The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations ...The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.展开更多
We construct new unidirectional coupling schemes for autonomous and nonautonomous drive systems, respectively. Each of these schemes makes the state of the response system asymptotically approach the first-order deriv...We construct new unidirectional coupling schemes for autonomous and nonautonomous drive systems, respectively. Each of these schemes makes the state of the response system asymptotically approach the first-order derivative of the state of the driver. From the point of view of geometry, the first-order derivative of the state of the driver can be viewed as a tangent vector of the trajectory of the driver, so the proposed schemes are named tangent response schemes. Numerical simulations of the Lorenz system and the forced Duffing oscillator verify the validity of the tangent response schemes. We further point out that the tangent response can be interpreted as a special kind of generalised synchronisation, thereby explaining why the response system can exhibit rich geometrical structures in its state space.展开更多
A mechanistic understanding and modeling of the coupled human and natural systems(CHANS)are frontier of geographical sciences and essential for promoting regional sustainability.Modeling regional CHANS in the Yellow R...A mechanistic understanding and modeling of the coupled human and natural systems(CHANS)are frontier of geographical sciences and essential for promoting regional sustainability.Modeling regional CHANS in the Yellow River Basin(YRB)featuring high water stress,intense human interference,and a fragile ecosystem has always been a complex challenge.Here,we propose a conceptual modeling framework to capture key human-natural components and their interactions,focusing on human-water dynamics.The modeling framework encompasses five human(Population,Economy,Energy,Food,and Water Demand)and five natural sectors(Water Supply,Sediment,Land,Carbon,and Climate)that can be either fully interactive or standalone.The modeling framework,implemented using the system dynamics(SD)approach,can well reproduce the basin's historical evolution in human-natural processes and predict future dynamics under various scenarios.The flexibility,adaptability,and potential for integration with diverse methods position the framework as an instructive tool for guiding regional CHANS modeling.Our insights highlight pathways to advance regional CHANS modeling and its application to address regional sustainability challenges.展开更多
With the floating structures pushing their activities to the ultra-deep water, model tests have presented a challenge due to the limitation of the existing wave basins. Therefore, the concept of truncated mooring syst...With the floating structures pushing their activities to the ultra-deep water, model tests have presented a challenge due to the limitation of the existing wave basins. Therefore, the concept of truncated mooring system is implemented to replace the full depth mooring system in the model tests, which aims to have the same dynamic responses as the full depth system. The truncated mooring system plays such a significant role that extra attention should be paid to the mooring systems with large truncation factor. Three different types of large truncation factor mooring system are being employed in the simulations, including the homogenously truncated mooring system, non-homogenously truncated mooring system and simplified truncated mooring system. A catenary moored semi-submersible operating at 1000 m water depth is presented. In addition, truncated mooring systems are proposed at the truncated water depth of 200 m. In order to explore the applicability of these truncated mooring systems, numerical simulations of the platform’s surge free decay interacting with three different styles of truncated mooring systems are studied in calm water. Furthermore, the mooring-induced damping of the truncated mooring systems is simulated in the regular wave. Finally, the platform motion responses and mooring line dynamics are simulated in irregular wave. All these simulations are implemented by employing full time domain coupled dynamic analysis, and the results are compared with those of the full depth simulations in the same cases. The results show that the mooring-induced damping plays a significant role in platform motion responses, and all truncated mooring systems are suitable for model tests with appropriate truncated mooring line diameters. However, a large diameter is needed for simplified truncated mooring lines. The suggestions are given to the selection of truncated mooring system for different situations as well as to the truncated mooring design criteria.展开更多
The dynamical character for a perturbed coupled nonlinear Schrodinger system with periodic boundary condition was studied. First, the dynamical character of perturbed and unperturbed systems on the invariant plane was...The dynamical character for a perturbed coupled nonlinear Schrodinger system with periodic boundary condition was studied. First, the dynamical character of perturbed and unperturbed systems on the invariant plane was analyzed by the spectrum of the linear operator. Then the existence of the locally invariant manifolds was proved by the singular perturbation theory and the fixed-point argument.展开更多
This paper presents the problem of generating four-wing （eight-wing） chaotic attractors. The adopted method consists in suitably coupling two （three） identical Lorenz systems. In analogy with the original Lorenz s...This paper presents the problem of generating four-wing （eight-wing） chaotic attractors. The adopted method consists in suitably coupling two （three） identical Lorenz systems. In analogy with the original Lorenz system, where the two wings of the butterfly attractor are located around the two equilibria with the unstable pair of complex-conjugate eigenvalues, this paper shows that the four wings （eight wings） of these novel attractors axe located around the four （eight） equilibria with two （three） pairs of unstable complex-conjugate eigenvalues.展开更多
