on the short-bearing model, the stability of a rigid Jeffcott rotor system is studied in a relatively wide parameter range by using Poincaré maps and the numerical integration method. The results of the calculation show that the period doubling bifurcation, quasi-periodic and chaotic motions may occur. In some typical parameter regions, the bifurcation diagrams, phase portrait, Poincaré maps and the frequency spectrums of the system are acquired with the numerical integration method. They demonstrate some motion state of the system. The fractal dimension concept is used to determine whether the system is in a state of chaotic motion. The analysis result of this paper provides the theoretical basis for qualitatively controlling the stable operating states of the rotors.展开更多
Ecological city(eco-city) and its planning approach are emerging concepts in urban study,urban planning,ecological economics,environmental policy and corporate environmental management.However,opinions remain divided ...Ecological city(eco-city) and its planning approach are emerging concepts in urban study,urban planning,ecological economics,environmental policy and corporate environmental management.However,opinions remain divided over the connotation and denotation of the term"ecological city",what key issues ecocity planning can solve,and its specific contents.In this study,we present 10 basic propositions that define the eco-city and clarify its key parameters,thereby providing the basis for discussing the assumptions and principles underlying different approaches to sustainable urban development.We then summarize the concept and principles of an eco-city,and define the main requirements for ecocity planning.We conclude that an eco-city is a city in which the urban population,scale of land use and intensity of human activities are limited to the regional resource and environmental carrying capacity,which does not cause increasing or irreversible damage to the regional ecosystem's structure,functions and processes.展开更多
Being one of their prominent exploitative characteristics, cutting tools durability depends on the character, intensity and the speed of wearing. Identification of tool wearing is of great significance for the purpose...Being one of their prominent exploitative characteristics, cutting tools durability depends on the character, intensity and the speed of wearing. Identification of tool wearing is of great significance for the purpose of avoiding sooner or later replacement of tools. The parameters of tool wearing can be measured by out-process and in-process-measuring systems. Given the extremely limiting role of the former in modern production lines, development of the latter (the indirect measuring systems) has gained prominence, The basis of indirect measuring systems comprises a set of various signals originating from the units of the system under treatment which stand in certain correlations with the wearing parameters. The paper presents mathematical models of axial force designed on the basis of experimental research in drilling tempered steel by twist drills made of high-speed steel manufactured by powder metallurgy.展开更多
Effects on sustainable development of climate change have been going further nowadays.National Five Year Development Plan in China should have specific policies on how to take climate change impacts into account throu...Effects on sustainable development of climate change have been going further nowadays.National Five Year Development Plan in China should have specific policies on how to take climate change impacts into account through the environmental planning.Key fields distribute in three levels of natural bearing capacity,production system and human settlements,and include seven aspects:ecosystems,water resources,disasters and risks,low-carbon economy,vulnerable departments,urbanization,and coastland.展开更多
In this study, dynamic characteristics of the small base isolation system using new friction bearings are investigated by excitation experiment, and compared to other one using previous bearings. Peak amplitude of the...In this study, dynamic characteristics of the small base isolation system using new friction bearings are investigated by excitation experiment, and compared to other one using previous bearings. Peak amplitude of the acceleration response waves on the small base isolation system is decreased to about 10%-25% compared to the input waves. Also root mean square amplitude is decreased to about 10%-40%. In case of the ball embedded a cylindrical sponge, the new bearing, the damping ratio increases with increasing width of the cylindrical sponge. The natural frequency does not change. On the other hand, in case of the marble plate that is previous bearing, the damping ratio increases with increasing curvature radius of the marble plate, the natural frequency also increases. Therefore, the small base isolation system using new friction bearing provides better performance. The responses of the base isolation system indicate nonlinier effects by friction force.展开更多
