A hybrid machine （HM） as a typical mechatronic device, is a useful tool to generate smooth motion, and combines the motions of a large constant speed motor with a small servo motor by means of a mechnical linkage me...A hybrid machine （HM） as a typical mechatronic device, is a useful tool to generate smooth motion, and combines the motions of a large constant speed motor with a small servo motor by means of a mechnical linkage mechanism, in order to provide a powerful programmable drive system. To achieve design objectives, a control system is required. To design a better control system and analyze the performance of an HM, a dynamic model is necessary. This paper first develops a dynamic model of an HM with a five-bar mechanism using a Lagrangian formulation. Then, several important properties which are very useful in system analysis, and control system design, are presented. Based on the developed dynamic model, two control approaches, computed torque, and combined computed torque and slide mode control, are adopted to control the HM system. Simulation results demonstrate the control performance and limitations of each control approach.展开更多
By the generalized variational principle of two kinds of variables in general me-chanics,it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic system...By the generalized variational principle of two kinds of variables in general me-chanics,it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then,one important formula of similar La-grangian classical relationship called the popularized Lagrangian classical rela-tionship was derived. From Vakonomic model,by two Lagrangian classical rela-tionships and the popularized Lagrangian classical relationship,the result is the same with Chetaev's model,and thus Chetaev's model and Vakonomic model were unified. Simultaneously,the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples,it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right.展开更多
The dynamic stall problem for blades is related to the general performance of wind turbines,where a varying flow field is introduced with a rapid change of the effective angle of attack (AOA).The objective of this wor...The dynamic stall problem for blades is related to the general performance of wind turbines,where a varying flow field is introduced with a rapid change of the effective angle of attack (AOA).The objective of this work is to study the aerodynamic performance of a sinusoidally oscillating NACA0012 airfoil.The coupled k-ω Menter's shear stress transport (SST) turbulence model and γ-Reθ transition model were used for turbulence closure.Lagrangian coherent structures (LCS) were utilized to analyze the dynamic behavior of the flow structures.The computational results were supported by the experiments.The results indicated that this numerical method can well describe the dynamic stall process.For the case with reduced frequency K =0.1,the lift and drag coefficients increase constantly with increasing angle prior to dynamic stall.When the AOA reaches the stall angle,the lift and drag coefficients decline suddenly due to the interplay between the first leading-and trailing-edge vortex.With further increase of the AOA,both the lift and drag coefficients experience a secondary rise and fall process because of formation and shedding of the secondary vortex.The results also reveal that the dynamic behavior of the flow structures can be effectively identified using the finite-time Lyapunov exponent (FTLE) field.The influence of the reduced frequency on the flow structures and energy extraction efficiency in the dynamic stall process is further discussed.When the reduced frequency increases,the dynamic stall is delayed and the total energy extraction efficiency is enhanced.With K =0.05,the amplitude of the dynamic coefficients fluctuates more significantly in the poststall process than in the case of K =0.1.展开更多
This paper presents an inverse problem in analytical dynamics. The inverse problem is to construct the Lagrangian when the integrals of a system are given. Firstly, the differential equations are obtained by using the...This paper presents an inverse problem in analytical dynamics. The inverse problem is to construct the Lagrangian when the integrals of a system are given. Firstly, the differential equations are obtained by using the time derivative of the integrals. Secondly, the differential equations can be written in the Lagrange equations under certain conditions and the Lagrangian can be obtained. Finally, two examples are given to illustrate the application of the result.展开更多
Recently,the notion of non-standard Lagrangians was discussed widely in literature in an attempt to explore the inverse variational problem of nonlinear differential equations.Different forms of non-standard Lagrangia...Recently,the notion of non-standard Lagrangians was discussed widely in literature in an attempt to explore the inverse variational problem of nonlinear differential equations.Different forms of non-standard Lagrangians were introduced in literature and have revealed nice mathematical and physical properties.One interesting form related to the inverse variational problem is the logarithmic Lagrangian,which has a number of motivating features related to the Li′enard-type and Emden nonlinear differential equations.Such types of Lagrangians lead to nonlinear dynamics based on non-standard Hamiltonians.In this communication,we show that some new dynamical properties are obtained in stellar dynamics if standard Lagrangians are replaced by Logarithmic Lagrangians and their corresponding non-standard Hamiltonians.One interesting consequence concerns the emergence of an extra pressure term,which is related to the gravitational field suggesting that gravitation may act as a pressure in a strong gravitational field.The case of the stellar halo of the Milky Way is considered.展开更多