The dynamic behaviour of the two-site coupled cavities model which is doped with ta wo-level system is investi-gated. The exact dynamic solutions in the general condition are obtained via Laplace transform. The simple...The dynamic behaviour of the two-site coupled cavities model which is doped with ta wo-level system is investi-gated. The exact dynamic solutions in the general condition are obtained via Laplace transform. The simple analytical solutions are obtained in several particular cases, which demonstrate the clear and simple physical picture for the quan-tum state transition of the system. In the large detuning or hoppling case, the quantum states transferring between qubits follow a slow periodic oscillation induced by the very weak excitation of the cavity mode. In the large coupling case, the system can be interpreted as two Jaynes-Cummings model subsystems which interact through photon hop between the two cavities. In the case of λ≈△〉〉 g, the quantum states transition of qubits is accompanied by the excitation of the cavity, and the cavity modes have the same dynamic behaviours and the amplitude of probability is equM to 0.25 which does not change with the variation of parameter.展开更多
To systematically study the vehicle-bridge coupled dynamic response and its change rule with different parameters, a vehicle model with seven degrees of freedom was built and the total potential energy of vehicle spac...To systematically study the vehicle-bridge coupled dynamic response and its change rule with different parameters, a vehicle model with seven degrees of freedom was built and the total potential energy of vehicle space vibration system was deduced. Considering the stimulation of road roughness, the dynamic response equation of vehicle-bridge coupled system was established in accordance with the elastic system principle of total potential energy with stationary value and the ＂set-in-right-position＂ rule. On the basis of the self-compiled Fortran program and bridge engineering, the dynamic response of long- span continuous girder bridge under vehicle load was studied. This study also included the calculation of vehicle impact coefficient, evaluation of vibration comfort, and analysis of dynamic response parameters. Results show the impact coefficient changes with lane number and is larger than the value calculated by the ＂general code for design of highway bridges and culverts （China）＂. The Dieckmann index of bridge vibration is also related to lane number, and the vibration comfort evaluation is good in normal conditions. The relevant conclusions from parametric analyses have practical significance to dynamic design and daily operation of long-span continuous girder bridges in expressways. Safety and comfort are expected to improve significantly with further control of the vibration of vehicle-bridge system.展开更多
In order to present a dynamic analysis method for the rigid-flexible coupled bar linkage system(RFCBLS),the flexible element motion equation was gotten by Lagrange Equation and the rigid element motion equation was go...In order to present a dynamic analysis method for the rigid-flexible coupled bar linkage system(RFCBLS),the flexible element motion equation was gotten by Lagrange Equation and the rigid element motion equation was gotten based on rigid constraint conditions.The multi-body system(MBS) is a complex mechanism and its components have quite different rigidities.If it is considered as a rigid MBS(RMBS) to do its dynamic analysis,elastic deformation's ignorance will lead to inaccurate analysis.If it is considered as a flexible MBS(FMBS) to establish,analyze,and solve the model,quite large system equations make it difficult to solve.The better method is as follows:the complex mechanism system is regarded as a rigid-flexible coupled system(RFCS) to make dynamic characteristic of rigid components be equivalent,system equation is established by FMBS' way,and system equation dimensions are reduced by transition matrices' introduction.A dynamic analysis method for rigid element and flexible element coupling was presented based on the FMBS.The analyzed crank slide-block mechanism results show that the dynamic analysis method for RFCBLS is quick and convenient.展开更多
Based on the deformation theory of elastic beams, the coupling effect between the coupling displacements of a point on the middle line of beam and large overall motion is presented. The 'coupling matrix library...Based on the deformation theory of elastic beams, the coupling effect between the coupling displacements of a point on the middle line of beam and large overall motion is presented. The 'coupling matrix library' and Jourdain's variation principle and single direction recursive formulation method are used to establish the general coupling dynamical equations of flexible multibody system. Two typical examples show the coupling effect between coupling displacements and large overall motion on the dynamics of flexible multibody system consisting of beams.展开更多
For establishing the refined numerical simulation model for coupled vibration between vehicle and bridge, the refined three-dimensional vehicle model is setup by multi-body system dynamics method, and finite element m...For establishing the refined numerical simulation model for coupled vibration between vehicle and bridge, the refined three-dimensional vehicle model is setup by multi-body system dynamics method, and finite element method of dynamic model is adopted to model the bridge. Taking Yujiang River Bridge on Nanning-Guangzhou railway line in China as study background, the?refined numerical simulation model of whole vehicle and whole bridge system for coupled vibration analysis is set up. The dynamic analysis model of the cable-stayed bridge is established by finite element method, and the natural vibration properties of the bridge are analyzed. The German ICE Electric Multiple Unit (EMU) train refined three-dimensional space vehicle model is set up by multi-system dynamics software SIMPACK, and the multiple non-linear properties are considered. The space vibration responses are calculated by co-simulation based on multi-body system dynamics and finite element method when the ICE EMU train passes the long span cable-stayed bridge at different speeds. In order to test if the bridge has the sufficient lateral or vertical rigidity and the operation stability is fine. The calculation results show: The operation safety can be guaranteed, and comfort?index is “excellent”. The bridge has sufficient rigidity, and vibration is in good condition.展开更多
