Cold-flow experiments on planar Expansion Deflection(ED)nozzle flows are conducted under a simulated startup-shutdown process of rocket motors.The purpose is to investigate the flow and performance characteristics in ...Cold-flow experiments on planar Expansion Deflection(ED)nozzle flows are conducted under a simulated startup-shutdown process of rocket motors.The purpose is to investigate the flow and performance characteristics in ED nozzles,capture the behavior of shock flapping,and explore asymmetric flow dynamics utilizing a symmetric nozzle.A total pressure condition,characterized by rapid rise followed by a slow fall,is employed to simulate the continuous startup and shutdown processes.The schlieren imaging technique and high-frequency pressure transducers are employed to obtain the flow information.The experimental results indicate that the flow characteristics differ between the startup and shutdown processes with a hysteresis observed in the nozzle wake mode transition.During the startup process,the shock waves are pushed outward of the nozzle,while during the shutdown process,the flow propagates inward dominated by Mach stems.Counterintuitive results are demonstrated,namely,the mode transition is not the cause of the sudden thrust decrease,and the moment of maximum thrust does not coincide with the moment of maximum total pressure.During the operation of the nozzle,two stages of shock wave flapping occur,accompanied by significant wall pressure oscillations.These oscillation frequencies are demonstrated to be related to the inherent acoustic frequencies of the test chamber.An improved pressure ratio method is proposed to predict the position of the shock oscillation separation point.The prediction results revealed the shock behavior during the flapping process.展开更多
The challenge of solving nonlinear problems in multi-connected domains with high accuracy has garnered significant interest.In this paper,we propose a unified wavelet solution method for accurately solving nonlinear b...The challenge of solving nonlinear problems in multi-connected domains with high accuracy has garnered significant interest.In this paper,we propose a unified wavelet solution method for accurately solving nonlinear boundary value problems on a two-dimensional(2D)arbitrary multi-connected domain.We apply this method to solve large deflection bending problems of complex plates with holes.Our solution method simplifies the treatment of the 2D multi-connected domain by utilizing a natural discretization approach that divides it into a series of one-dimensional(1D)intervals.This approach establishes a fundamental relationship between the highest-order derivative in the governing equation of the problem and the remaining lower-order derivatives.By combining a wavelet high accuracy integral approximation format on 1D intervals,where the convergence order remains constant regardless of the number of integration folds,with the collocation method,we obtain a system of algebraic equations that only includes discrete point values of the highest order derivative.In this process,the boundary conditions are automatically replaced using integration constants,eliminating the need for additional processing.Error estimation and numerical results demonstrate that the accuracy of this method is unaffected by the degree of nonlinearity of the equations.When solving the bending problem of multi-perforated complex-shaped plates under consideration,it is evident that directly using higher-order derivatives as unknown functions significantly improves the accuracy of stress calculation,even when the stress exhibits large gradient variations.Moreover,compared to the finite element method,the wavelet method requires significantly fewer nodes to achieve the same level of accuracy.Ultimately,the method achieves a sixth-order accuracy and resembles the treatment of one-dimensional problems during the solution process,effectively avoiding the need for the complex 2D meshing process typically required by conventional methods when solving problems with multi-connected domains.展开更多
In weak field limits,we compute the deflection angle of a gravitational decoupling extended black hole(BH)solution.We obtained the Gaussian optical curvature by examining the null geodesic equations with the help of G...In weak field limits,we compute the deflection angle of a gravitational decoupling extended black hole(BH)solution.We obtained the Gaussian optical curvature by examining the null geodesic equations with the help of Gauss-Bonnet theorem(GBT).We also looked into the deflection angle of light by a black hole in weak field limits with the use of the Gibbons-Werner method.We verify the graphical behavior of the black hole after determining the deflection angle of light.Additionally,in the presence of the plasma medium,we also determine the deflection angle of the light and examine its graphical behavior.Furthermore,we compute the Einstein ring via gravitational decoupling extended black hole solution.We also compute the quasi-periodic oscillations and discuss their graphical behavior.展开更多