As one of the most important steps in the design of bearing-less rotor systems,the design of flexible beam has received much research attention.Because of the very complex working environment of helicopter,the flexibl...As one of the most important steps in the design of bearing-less rotor systems,the design of flexible beam has received much research attention.Because of the very complex working environment of helicopter,the flexible beam should satisfy both the strength and dynamic requirements.However,traditional optimization research focused only on either the strength or dynamical characteristics.To sufficiently improve the performance of the flexible beam,both aspects must be considered.This paper proposes a two-stage optimization method based on the Hamilton variational principle:Variational asymptotic beam section analysis(VABS)program and genetic algorithm(GA).Consequently,a two-part analysis model based on the Hamilton variational principle and VABS is established to calculate section characteristics and structural dynamics characteristics,respectively.Subsequently,the two parts are combined to establish a two-stage optimization process and search with GA to obtain the best dynamic characteristics combinations.Based on the primary optimization results,the section characteristics of the flexible beam are further optimized using GA.The optimization results show that the torsional stiffness decreases by 36.1%compared with the full 0°laying scheme without optimization and the dynamic requirements are achieved.The natural frequencies of flapping and torsion meet the requirements(0.5 away from the passing frequencies of the blade,0.25 away from the excitation force frequency,and the flapping and torsion frequencies keep a corresponding distance).The results indicate that the optimization method can significantly improve the performance of the flexible beam.展开更多
文摘An energy-based ecological footprint model was set up to monitor the sustainable development status of a specific marine system. This model used unit energy value and energy density to convert the consumption into ecological productive areas. It can reflect the utilization degree of resources in the regional development. Then, the quantitative analysis of sustainable development was done by comparing the size of the areas. We defined the concept of energy-based ecological footprint of marine and built energy-based ecological footprint model of marine. Then we applied this model to marine ecological system of Shandong province to evaluate its sustainable development statue. The results showed that the energy-based marine ecological footprint of the marine ecological system in Shandong province was 1.74 × 106 hm^2 in 2010, and the energy-based ecological carrying capacity of this area was 1.60×107 hm^2 per capita. Thus, the marine ecological system of Shandong province has strong sustainability.
文摘The coupled dynamic characteristics of the conical electromagnetic bearing are presented and their definitions are given. On the basis of the analyses of the characteristics, the dynamic model of five degrees of freedom (five-DOF) rotor-conical electromagnetic bearing system is made, and the influence of the coupled characteristics on the system optimal controller is analyzed.
基金Projects(51078359, 51208522) supported by the National Natural Science Foundation of ChinaProjects(20110491269, 2012T50708) supported by China Postdoctoral Science FoundationProject supported by Postdoctoral Science Foundation of Central South University, China
文摘Based on the slip-line field theory, a two-dimensional slip failure mechanism with mesh-like rigid block system was constructed to analyze the ultimate bearing capacity problems of rough foundation within the framework of the upper bound limit analysis theorem. In the velocity discontinuities in transition area, the velocity changes in radial and tangent directions are allowed. The objective functions of the stability problems of geotechnical structures are obtained by equating the work rate of external force to internal dissipation along the velocity discontinuities, and then the objective functions are transformed as an upper-bound mathematic optimization model. The upper bound solutions for the objective functions are obtained by use of the nonlinear sequential quadratic programming and interior point method. From the numerical results and comparative analysis, it can be seen that the method presented in this work gives better calculation results than existing upper bound methods and can be used to establish the more accurate plastic collapse load for the ultimate bearing capacity of rough foundation.
基金Projects(51605051,51975068)supported by the National Natural Science Foundation of ChinaProject(3102020HHZY030001)supported by the Fundamental Research Funds for the Central Universities,China。
文摘Vibrations of a rotor-bearing system(RBS)can be affected by the frictional forces between the components of the inherent bearings.Thus,an in-depth investigation of the influences of the frictional moments of the bearings on the vibrations of the RBS can be helpful for understanding the vibration mechanisms in the rotating machinery.In this study,an improved dynamic model of a RBS considering different frictional force models is presented.A comparative investigation on the influences of the empirical and analytical frictional force models on the vibration characteristics of the RBS is proposed.The empirical frictional force models include Palmgren’s and SKF’s models.The analytical frictional force model considers the rolling friction caused by the radial elastic material hysteresis,slipping friction between the ball and races,viscosity friction caused by the lubricating oil,and contact friction between the ball and cage.The influences of the external load and rotational speed on the vibrations of the RBS are analyzed.The comparative results show that the analytical frictional force model can give a more reasonable method for formulating the effects of the friction forces in the bearings on the vibrations of the RBS.The results also demonstrate that the friction forces in the bearings can significantly affect the vibrations of the RBSs.
