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On the diophantine equation x^2-Dy^2=n

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Science China Mathematics 2013年第2期56卷 227-238页

作者： wei dasheng Academy of Mathematics and Systems Science Chinese Academy of Sciences

We propose a method to determine the solvability of the diophantine equation x^2 - Dy^2 = n for the following two cases：the following two cases：（1） D = pq, where p, q ≡ 1 mod 4 are distinct primes with （q） = 1 and p q （p/q（q/p）4 = -1.（2） D = 2p1P2 ... Pro, where Pi ≡ 1 mod 8, 1 ≤ i ≤m are distinct primes and D = r2 ＋s2 with r, s ≡±3 mod 8.

关键词： torus Hilbert class field reciprocity law

Lock-in phenomenon of tip clearance flow and its influence on aerodynamic damping under specified vibration on an axial transonic compressor rotor

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Chinese Journal of Aeronautics 2022年第3期35卷 185-200页

作者： Le HAN dasheng wei Yanrong WANG Mingchang FANG School of Energy and Power Engineering Beihang UniversityBeijing 100083China Collaborative Innovation Center for Advanced Aero-Engine Beijing 100083China

In this study,the lock-in phenomenon of Tip Clearance Flow(TCF)instabilities and their relationship to blade vibration are investigated numerically on an axial transonic rotor with a large tip *** capabilities of simulating instability flow and lock-in phenomenon are verified on a transonic rotor and a NACA0012 airfoil by comparing with the test data,*** lock-in phenomenon is first numerically confirmed that may occur to TCF instabilities when its frequency is close to the blade vibration *** lock-in region becomes wider with the vibration amplitude increasing,and it is also affected by modal *** the rotor at the simulation conditions in this study,the bending mode results in a wider lock-in region than the torsional *** the lock-in region,the phase difference between the Tip Clearance Vortex(TCV)and the blade vibration changes with the flow condition and the frequency ratio of the blade vibration and the TCV *** frequency of the TCV instabilities reduces with the mass flow ***,reducing mass flow and increasing frequency ratio have similar effects on the TCV phase,which causes a significant variation on the unsteady pressure amplitude in the blade tip ***,the aerodynamic damping changes significantly with the TCV *** aerodynamic damping displays a nonlinear relationship with the vibration amplitude,and it changes from negative to positive with the vibration amplitude increasing at the same frequency *** negative damping is mainly provided by the tip area of the *** unlocked conditions,the period of the TCF instabilities fluctuates over time,and it cannot be directly separated by their frequency *** Blade Phase Angle(IBPA)also has an important influence on the feature of the TCV *** occurrence of frequency lock-in also requires“appropriate”*** the examined working conditions,the frequency lock-in occurs under 0 ND(Nodal Diameter),but not un

关键词： Aerodynamic damping Inter blade phase angle Lock-in Specified blade vibration Tip clearance flow instabilities

A discussion of fatigue properties of notched specimens subjected to prestressing treatment machined from FGH4097

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Chinese Journal of Aeronautics 2024年第4期37卷 508-523页

作者： Rongxi SHI dasheng wei Le HAN Shun YANG School of Energy and Power Engineering Beihang UniversityBeijing 100191China Jiangxi Research Institute Beihang UniversityNanchang 330096China Research Institute of Aero-Engine Beihang UniversityBeijing 100191China

Experimental and numerical investigations were performed to reveal the effect of prestress on the fatigue properties of FGH4097 so as to quantitatively evaluate the overspeed benefit of the disc of aeroengine. A corresponding experiment was performed to examine the effect of prestress on the fatigue life of FGH97. A complete model describing the fatigue properties of the prestressed notch specimen was proposed. After the modification of mean stress, stress gradient and prestressing treatment, the model is finally verified by fatigue test of presstressed notch specimens machined from FGH4097 with satisfactory accuracy and good engineering applicability. The new model highlights that for the variable fatigue loads, the introduction of appropriate prestress is expected to benefit to the notch specimens and certainly to the disc of aeroengine regards of their fatigue properties. Both the calculation method of fatigue life parameters and the prestress correction model are proved to have good prediction accuracy.