This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is trans...This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when all subnetworks are synchronizable, a delay-dependent sufficient condition is given in terms of linear matrix inequalities （LMIs） which guarantees the solvability of the synchronization problem under an average dwell time scheme. We extend this result to the case that not all subnetworks are synchronizable. It is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfy an extra condition, then the problem is also solvable. Two numerical examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.展开更多
The flight-structural dynamics of a high-aspect-ratio wing challenge the flight control design.This paper develops a reduced model of coupled dynamics with stability consideration.The structural dynamics are formulate...The flight-structural dynamics of a high-aspect-ratio wing challenge the flight control design.This paper develops a reduced model of coupled dynamics with stability consideration.The structural dynamics are formulated with dihedrals,and the central loads drive the deformation.The control-oriented model with essential coupled dynamics is formulated.Modal sensitivity anal-ysis and input–output pairing are performed to identify the control structure.Besides,an example of flight control design is provided to discuss the necessity of considering structural dynamics in controller design.Analytical coupled flight dynamics provide a system-theoretic approach for sta-bility and facilitate model-based control techniques.Simulation results reveal the characteristics of flight-structural coupled dynamics and demonstrate that the influence of flexible modes should be considered in control design,especially in lateral dynamics.展开更多
Rock drilling machine,INSTRON testing system,and SHPB device are updated to investigate the characteristics of rocks at great depth,with high loads from overburden,tectonic stresses and dynamic impacts due to blasting...Rock drilling machine,INSTRON testing system,and SHPB device are updated to investigate the characteristics of rocks at great depth,with high loads from overburden,tectonic stresses and dynamic impacts due to blasting and boring.It is verified that these testing systems can be used to study the mechanical properties of rock material under coupled static and dynamic loading condition and give useful guidance for the deep mining and underground cavern excavation.Various tests to determine the rock strength,fragmentation behavior,and energy absorption were conducted using the updated testing systems.It is shown that under coupled static-dynamic loads,if the axial prestress is lower than its elastic limit,the rock strength is higher than the individual static or dynamic strength.At the same axial prestress,rock strength under coupled loads rises with the increasing strain rates.Under coupled static and dynamic loads,rock is observed to fail with tensile mode.While shear failure may exist if axial prestress is high enough.In addition,it is shown that the percentage of small particles increases with the increasing axial prestress and impact load based on the analysis of the particle-size distribution of fragments.It is also suggested that the energy absorption ratio of a specimen varies with coupled loads,and the maximum energy absorption ratio for a rock can be obtained with an appropriate combination of static and dynamic loads.展开更多
In this paper, the synchronization problem of three homodromy coupled exciters in a non-resonant vibrating system of plane motion is studied. By introducing the average method of modified small parameters, we deduced ...In this paper, the synchronization problem of three homodromy coupled exciters in a non-resonant vibrating system of plane motion is studied. By introducing the average method of modified small parameters, we deduced dimensionless coupling equation of three exciters, which converted the problem of synchronization into that of the existence and stability of zero solutions for the average differential equations of the small parameters. Based on the dimensionless coupling torques and characteristics of the cor- responding limited functions, the synchronization criterion for three exciters was derived as the absolute value of dimensionless residual torque difference between arbitrary two motors being less than the maximum of their dimensionless coupling torques. The stability criterion of its synchronous state lies in the double-condition that the inertia coupling matrix is positive definite and all its elements are positive as well. The synchronization determinants are the coefficients of synchronization ability, also called as the general dynamical symmetry coefficients. The double-equilibrium state of the vibrating system is manifested by numeric method, and the numeric and simulation results derived thereof indicate the indispensable and crucial role the structural parameters of the vibrating system play in the stability criterion of synchronous operation. Besides, by adjusting its structural parameters, the elliptical motion of the vibrating system successfully met the requirements in engineering applications.展开更多