Based on the equivalence principle of deflection and stress, the concentrated vehicle load which acts on the center of continuously reinforced concrete pavement （CRCP） is translated into the equivalent half-wave sin...Based on the equivalence principle of deflection and stress, the concentrated vehicle load which acts on the center of continuously reinforced concrete pavement （CRCP） is translated into the equivalent half-wave sine load by the Fourier transform. On the basis of this transform and the small deflection theory of elastic thin plates, the deflection and stress formulae of CRCP under the concentrated vehicle load with a hollow foundation are put forward. The sensitivity of parameters is analyzed. The results show that maximum deflection is directly proportional to the concentrated vehicle load and the slab width, and inversely proportional to the lateral bending stiffness and slab thickness. The effects of slab width and thickness are significant with regard to maximum deflection. Maximum stress is directly proportional to the concentrated vehicle load and the slab width as well as inversely proportional to slab thickness. The effect of slab thickness is significant with regard to maximum stress. According to the calculation results, the most effective measure to reduce maximum deflection and stress is to increase slab thickness.展开更多
为高效分析滑行道桥在损伤情况下的安全通行能力,探究不同损伤情况下的滑行道桥响应参数,本文采用数值模拟的方法,建立飞机-滑行道桥耦合振动损伤模型,进行滑行道桥安全承载力学性能评估实验分析。根据相关规范,针对滑行道桥不同损伤类...为高效分析滑行道桥在损伤情况下的安全通行能力,探究不同损伤情况下的滑行道桥响应参数,本文采用数值模拟的方法,建立飞机-滑行道桥耦合振动损伤模型,进行滑行道桥安全承载力学性能评估实验分析。根据相关规范,针对滑行道桥不同损伤类型(整体损伤、支座损伤、局部裂缝),以5%、10%、15%、20%、25%量化滑行道桥整体刚度损伤程度和20%、40%、60%、80%、100%量化支座刚度损伤程度;根据预应力筋的位置,设置20、40、60、80、100 mm 5种裂缝深度来量化裂缝损伤。结合不同机型的荷载作用,探究分析不同工况下滑行道桥的2个响应参数(频率和跨中挠度),验证损伤分级可行性并进行相关滑行道桥安全承载能力分析。结果表明,不同损伤类型(整体损伤、支座损伤、局部裂缝)滑行道桥的频率和跨中挠度变化均与损伤程度呈现明显的相关性,且不同损伤类型对滑行道桥的结构响应有显著影响。展开更多
In this paper,a comparative analysis of two beams’deflections,one supported-embedded beam and a bi-supported beam,is presented.For such comparison,first the respective second-order linear Ordinary Differential Equati...In this paper,a comparative analysis of two beams’deflections,one supported-embedded beam and a bi-supported beam,is presented.For such comparison,first the respective second-order linear Ordinary Differential Equations(ODEs)were obtained.Along with the boundary conditions,there are two Boundary Value Problems(BVPs),making it possible to perform their numerical and analytical solutions.For numerical solutions,a Matlab algorithm was implemented based on the Finite Difference Method(FDM).The analytical solutions were also obtained for comparison with the numerical ones and with the validation method.In the end we analyzed the shapes of the elastic lines of the two beams caused by the loads coming from the weight of each one.展开更多
基金supported by the National Natural Science Foundation of China(No.12002102)。
文摘Cold-flow experiments on planar Expansion Deflection(ED)nozzle flows are conducted under a simulated startup-shutdown process of rocket motors.The purpose is to investigate the flow and performance characteristics in ED nozzles,capture the behavior of shock flapping,and explore asymmetric flow dynamics utilizing a symmetric nozzle.A total pressure condition,characterized by rapid rise followed by a slow fall,is employed to simulate the continuous startup and shutdown processes.The schlieren imaging technique and high-frequency pressure transducers are employed to obtain the flow information.The experimental results indicate that the flow characteristics differ between the startup and shutdown processes with a hysteresis observed in the nozzle wake mode transition.During the startup process,the shock waves are pushed outward of the nozzle,while during the shutdown process,the flow propagates inward dominated by Mach stems.Counterintuitive results are demonstrated,namely,the mode transition is not the cause of the sudden thrust decrease,and the moment of maximum thrust does not coincide with the moment of maximum total pressure.During the operation of the nozzle,two stages of shock wave flapping occur,accompanied by significant wall pressure oscillations.These oscillation frequencies are demonstrated to be related to the inherent acoustic frequencies of the test chamber.An improved pressure ratio method is proposed to predict the position of the shock oscillation separation point.The prediction results revealed the shock behavior during the flapping process.
基金supported by the National Natural Science Foundation of China(Grant No.11925204).