基金Under the auspices of National Natural Science Foundation of China (No. 40971101)Major Project of 11th Five-Year Scientific and Technological Support Plan of China (No. 2006BAJ14B03)
文摘Studying the carrying capacity of resources and environment of city clusters in the central China has important practical guidance significance for promoting the healthy, sustainable and stable development of this region. According to their influencing factors and reciprocity mechanism, using system dynamics approaches, this paper built a SD model for measuring the carrying capacity of resources and environment of the city clusters in the central China, and through setting different development models, the comprehensive measurement analysis on the carrying capacity was carried out. The results show that the model of promoting socio-economic development under the protection of resources and environment is the optimal model for promoting the harmony development of resources, environment, society and economy in the city clusters. According to this model, the optimum population scale of the city clusters in 2020 is 42.80×106 persons, and the moderate economic development scale is 22.055×1012 yuan (RMB). In 1996-2020, the carrying capacity of resources and environment in the city clusters took on obvious phase-change characteristics. During the studied period, it is basically at the initial development stage, and will come through the development process from slow development to speedup development.
文摘Based on the relationship between water environment system and human society, water environment carrying capacity (WECC) probes into supporting ability of complex water environment system to the human society. Recent years, due to the shortage of water resources and serious water pollution in several watersheds in China, the research of watershed water environment carrying capacity (WWECC) becomes very important. The conception, connotation and method of representation of WWECC are discussed deeply in this paper. It shows that WWECC is a kind of index that instructs whether the water environment system in watershed can continue to support the development of social economy and ecology, it is dimensionless number.
基金Supported by the Natural Science Foundation of China under Grant No.50675162the Program of Introducing Talents of Discipline to Universities under Grant No.B08031the Key Project of Hubei Province Science & Technology Fund under Grant No.2008CAD027
文摘Thrust bearing is a key component of the propulsion system of a ship. It transfers the propulsive forces from the propeller to the ship's hull, allowing the propeller to push the ship ahead. The performance of a thrust bearing pad is critical. When the thrust bearing becomes damaged, it can cause the ship to lose power and can also affect its operational safety. For this paper, the distribution of the pressure field of a thrust pad was calculated with numerical method, applying Reynolds equation. Thrust bearing properties for loads were analyzed, given variations in outlet thickness of the pad and variations between the load and the slope of the pad. It was noticed that the distribution of pressure was uneven. As a result, increases of both the outlet thickness and the slope coefficient of the pad were able to improve load beating capability.
文摘Classical beat phenomenon has been observed in most combined systems. The focus of this paper is to provide a better understanding of this phenomenon in an offshore pile-supported pipeline system. The beat phenomeon is caused by the coupling movement of the pipeline and its vertical pile support under certain conditions. It can induce excessive vibration and cause fatigue failure at pipe elbow. However, in some circumstances it does not exist. Numerical results in both frequency and time domains are presented to elucidate this phenomenon in a combined pipeline system. The conclusions of this paper could give constructive guidance to future design of simply supported pipeline systems.
基金Supported by the National Basic Research Program (973 Program) of China (Nos.2009CB421102 and 2005CB422005-01)the Second Scheme of CAS Action Plan for the Development of Western China (No.KZCX2-XB2-06-02)the National Key Technology R&D Program of China (No.2006BAC01A02-01)
文摘Remote sensing data from the Terra Moderate-Resolution Imaging Spectroradiometer (MODIS) and geospatial data were used to estimate grass yield and livestock carrying capacity in the Tibetan Autonomous Prefecture of Golog, Qing-hai, China. The MODIS-derived normalized difference vegetation index (MODIS-NDVI) data were correlated with the aboveground green biomass (AGGB) data from the aboveground harvest method. Regional regression model between the MODIS-NDVI and the common logarithm (LOG10) of the AGGB was significant (r2 = 0.51, P < 0.001), it was, there-fore, used to calculate the maximum carrying capacity in sheep-unit year per hectare. The maximum livestock carrying capacity was then adjusted to the theoretical livestock carrying capacity by the reduction factors (slope, distance to water, and soil erosion). Results indicated that the grassland conditions became worse, with lower aboveground palatable grass yield, plant height, and cover compared with the results obtained in 1981. At the same time, although the actual livestock numbers decreased, they still exceeded the proper theoretical livestock carrying capacity, and overgrazing rates ranged from 27.27% in Darlag County to 293.99% in Baima County. Integrating remote sensing and geographical information system technologies, the spatial and temporal conditions of the alpine grassland, trend, and projected stocking rates could be forecasted for decision making.