Dynamic optimization of electromechanical coupling system is a significant engineering problem in the field of mechatronics. The performance improvement of electromechanical equipment depends on the system design para...Dynamic optimization of electromechanical coupling system is a significant engineering problem in the field of mechatronics. The performance improvement of electromechanical equipment depends on the system design parameters. Aiming at the spindle unit of refitted machine tool for solid rocket, the vibration acceleration of tool is taken as objective function, and the electromechanical system design parameters are appointed as design variables. Dynamic optimization model is set up by adopting Lagrange-Maxwell equations, Park transform and electromechanical system energy equations. In the procedure of seeking high efficient optimization method, exponential function is adopted to be the weight function of particle swarm optimization algorithm. Exponential inertia weight particle swarm algorithm（EPSA）, is formed and applied to solve the dynamic optimization problem of electromechanical system. The probability density function of EPSA is presented and used to perform convergence analysis. After calculation, the optimized design parameters of the spindle unit are obtained in limited time period. The vibration acceleration of the tool has been decreased greatly by the optimized design parameters. The research job in the paper reveals that the problem of dynamic optimization of electromechanical system can be solved by the method of combining system dynamic analysis with reformed swarm particle optimizati on. Such kind of method can be applied in the design of robots, NC machine, and other electromechanical equipments.展开更多
In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration...In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration, the equations of motion of the coupled two-pipe system are obtained. The two coupled nonlinear partial differential equations, discretized using the fourth- order Galerkin method, are solved by a fourth-order Runge-Kutta integration algorithm. Results show that the connection stiffness has a significant effect on the dynamical behavior of the coupled system. It is found that for some parameter values the motion types of the two pipes might be synchronous.展开更多
Considering the axial and radial loads, a math- ematical model of angular contact ball bearing is deduced with Hertz contact theory. With the coupling effects of lateral, torsional and axial vibrations taken into acco...Considering the axial and radial loads, a math- ematical model of angular contact ball bearing is deduced with Hertz contact theory. With the coupling effects of lateral, torsional and axial vibrations taken into account, a lumped-parameter nonlinear dynamic model of helical gearrotor-bearing system （HGRBS） is established to obtain the transmission system dynamic response to the changes of dif- ferent parameters. The vibration differential equations of the drive system are derived through the Lagrange equation, which considers the kinetic and potential energies, the dis- sipative function and the internal/external excitation. Based on the Runge-Kutta numerical method, the dynamics of the HGRBS is investigated, which describes vibration properties of HGRBS more comprehensively. The results show that the vibration amplitudes have obvious fluctuation, and the frequency multiplication and random frequency components become increasingly obvious with changing rotational speed and eccentricity at gear and bearing positions. Axial vibration of the HGRBS also has some fluctuations. The bearing has self-variable stiffness frequency, which should be avoided in engineering design. In addition, the bearing clearance needs little attention due to its slightly discernible effect on vibration response. It is suggested that a careful examination should be made in modelling the nonlinear dynamic behavior of a helical gear-rotor-bearing system.展开更多
The existence of rolling deformation area in the rolling mill system is the main characteristic which dis- tinguishes the other machinery. In order to analyze the dynamic property of roll system＇s flexural deformatio...The existence of rolling deformation area in the rolling mill system is the main characteristic which dis- tinguishes the other machinery. In order to analyze the dynamic property of roll system＇s flexural deformation, it is necessary to consider the transverse periodic movement of stock in the rolling deformation area which is caused by the flexural deformation movement of roll system simul- taneously. Therefore, the displacement field of roll system and flow of metal in the deformation area is described by kinematic analysis in the dynamic system. Through intro- ducing the lateral displacement function of metal in the deformation area, the dynamic variation of per unit width rolling force can be determined at the same time. Then the coupling law caused by the co-effect of rigid movement and flexural deformation of the system structural elements is determined. Furthermore, a multi-parameter coupling dynamic model of the roll system and stock is established by the principle of virtual work. More explicitly, the cou- pled motion modal analysis was made for the roll system. Meanwhile, the analytical solutions for the flexural defor- mation movement＇s mode shape functions of rolls are discussed. In addition, the dynamic characteristic of the lateral flow of metal in the rolling deformation area has been analyzed at the same time. The establishment ofdynamic lateral displacement function of metal in the deformation area makes the foundation for analyzing the coupling law between roll system and rolling deformation area, and provides a theoretical basis for the realization of the dynamic shape control of steel strip.展开更多
Nonlinear coupled dynamics of a liquid-filled spherical container in microgravity are investigated. The governing equations of the low-gravity liquid sloshing in a convex axisymmetrical container subjected to lateral ...Nonlinear coupled dynamics of a liquid-filled spherical container in microgravity are investigated. The governing equations of the low-gravity liquid sloshing in a convex axisymmetrical container subjected to lateral excitation is obtained by the variational principle and solved with a modal analysis method. The variational formulas are transformed into a frequency equation in the form of a standard eigenvalue problem by the Galerkin method, in which admissible functions for the velocity potential and the liquid flee surface displacement are determined analytically in terms of the Gaussian hypergeometric series. The coupled dynamic equations of the liquid-filled container are derived using the Lagrange＇s method and are numerically solved. The time histories of the modal solutions are obtained in numerical simulations.展开更多
基金supported by the National Key R&D Program of China(Grant No.2022YFA1604200)the National Natural Science Foundation of China(Grant No.12261131495)Institute of Systems Science,Beijing Wuzi University(Grant No.BWUISS21).