This paper presents the fractional-order dynamics of the double pendulum by means of fractional-order modeling. Equations of motion have been derived for cases with and without external forcing. Generalized force term...This paper presents the fractional-order dynamics of the double pendulum by means of fractional-order modeling. Equations of motion have been derived for cases with and without external forcing. Generalized force terms have been obtained for five different cases of forcing. Both integer and fractional-order analysis have been carried out. Phase diagrams have been plotted to visualize the effect of fractional order approach. The originality of this work arises from the fact that the double pendulum has been modeled with the fractional dynamics approach. The governing equations of motion of the system have been obtained through fractional variational principles.展开更多
This paper considers fluid mixing driven by inflows connected to a circular shallow lake using a numerical framework consisting of a shallow water hydrodynamic model and a passive particle-tracking model.With the flow...This paper considers fluid mixing driven by inflows connected to a circular shallow lake using a numerical framework consisting of a shallow water hydrodynamic model and a passive particle-tracking model.With the flow field driven by alternate inflows predicted by a shallow water model,particle trajectories are traced out using a particle tracking model.The horizontal fluid mixing dynamics are then interpreted using dynamics system analysis approaches including finite-time Lyapunov exponent(FTLE)and Lagrangian coherent structure(LCS).From the simulation results,it is confirmed that periodic inflows are able to create a weak dynamic system in an idealised circular lake,with the particle dynamics controlled by a single dimensionless parameter associated with the inflow duration.The mixing and transport property of the lake changes from regular to chaotic as the value of the dimensionless parameter increases until global chaotic particle dynamics is achieved.By further analysing the advection of particles injected continuously to the inflows(freshwater),the fate of“freshwater”particles in a“polluted”lake is tracked and revealed.The results provide useful guidance for engineering applications,i.e.,transferring freshwater from rivers to improve the water quality in polluted water bodies such as lakes.The presented approach will be able to facilitate the design of‘optimised’schemes for such engineering implementation.展开更多
Semi-Lagrangian(S-L)methods have no CFL stability constraint,and are more stable than the Eulerian methods.In the literature,the S-L method for the levelset re-initialization equation was complicated,which may be unne...Semi-Lagrangian(S-L)methods have no CFL stability constraint,and are more stable than the Eulerian methods.In the literature,the S-L method for the levelset re-initialization equation was complicated,which may be unnecessary.Since the re-initialization procedure is auxiliary,we propose to use the first-order S-L scheme coupled with a projection technique to improve the accuracy at the grid points just adjacent to the interface.Standard second-order S-L method is used for evolving the level-set convection equation.The implementation is simple,including on the block-structured adaptive mesh.The efficiency of the S-L method is demonstrated by extensive numerical examples including passive convection of interfaces with corners/kinks/large deformation under given velocity fields,a geometrical flow with topological changes,simulations of bubble/droplet dynamics in incompressible twophase flows.In terms of accuracy it is comparable to the other existing methods.展开更多
基金The work was supported in part by the EPSRC research council(No. GR/M29108/01).
文摘A hybrid machine （HM） as a typical mechatronic device, is a useful tool to generate smooth motion, and combines the motions of a large constant speed motor with a small servo motor by means of a mechnical linkage mechanism, in order to provide a powerful programmable drive system. To achieve design objectives, a control system is required. To design a better control system and analyze the performance of an HM, a dynamic model is necessary. This paper first develops a dynamic model of an HM with a five-bar mechanism using a Lagrangian formulation. Then, several important properties which are very useful in system analysis, and control system design, are presented. Based on the developed dynamic model, two control approaches, computed torque, and combined computed torque and slide mode control, are adopted to control the HM system. Simulation results demonstrate the control performance and limitations of each control approach.
基金Supported by the National Natural Science Foundation of China (Grant No. 10272034)the Research Fund for the Doctoral Program of Higher Education of Chinathe Basic Research Foundation of Harbin Engineering University (Grant No. 20060217020)
文摘By the generalized variational principle of two kinds of variables in general me-chanics,it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then,one important formula of similar La-grangian classical relationship called the popularized Lagrangian classical rela-tionship was derived. From Vakonomic model,by two Lagrangian classical rela-tionships and the popularized Lagrangian classical relationship,the result is the same with Chetaev's model,and thus Chetaev's model and Vakonomic model were unified. Simultaneously,the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples,it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right.
基金the National Postdoctoral Program for Innovative Talents(Grant BX201700126)the China Postdoctoral Science Foundation(Grant 2017M620043)+1 种基金the National Natural Science Foundation of China(Grants 51679005 and 91752105)the National Natural Science Foundation of Beijing(Grant 3172029).