关键词： Turbine blisk Overspeed test Prestress Fatigue life prediction FGH4097

Introduction of fretting-contact-induced crack closure: Numerical simulation of crack initiation and growth path in disk/blade attachment

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Chinese Journal of Aeronautics 2019年第8期32卷 1923-1932页

作者： Chen HU dasheng wei Yanrong WANG Xianghua JIANG School of Energy and Power Engineering Beihang University

Fretting fatigue crack initiation and growth in titanium alloy dovetail assembly was investigated by the Finite Element Method(FEM). Firstly, contact stress was calculated precisely with an elastic–plastic material model. Secondly, the location and angle of crack initiation were determined by the parameter of the maximum shear stress range on the critical plane, and the angle of crack growth was predicted by the Maximum Tangential Stress(MTS) criterion, which showed agreement with experimental observation. Finally, the fretting-contact-induced crack closure behavior was simulated by the node release technique in software ABAQUS with both elastic and elastic–plastic material models. The simulation shows that the variation of the contact status between fretting surfaces will result in crack closure even for the elastic material model. The fretting crack closure ratio decreases as the crack grows out of the contact area and it has great impact on the effective range of Stress Intensity Factor(SIF) as well as the crack growth rate.

关键词： Crack closure Crack growth Crack initiation Finite element method Fretting fatigue

Thermal oxidation description methodology of thermal barrier coatings on gas turbine blades considering service characteristics

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Chinese Journal of Aeronautics 2024年第6期37卷 410-424页

作者： Qiannan TAO Yanrong WANG dasheng wei Shun YANG School of Energy and Power Engineering Beihang UniversityBeijing 100191China Jiangxi Research Institute of Beihang University Nanchang 330096China

Predicting the thickness of Thermally Grown Oxide(TGO)and the residual stresses induced by TGO growth in the Thermal Barrier Coatings(TBCs)is significant work in analyzing the failure of *** practical applications,the operating temperature,oxygen partial pressure,aluminium content in TBCs,and porosity of the topcoat affect the oxidation ***,a novel oxidation rate model is proposed to describe the effect of such *** parameters in the proposed model were fitted with isothermal degradation test data from prior ***,a method for calculating the residual stress in a disk-shaped specimen was developed based on the oxidized growth strain model and the oxidized ***,a variable-temperature oxidation experiment was performed to validate the new oxidation *** average error between the predicted and experimental thicknesses is approximately 10%,and the average error between the residual stresses is 30%.Under the variable-temperature condition,the error between the predicted thickness and the average experimental thickness is 3.9%.

关键词： Thermal barrier coatings Oxidation Gas turbine Residual stresses Sintering

A new fatigue life prediction model considering the creep-fatigue interaction effect based on the Walker total strain equation

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Chinese Journal of Aeronautics 2020年第9期33卷 2382-2394页

作者： Siyuan CHEN dasheng wei Jialiang WANG Yanrong WANG Xianghua JIANG School of Energy and Power Engineering Beihang UniversityBeijing 100083China Beijing Key Laboratory of Aero-Engine Structure and Strength Beijing 100083China Jiangxi Research Institute Beihang UniversityNanchang 330096China Science and Technology on Scramjet Laboratory Beijing Power Machinery InstituteBeijing 100074China

The performance of high-temperature components of aero-engines under the CreepFatigue Interaction(CFI)behavior gets more attention *** this research,the creepfatigue tests of two superalloys of Powder Metallurgy(PM)FGH96 and direct aging GH4169 were performed at 650°C with different types of dwell,and the fracture morphology of FGH96 specimens was observed by Scanning Electron Microscopy(SEM)to analyze the creep-fatigue fracture feature and crack ***,according to phenomenology,the effect of dwell was introduced to develop a new uniaxial fatigue life prediction model based on the total strain equation,which has capability to take dwell time and load ratio into account *** equations were utilized to model the test data of PM FGH96 and GH4169,together with data of another superalloy PM FGH95 conducted previously.A prominent prediction ability of the model in creep-fatigue life prediction of different superalloys has been *** data points of test data and estimated data are located within two times scatter band,which is ideal in engineering.