文摘The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.
文摘We construct new unidirectional coupling schemes for autonomous and nonautonomous drive systems, respectively. Each of these schemes makes the state of the response system asymptotically approach the first-order derivative of the state of the driver. From the point of view of geometry, the first-order derivative of the state of the driver can be viewed as a tangent vector of the trajectory of the driver, so the proposed schemes are named tangent response schemes. Numerical simulations of the Lorenz system and the forced Duffing oscillator verify the validity of the tangent response schemes. We further point out that the tangent response can be interpreted as a special kind of generalised synchronisation, thereby explaining why the response system can exhibit rich geometrical structures in its state space.
基金supported by the National Natural Science Foundation of China(Grant No.42041007)the Fundamental Research Funds for the Central Universities。
文摘A mechanistic understanding and modeling of the coupled human and natural systems(CHANS)are frontier of geographical sciences and essential for promoting regional sustainability.Modeling regional CHANS in the Yellow River Basin(YRB)featuring high water stress,intense human interference,and a fragile ecosystem has always been a complex challenge.Here,we propose a conceptual modeling framework to capture key human-natural components and their interactions,focusing on human-water dynamics.The modeling framework encompasses five human(Population,Economy,Energy,Food,and Water Demand)and five natural sectors(Water Supply,Sediment,Land,Carbon,and Climate)that can be either fully interactive or standalone.The modeling framework,implemented using the system dynamics(SD)approach,can well reproduce the basin's historical evolution in human-natural processes and predict future dynamics under various scenarios.The flexibility,adaptability,and potential for integration with diverse methods position the framework as an instructive tool for guiding regional CHANS modeling.Our insights highlight pathways to advance regional CHANS modeling and its application to address regional sustainability challenges.
基金financially supported by the National Natural Science Foundation of China(Grant No.51379095)
文摘With the floating structures pushing their activities to the ultra-deep water, model tests have presented a challenge due to the limitation of the existing wave basins. Therefore, the concept of truncated mooring system is implemented to replace the full depth mooring system in the model tests, which aims to have the same dynamic responses as the full depth system. The truncated mooring system plays such a significant role that extra attention should be paid to the mooring systems with large truncation factor. Three different types of large truncation factor mooring system are being employed in the simulations, including the homogenously truncated mooring system, non-homogenously truncated mooring system and simplified truncated mooring system. A catenary moored semi-submersible operating at 1000 m water depth is presented. In addition, truncated mooring systems are proposed at the truncated water depth of 200 m. In order to explore the applicability of these truncated mooring systems, numerical simulations of the platform’s surge free decay interacting with three different styles of truncated mooring systems are studied in calm water. Furthermore, the mooring-induced damping of the truncated mooring systems is simulated in the regular wave. Finally, the platform motion responses and mooring line dynamics are simulated in irregular wave. All these simulations are implemented by employing full time domain coupled dynamic analysis, and the results are compared with those of the full depth simulations in the same cases. The results show that the mooring-induced damping plays a significant role in platform motion responses, and all truncated mooring systems are suitable for model tests with appropriate truncated mooring line diameters. However, a large diameter is needed for simplified truncated mooring lines. The suggestions are given to the selection of truncated mooring system for different situations as well as to the truncated mooring design criteria.
文摘The dynamical character for a perturbed coupled nonlinear Schrodinger system with periodic boundary condition was studied. First, the dynamical character of perturbed and unperturbed systems on the invariant plane was analyzed by the spectrum of the linear operator. Then the existence of the locally invariant manifolds was proved by the singular perturbation theory and the fixed-point argument.
文摘This paper presents the problem of generating four-wing （eight-wing） chaotic attractors. The adopted method consists in suitably coupling two （three） identical Lorenz systems. In analogy with the original Lorenz system, where the two wings of the butterfly attractor are located around the two equilibria with the unstable pair of complex-conjugate eigenvalues, this paper shows that the four wings （eight wings） of these novel attractors axe located around the four （eight） equilibria with two （three） pairs of unstable complex-conjugate eigenvalues.