文摘The dynamic stall problem for blades is related to the general performance of wind turbines,where a varying flow field is introduced with a rapid change of the effective angle of attack (AOA).The objective of this work is to study the aerodynamic performance of a sinusoidally oscillating NACA0012 airfoil.The coupled k-ω Menter's shear stress transport (SST) turbulence model and γ-Reθ transition model were used for turbulence closure.Lagrangian coherent structures (LCS) were utilized to analyze the dynamic behavior of the flow structures.The computational results were supported by the experiments.The results indicated that this numerical method can well describe the dynamic stall process.For the case with reduced frequency K =0.1,the lift and drag coefficients increase constantly with increasing angle prior to dynamic stall.When the AOA reaches the stall angle,the lift and drag coefficients decline suddenly due to the interplay between the first leading-and trailing-edge vortex.With further increase of the AOA,both the lift and drag coefficients experience a secondary rise and fall process because of formation and shedding of the secondary vortex.The results also reveal that the dynamic behavior of the flow structures can be effectively identified using the finite-time Lyapunov exponent (FTLE) field.The influence of the reduced frequency on the flow structures and energy extraction efficiency in the dynamic stall process is further discussed.When the reduced frequency increases,the dynamic stall is delayed and the total energy extraction efficiency is enhanced.With K =0.05,the amplitude of the dynamic coefficients fluctuates more significantly in the poststall process than in the case of K =0.1.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10272021, 10572021） and the Doctoral Programme Foundation of Institution of Higher Education of China （Grant No 20040007022）.
文摘This paper presents an inverse problem in analytical dynamics. The inverse problem is to construct the Lagrangian when the integrals of a system are given. Firstly, the differential equations are obtained by using the time derivative of the integrals. Secondly, the differential equations can be written in the Lagrange equations under certain conditions and the Lagrangian can be obtained. Finally, two examples are given to illustrate the application of the result.
文摘Recently,the notion of non-standard Lagrangians was discussed widely in literature in an attempt to explore the inverse variational problem of nonlinear differential equations.Different forms of non-standard Lagrangians were introduced in literature and have revealed nice mathematical and physical properties.One interesting form related to the inverse variational problem is the logarithmic Lagrangian,which has a number of motivating features related to the Li′enard-type and Emden nonlinear differential equations.Such types of Lagrangians lead to nonlinear dynamics based on non-standard Hamiltonians.In this communication,we show that some new dynamical properties are obtained in stellar dynamics if standard Lagrangians are replaced by Logarithmic Lagrangians and their corresponding non-standard Hamiltonians.One interesting consequence concerns the emergence of an extra pressure term,which is related to the gravitational field suggesting that gravitation may act as a pressure in a strong gravitational field.The case of the stellar halo of the Milky Way is considered.
文摘This paper presents the fractional-order dynamics of the double pendulum by means of fractional-order modeling. Equations of motion have been derived for cases with and without external forcing. Generalized force terms have been obtained for five different cases of forcing. Both integer and fractional-order analysis have been carried out. Phase diagrams have been plotted to visualize the effect of fractional order approach. The originality of this work arises from the fact that the double pendulum has been modeled with the fractional dynamics approach. The governing equations of motion of the system have been obtained through fractional variational principles.
基金Project supported by the National Natural Science Foundation of China(Grant No.11371117).
文摘This paper considers fluid mixing driven by inflows connected to a circular shallow lake using a numerical framework consisting of a shallow water hydrodynamic model and a passive particle-tracking model.With the flow field driven by alternate inflows predicted by a shallow water model,particle trajectories are traced out using a particle tracking model.The horizontal fluid mixing dynamics are then interpreted using dynamics system analysis approaches including finite-time Lyapunov exponent(FTLE)and Lagrangian coherent structure(LCS).From the simulation results,it is confirmed that periodic inflows are able to create a weak dynamic system in an idealised circular lake,with the particle dynamics controlled by a single dimensionless parameter associated with the inflow duration.The mixing and transport property of the lake changes from regular to chaotic as the value of the dimensionless parameter increases until global chaotic particle dynamics is achieved.By further analysing the advection of particles injected continuously to the inflows(freshwater),the fate of“freshwater”particles in a“polluted”lake is tracked and revealed.The results provide useful guidance for engineering applications,i.e.,transferring freshwater from rivers to improve the water quality in polluted water bodies such as lakes.The presented approach will be able to facilitate the design of‘optimised’schemes for such engineering implementation.
基金This work is partially supported by National natural science fund of China(No.91430213 and No.11571293)Hunan Provincial Innovation Foundation for Postgraduate(No.CX2015B208)。
文摘Semi-Lagrangian(S-L)methods have no CFL stability constraint,and are more stable than the Eulerian methods.In the literature,the S-L method for the levelset re-initialization equation was complicated,which may be unnecessary.Since the re-initialization procedure is auxiliary,we propose to use the first-order S-L scheme coupled with a projection technique to improve the accuracy at the grid points just adjacent to the interface.Standard second-order S-L method is used for evolving the level-set convection equation.The implementation is simple,including on the block-structured adaptive mesh.The efficiency of the S-L method is demonstrated by extensive numerical examples including passive convection of interfaces with corners/kinks/large deformation under given velocity fields,a geometrical flow with topological changes,simulations of bubble/droplet dynamics in incompressible twophase flows.In terms of accuracy it is comparable to the other existing methods.