关键词： Creep-fatigue interaction(CFI) Creep-fatigue test Life prediction Low-cycle fatigue(LCF) Superalloy

Effect of Mg on Microstructure and Growth Kinetics of Zn-22.3Al-1.1Si Coating

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Journal of Wuhan University of Technology(Materials Science) 2019年第2期34卷 373-382页

作者：涂浩 wei dasheng ZHOU Shengjie LIU Ya WU Changjun WANG Jianhua 苏旭平 Jiangsu Key Laboratory of Materials Surface Science and Technology Changzhou University Jiangsu Collaborative Innovation Center of Photovolatic Science and Engineering Changzhou University

The effects of Mg on the microstructure and growth kinetics of the hot-dip Zn-22.3 Al-1.1 Si-x Mg(x = 0, 0.2, 0.4, and 0.6) coatings were investigated in detail. Scanning electron microscopy with energy dispersive spectroscopy and X-ray diffraction studies revealed the presence of η-Zn, α-Al, Zn/Al eutectoid,(Si), Al/Si eutectic, and Zn/Al/Mg_2 Zn11 ternary eutectic on the top surface of these Mg-containing coatings. Especially, a small amount of MgZn2 phase appears in top surface of Zn-22.3 Al-1.1 Si-0.6 Mg coating. Five phases are found in the alloy layers, i e, Fe_2 Al_5, FeAl_3, τ_(5C), τ_(5H), and τ_1. The addition of 0.2% Mg can delay the emergence of FeAl_3 phase. When the Mg content is more than 0.2%, the outer layers of coating change from τ_(5C) to τ_(5H) phase. The growth of the inhibition layer is diffusion controlled for various Mg content baths. Mg improves the corrosion resistance of the Mg-containing coatings, and the Zn-22.3 Al-1.1 Si-0.6 Mg coating possesses the highest protective properties.

关键词： Mg microstructure growth kinetics inhibition layer diffusion

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孔隙形状及孔隙率对多孔材料弹性性能的影响

复合材料学报 2014年第5期31卷 1277-1283页

作者：沈明魏大盛北京航空航天大学能源与动力工程学院北京100191

利用通用单胞法(GMC)计算了不同孔隙形状及孔隙率对多孔材料等效弹性参数的影响,计算中分别采用二维方形、圆形孔隙模型和三维立方体、球形孔隙模型模拟多孔材料。不同孔隙率下等效弹性参数的计算结果表明:不同孔隙形状下,多孔材料等效... 详细信息

利用通用单胞法(GMC)计算了不同孔隙形状及孔隙率对多孔材料等效弹性参数的影响,计算中分别采用二维方形、圆形孔隙模型和三维立方体、球形孔隙模型模拟多孔材料。不同孔隙率下等效弹性参数的计算结果表明:不同孔隙形状下,多孔材料等效弹性参数随孔隙率增大的退化程度不同;通过对比二维简化模型与三维模型的差异,发现二维简化模型对多孔材料等效弹性参数的估算值偏低。进一步将GMC计算结果和已有文献实验结果进行比较,发现两者具有较高的吻合度。最后将GMC模型与有限元、经验模型进行对比,得出GMC模型的局限性。综合计算结果,GMC具有一定的计算精度,可应用于工程实际分析中。

关键词：通用单胞法多孔材料孔隙形状孔隙率弹性性能

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榫连结构的高应力梯度及破坏分析

北京航空航天大学学报 2010年第10期36卷 1184-1188页

作者：魏大盛王延荣北京航空航天大学能源与动力工程学院北京100191

某燕尾形榫连结构的分析表明叶盘榫齿/榫槽接触区边缘存在较高的应力梯度,接触应力的有限元解同网格疏密程度密切相关.通过建立一系列不同密度网格的模型,对此问题展开有限元建模分析,以改善接触应力的求解精度,同时深入讨论材料弹塑性... 详细信息

某燕尾形榫连结构的分析表明叶盘榫齿/榫槽接触区边缘存在较高的应力梯度,接触应力的有限元解同网格疏密程度密切相关.通过建立一系列不同密度网格的模型,对此问题展开有限元建模分析,以改善接触应力的求解精度,同时深入讨论材料弹塑性对接触应力的影响.在弹塑性接触应力分析的基础上,采用断裂力学方法建立了榫连结构高应力梯度位置的破坏分析模型,判断裂纹的萌生及扩展方向,以进行结构的强度及寿命分析.

关键词：榫连结构高应力梯度破坏裂纹萌生断裂力学