基金Project supported by the Science and Technology Plan of Hunan Province,China (Grant No. 2010FJ3081)the Natural Science Foundation of Hunan Province of China (Grant No. 11JJ3003)
文摘The dynamic behaviour of the two-site coupled cavities model which is doped with ta wo-level system is investi-gated. The exact dynamic solutions in the general condition are obtained via Laplace transform. The simple analytical solutions are obtained in several particular cases, which demonstrate the clear and simple physical picture for the quan-tum state transition of the system. In the large detuning or hoppling case, the quantum states transferring between qubits follow a slow periodic oscillation induced by the very weak excitation of the cavity mode. In the large coupling case, the system can be interpreted as two Jaynes-Cummings model subsystems which interact through photon hop between the two cavities. In the case of λ≈△〉〉 g, the quantum states transition of qubits is accompanied by the excitation of the cavity, and the cavity modes have the same dynamic behaviours and the amplitude of probability is equM to 0.25 which does not change with the variation of parameter.
基金provided by the National Natural Science Foundation of China (51378504)Funding Project of Traffic Science and Technology Program of Hunan Province (201022)
文摘To systematically study the vehicle-bridge coupled dynamic response and its change rule with different parameters, a vehicle model with seven degrees of freedom was built and the total potential energy of vehicle space vibration system was deduced. Considering the stimulation of road roughness, the dynamic response equation of vehicle-bridge coupled system was established in accordance with the elastic system principle of total potential energy with stationary value and the ＂set-in-right-position＂ rule. On the basis of the self-compiled Fortran program and bridge engineering, the dynamic response of long- span continuous girder bridge under vehicle load was studied. This study also included the calculation of vehicle impact coefficient, evaluation of vibration comfort, and analysis of dynamic response parameters. Results show the impact coefficient changes with lane number and is larger than the value calculated by the ＂general code for design of highway bridges and culverts （China）＂. The Dieckmann index of bridge vibration is also related to lane number, and the vibration comfort evaluation is good in normal conditions. The relevant conclusions from parametric analyses have practical significance to dynamic design and daily operation of long-span continuous girder bridges in expressways. Safety and comfort are expected to improve significantly with further control of the vibration of vehicle-bridge system.
基金Key Laboratory of Fundamental Science for National Defense,China(No. HIT. KLOF. 2009058)
文摘In order to present a dynamic analysis method for the rigid-flexible coupled bar linkage system(RFCBLS),the flexible element motion equation was gotten by Lagrange Equation and the rigid element motion equation was gotten based on rigid constraint conditions.The multi-body system(MBS) is a complex mechanism and its components have quite different rigidities.If it is considered as a rigid MBS(RMBS) to do its dynamic analysis,elastic deformation's ignorance will lead to inaccurate analysis.If it is considered as a flexible MBS(FMBS) to establish,analyze,and solve the model,quite large system equations make it difficult to solve.The better method is as follows:the complex mechanism system is regarded as a rigid-flexible coupled system(RFCS) to make dynamic characteristic of rigid components be equivalent,system equation is established by FMBS' way,and system equation dimensions are reduced by transition matrices' introduction.A dynamic analysis method for rigid element and flexible element coupling was presented based on the FMBS.The analyzed crank slide-block mechanism results show that the dynamic analysis method for RFCBLS is quick and convenient.
基金the National Natural Science Foundation of China(No.19832040)
文摘Based on the deformation theory of elastic beams, the coupling effect between the coupling displacements of a point on the middle line of beam and large overall motion is presented. The 'coupling matrix library' and Jourdain's variation principle and single direction recursive formulation method are used to establish the general coupling dynamical equations of flexible multibody system. Two typical examples show the coupling effect between coupling displacements and large overall motion on the dynamics of flexible multibody system consisting of beams.
文摘For establishing the refined numerical simulation model for coupled vibration between vehicle and bridge, the refined three-dimensional vehicle model is setup by multi-body system dynamics method, and finite element method of dynamic model is adopted to model the bridge. Taking Yujiang River Bridge on Nanning-Guangzhou railway line in China as study background, the?refined numerical simulation model of whole vehicle and whole bridge system for coupled vibration analysis is set up. The dynamic analysis model of the cable-stayed bridge is established by finite element method, and the natural vibration properties of the bridge are analyzed. The German ICE Electric Multiple Unit (EMU) train refined three-dimensional space vehicle model is set up by multi-system dynamics software SIMPACK, and the multiple non-linear properties are considered. The space vibration responses are calculated by co-simulation based on multi-body system dynamics and finite element method when the ICE EMU train passes the long span cable-stayed bridge at different speeds. In order to test if the bridge has the sufficient lateral or vertical rigidity and the operation stability is fine. The calculation results show: The operation safety can be guaranteed, and comfort?index is “excellent”. The bridge has sufficient rigidity, and vibration is in good condition.