文摘The challenge of solving nonlinear problems in multi-connected domains with high accuracy has garnered significant interest.In this paper,we propose a unified wavelet solution method for accurately solving nonlinear boundary value problems on a two-dimensional(2D)arbitrary multi-connected domain.We apply this method to solve large deflection bending problems of complex plates with holes.Our solution method simplifies the treatment of the 2D multi-connected domain by utilizing a natural discretization approach that divides it into a series of one-dimensional(1D)intervals.This approach establishes a fundamental relationship between the highest-order derivative in the governing equation of the problem and the remaining lower-order derivatives.By combining a wavelet high accuracy integral approximation format on 1D intervals,where the convergence order remains constant regardless of the number of integration folds,with the collocation method,we obtain a system of algebraic equations that only includes discrete point values of the highest order derivative.In this process,the boundary conditions are automatically replaced using integration constants,eliminating the need for additional processing.Error estimation and numerical results demonstrate that the accuracy of this method is unaffected by the degree of nonlinearity of the equations.When solving the bending problem of multi-perforated complex-shaped plates under consideration,it is evident that directly using higher-order derivatives as unknown functions significantly improves the accuracy of stress calculation,even when the stress exhibits large gradient variations.Moreover,compared to the finite element method,the wavelet method requires significantly fewer nodes to achieve the same level of accuracy.Ultimately,the method achieves a sixth-order accuracy and resembles the treatment of one-dimensional problems during the solution process,effectively avoiding the need for the complex 2D meshing process typically required by conventional methods when solving problems with multi-connected domains.
基金funded by the National Natural Science Foundation of China under Grant No.11975145。
文摘In weak field limits,we compute the deflection angle of a gravitational decoupling extended black hole(BH)solution.We obtained the Gaussian optical curvature by examining the null geodesic equations with the help of Gauss-Bonnet theorem(GBT).We also looked into the deflection angle of light by a black hole in weak field limits with the use of the Gibbons-Werner method.We verify the graphical behavior of the black hole after determining the deflection angle of light.Additionally,in the presence of the plasma medium,we also determine the deflection angle of the light and examine its graphical behavior.Furthermore,we compute the Einstein ring via gravitational decoupling extended black hole solution.We also compute the quasi-periodic oscillations and discuss their graphical behavior.
基金The Science Foundation of Ministry of Transport of the People's Republic of China(No.200731822301-7)
文摘Based on the equivalence principle of deflection and stress, the concentrated vehicle load which acts on the center of continuously reinforced concrete pavement （CRCP） is translated into the equivalent half-wave sine load by the Fourier transform. On the basis of this transform and the small deflection theory of elastic thin plates, the deflection and stress formulae of CRCP under the concentrated vehicle load with a hollow foundation are put forward. The sensitivity of parameters is analyzed. The results show that maximum deflection is directly proportional to the concentrated vehicle load and the slab width, and inversely proportional to the lateral bending stiffness and slab thickness. The effects of slab width and thickness are significant with regard to maximum deflection. Maximum stress is directly proportional to the concentrated vehicle load and the slab width as well as inversely proportional to slab thickness. The effect of slab thickness is significant with regard to maximum stress. According to the calculation results, the most effective measure to reduce maximum deflection and stress is to increase slab thickness.
文摘为高效分析滑行道桥在损伤情况下的安全通行能力,探究不同损伤情况下的滑行道桥响应参数,本文采用数值模拟的方法,建立飞机-滑行道桥耦合振动损伤模型,进行滑行道桥安全承载力学性能评估实验分析。根据相关规范,针对滑行道桥不同损伤类型(整体损伤、支座损伤、局部裂缝),以5%、10%、15%、20%、25%量化滑行道桥整体刚度损伤程度和20%、40%、60%、80%、100%量化支座刚度损伤程度;根据预应力筋的位置,设置20、40、60、80、100 mm 5种裂缝深度来量化裂缝损伤。结合不同机型的荷载作用,探究分析不同工况下滑行道桥的2个响应参数(频率和跨中挠度),验证损伤分级可行性并进行相关滑行道桥安全承载能力分析。结果表明,不同损伤类型(整体损伤、支座损伤、局部裂缝)滑行道桥的频率和跨中挠度变化均与损伤程度呈现明显的相关性,且不同损伤类型对滑行道桥的结构响应有显著影响。
文摘In this paper,a comparative analysis of two beams’deflections,one supported-embedded beam and a bi-supported beam,is presented.For such comparison,first the respective second-order linear Ordinary Differential Equations(ODEs)were obtained.Along with the boundary conditions,there are two Boundary Value Problems(BVPs),making it possible to perform their numerical and analytical solutions.For numerical solutions,a Matlab algorithm was implemented based on the Finite Difference Method(FDM).The analytical solutions were also obtained for comparison with the numerical ones and with the validation method.In the end we analyzed the shapes of the elastic lines of the two beams caused by the loads coming from the weight of each one.