文摘Based on the short-bearing model, the stability of a rigid Jeffcott rotor system is studied in a relatively wide parameter range by using Poincaré maps and the numerical integration method. The results of the calculation show that the period doubling bifurcation, quasi-periodic and chaotic motions may occur. In some typical parameter regions, the bifurcation diagrams, phase portrait, Poincaré maps and the frequency spectrums of the system are acquired with the numerical integration method. They demonstrate some motion state of the system. The fractal dimension concept is used to determine whether the system is in a state of chaotic motion. The analysis result of this paper provides the theoretical basis for qualitatively controlling the stable operating states of the rotors.
基金supported by the Knowledge Innovation Project of Chinese Academy of Sciences (grant no. KZCX2-YW-422)
文摘Ecological city(eco-city) and its planning approach are emerging concepts in urban study,urban planning,ecological economics,environmental policy and corporate environmental management.However,opinions remain divided over the connotation and denotation of the term"ecological city",what key issues ecocity planning can solve,and its specific contents.In this study,we present 10 basic propositions that define the eco-city and clarify its key parameters,thereby providing the basis for discussing the assumptions and principles underlying different approaches to sustainable urban development.We then summarize the concept and principles of an eco-city,and define the main requirements for ecocity planning.We conclude that an eco-city is a city in which the urban population,scale of land use and intensity of human activities are limited to the regional resource and environmental carrying capacity,which does not cause increasing or irreversible damage to the regional ecosystem's structure,functions and processes.
文摘Being one of their prominent exploitative characteristics, cutting tools durability depends on the character, intensity and the speed of wearing. Identification of tool wearing is of great significance for the purpose of avoiding sooner or later replacement of tools. The parameters of tool wearing can be measured by out-process and in-process-measuring systems. Given the extremely limiting role of the former in modern production lines, development of the latter (the indirect measuring systems) has gained prominence, The basis of indirect measuring systems comprises a set of various signals originating from the units of the system under treatment which stand in certain correlations with the wearing parameters. The paper presents mathematical models of axial force designed on the basis of experimental research in drilling tempered steel by twist drills made of high-speed steel manufactured by powder metallurgy.
基金Natural Science Foundation of China (Grant No.40976021,40901081,41101141)
文摘Effects on sustainable development of climate change have been going further nowadays.National Five Year Development Plan in China should have specific policies on how to take climate change impacts into account through the environmental planning.Key fields distribute in three levels of natural bearing capacity,production system and human settlements,and include seven aspects:ecosystems,water resources,disasters and risks,low-carbon economy,vulnerable departments,urbanization,and coastland.
文摘In this study, dynamic characteristics of the small base isolation system using new friction bearings are investigated by excitation experiment, and compared to other one using previous bearings. Peak amplitude of the acceleration response waves on the small base isolation system is decreased to about 10%-25% compared to the input waves. Also root mean square amplitude is decreased to about 10%-40%. In case of the ball embedded a cylindrical sponge, the new bearing, the damping ratio increases with increasing width of the cylindrical sponge. The natural frequency does not change. On the other hand, in case of the marble plate that is previous bearing, the damping ratio increases with increasing curvature radius of the marble plate, the natural frequency also increases. Therefore, the small base isolation system using new friction bearing provides better performance. The responses of the base isolation system indicate nonlinier effects by friction force.
基金supported by the Foundation of National Key Laboratory of Rotorcraft Aeromechanics,Nanjing University of Aeronautics and Astronautics(No.614222004030917)。
文摘As one of the most important steps in the design of bearing-less rotor systems,the design of flexible beam has received much research attention.Because of the very complex working environment of helicopter,the flexible beam should satisfy both the strength and dynamic requirements.However,traditional optimization research focused only on either the strength or dynamical characteristics.To sufficiently improve the performance of the flexible beam,both aspects must be considered.This paper proposes a two-stage optimization method based on the Hamilton variational principle:Variational asymptotic beam section analysis(VABS)program and genetic algorithm(GA).Consequently,a two-part analysis model based on the Hamilton variational principle and VABS is established to calculate section characteristics and structural dynamics characteristics,respectively.Subsequently,the two parts are combined to establish a two-stage optimization process and search with GA to obtain the best dynamic characteristics combinations.Based on the primary optimization results,the section characteristics of the flexible beam are further optimized using GA.The optimization results show that the torsional stiffness decreases by 36.1%compared with the full 0°laying scheme without optimization and the dynamic requirements are achieved.The natural frequencies of flapping and torsion meet the requirements(0.5 away from the passing frequencies of the blade,0.25 away from the excitation force frequency,and the flapping and torsion frequencies keep a corresponding distance).The results indicate that the optimization method can significantly improve the performance of the flexible beam.