基金the National Natural Science Foundation of China (No.60874024, 60574013).
文摘This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when all subnetworks are synchronizable, a delay-dependent sufficient condition is given in terms of linear matrix inequalities （LMIs） which guarantees the solvability of the synchronization problem under an average dwell time scheme. We extend this result to the case that not all subnetworks are synchronizable. It is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfy an extra condition, then the problem is also solvable. Two numerical examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.
基金co-supported by the Natural Science Founda-tion of Jiangsu Province,China(No.BK20200437)the National Natural Science Foundation of China(No.62103187)the Fundamental Research Funds for the Cen-tral Universities,China(No.NT2022025).
文摘The flight-structural dynamics of a high-aspect-ratio wing challenge the flight control design.This paper develops a reduced model of coupled dynamics with stability consideration.The structural dynamics are formulated with dihedrals,and the central loads drive the deformation.The control-oriented model with essential coupled dynamics is formulated.Modal sensitivity anal-ysis and input–output pairing are performed to identify the control structure.Besides,an example of flight control design is provided to discuss the necessity of considering structural dynamics in controller design.Analytical coupled flight dynamics provide a system-theoretic approach for sta-bility and facilitate model-based control techniques.Simulation results reveal the characteristics of flight-structural coupled dynamics and demonstrate that the influence of flexible modes should be considered in control design,especially in lateral dynamics.
基金Supported by the National Natural Science Foundation of China (10872218,50934006,50534030)Research Foundation for the Doctoral Program of Higher Education of China (200805331143)
文摘Rock drilling machine,INSTRON testing system,and SHPB device are updated to investigate the characteristics of rocks at great depth,with high loads from overburden,tectonic stresses and dynamic impacts due to blasting and boring.It is verified that these testing systems can be used to study the mechanical properties of rock material under coupled static and dynamic loading condition and give useful guidance for the deep mining and underground cavern excavation.Various tests to determine the rock strength,fragmentation behavior,and energy absorption were conducted using the updated testing systems.It is shown that under coupled static-dynamic loads,if the axial prestress is lower than its elastic limit,the rock strength is higher than the individual static or dynamic strength.At the same axial prestress,rock strength under coupled loads rises with the increasing strain rates.Under coupled static and dynamic loads,rock is observed to fail with tensile mode.While shear failure may exist if axial prestress is high enough.In addition,it is shown that the percentage of small particles increases with the increasing axial prestress and impact load based on the analysis of the particle-size distribution of fragments.It is also suggested that the energy absorption ratio of a specimen varies with coupled loads,and the maximum energy absorption ratio for a rock can be obtained with an appropriate combination of static and dynamic loads.
基金supported by the National Key Technology R&D Program (2009BAG12A01-F01-3)the National Natural Science Foundation of China (51075063)
文摘In this paper, the synchronization problem of three homodromy coupled exciters in a non-resonant vibrating system of plane motion is studied. By introducing the average method of modified small parameters, we deduced dimensionless coupling equation of three exciters, which converted the problem of synchronization into that of the existence and stability of zero solutions for the average differential equations of the small parameters. Based on the dimensionless coupling torques and characteristics of the cor- responding limited functions, the synchronization criterion for three exciters was derived as the absolute value of dimensionless residual torque difference between arbitrary two motors being less than the maximum of their dimensionless coupling torques. The stability criterion of its synchronous state lies in the double-condition that the inertia coupling matrix is positive definite and all its elements are positive as well. The synchronization determinants are the coefficients of synchronization ability, also called as the general dynamical symmetry coefficients. The double-equilibrium state of the vibrating system is manifested by numeric method, and the numeric and simulation results derived thereof indicate the indispensable and crucial role the structural parameters of the vibrating system play in the stability criterion of synchronous operation. Besides, by adjusting its structural parameters, the elliptical motion of the vibrating system successfully met the requirements in engineering applications.
基金supported by National Natural Science Foundation of China (Grant No. 50675095)
文摘Dynamic optimization of electromechanical coupling system is a significant engineering problem in the field of mechatronics. The performance improvement of electromechanical equipment depends on the system design parameters. Aiming at the spindle unit of refitted machine tool for solid rocket, the vibration acceleration of tool is taken as objective function, and the electromechanical system design parameters are appointed as design variables. Dynamic optimization model is set up by adopting Lagrange-Maxwell equations, Park transform and electromechanical system energy equations. In the procedure of seeking high efficient optimization method, exponential function is adopted to be the weight function of particle swarm optimization algorithm. Exponential inertia weight particle swarm algorithm（EPSA）, is formed and applied to solve the dynamic optimization problem of electromechanical system. The probability density function of EPSA is presented and used to perform convergence analysis. After calculation, the optimized design parameters of the spindle unit are obtained in limited time period. The vibration acceleration of the tool has been decreased greatly by the optimized design parameters. The research job in the paper reveals that the problem of dynamic optimization of electromechanical system can be solved by the method of combining system dynamic analysis with reformed swarm particle optimizati on. Such kind of method can be applied in the design of robots, NC machine, and other electromechanical equipments.
基金Project supported by the National Natural Science Foundation of China(Nos.11172107 and 11172109)the Program for New Century Excellent Talents in University(No.NCET-11-0183)
文摘In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration, the equations of motion of the coupled two-pipe system are obtained. The two coupled nonlinear partial differential equations, discretized using the fourth- order Galerkin method, are solved by a fourth-order Runge-Kutta integration algorithm. Results show that the connection stiffness has a significant effect on the dynamical behavior of the coupled system. It is found that for some parameter values the motion types of the two pipes might be synchronous.
基金supported by the National Natural Science Fundation of China(51105063)the Fundamental Research Funds for the Central Universities(N120403004)
文摘Considering the axial and radial loads, a math- ematical model of angular contact ball bearing is deduced with Hertz contact theory. With the coupling effects of lateral, torsional and axial vibrations taken into account, a lumped-parameter nonlinear dynamic model of helical gearrotor-bearing system （HGRBS） is established to obtain the transmission system dynamic response to the changes of dif- ferent parameters. The vibration differential equations of the drive system are derived through the Lagrange equation, which considers the kinetic and potential energies, the dis- sipative function and the internal/external excitation. Based on the Runge-Kutta numerical method, the dynamics of the HGRBS is investigated, which describes vibration properties of HGRBS more comprehensively. The results show that the vibration amplitudes have obvious fluctuation, and the frequency multiplication and random frequency components become increasingly obvious with changing rotational speed and eccentricity at gear and bearing positions. Axial vibration of the HGRBS also has some fluctuations. The bearing has self-variable stiffness frequency, which should be avoided in engineering design. In addition, the bearing clearance needs little attention due to its slightly discernible effect on vibration response. It is suggested that a careful examination should be made in modelling the nonlinear dynamic behavior of a helical gear-rotor-bearing system.
基金Supported by National Natural Science Foundation of China(Grant No.51375424)
文摘The existence of rolling deformation area in the rolling mill system is the main characteristic which dis- tinguishes the other machinery. In order to analyze the dynamic property of roll system＇s flexural deformation, it is necessary to consider the transverse periodic movement of stock in the rolling deformation area which is caused by the flexural deformation movement of roll system simul- taneously. Therefore, the displacement field of roll system and flow of metal in the deformation area is described by kinematic analysis in the dynamic system. Through intro- ducing the lateral displacement function of metal in the deformation area, the dynamic variation of per unit width rolling force can be determined at the same time. Then the coupling law caused by the co-effect of rigid movement and flexural deformation of the system structural elements is determined. Furthermore, a multi-parameter coupling dynamic model of the roll system and stock is established by the principle of virtual work. More explicitly, the cou- pled motion modal analysis was made for the roll system. Meanwhile, the analytical solutions for the flexural defor- mation movement＇s mode shape functions of rolls are discussed. In addition, the dynamic characteristic of the lateral flow of metal in the rolling deformation area has been analyzed at the same time. The establishment ofdynamic lateral displacement function of metal in the deformation area makes the foundation for analyzing the coupling law between roll system and rolling deformation area, and provides a theoretical basis for the realization of the dynamic shape control of steel strip.
基金the National Natural Science Foundation of China(Nos.10572022,10772026)
文摘Nonlinear coupled dynamics of a liquid-filled spherical container in microgravity are investigated. The governing equations of the low-gravity liquid sloshing in a convex axisymmetrical container subjected to lateral excitation is obtained by the variational principle and solved with a modal analysis method. The variational formulas are transformed into a frequency equation in the form of a standard eigenvalue problem by the Galerkin method, in which admissible functions for the velocity potential and the liquid flee surface displacement are determined analytically in terms of the Gaussian hypergeometric series. The coupled dynamic equations of the liquid-filled container are derived using the Lagrange＇s method and are numerically solved. The time histories of the modal solutions are obtained in numerical simulations.
