The combined gradient representations for generalized Birkhoffian systems in event space are studied.Firstly,the definitions of six kinds of combined gradient systems and corresponding differential equations are given...The combined gradient representations for generalized Birkhoffian systems in event space are studied.Firstly,the definitions of six kinds of combined gradient systems and corresponding differential equations are given.Secondly,the conditions under which generalized Birkhoffian systems become combined gradient systems are obtained. Finally,the characteristics of combined gradient systems are used to study the stability of generalized Birkhoffian systems in event space. Seven examples are given to illustrate the results.展开更多
Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the general...Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized BirkhoiYian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.展开更多
In this paper, equilibrium stability of generalized Birkhoff's autonomous system is discussed. First, equilibrium equations of generalized Birkhoff's autonomous system are set up, and the n the linear approx...In this paper, equilibrium stability of generalized Birkhoff's autonomous system is discussed. First, equilibrium equations of generalized Birkhoff's autonomous system are set up, and the n the linear approximate method and direct method of stability in equilibrium st ate are studied. Some results on equilibrium of generalized Birkhoff's autonomou s system are obtained on the basis of Lyapunov's thorem. Last, the applica tion of the results is illustrated with an example.展开更多
We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law ...We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.展开更多
The skew-gradient representation of a generalized Birkhoffian system is studied. A condition under which the generalized Birkhoffian system can be considered as a skew-gradient system is obtained. The properties of th...The skew-gradient representation of a generalized Birkhoffian system is studied. A condition under which the generalized Birkhoffian system can be considered as a skew-gradient system is obtained. The properties of the skew-gradient system are used to study the properties, especially the stability, of the generalized Birkhoffian system. Some examples are given to illustrate the application of the result.展开更多
Two kinds of generalized gradient systems are proposed and the characteristics of the two systems are studied. The conditions under which a holonomic mechanical system can be considered as one of the two generalized g...Two kinds of generalized gradient systems are proposed and the characteristics of the two systems are studied. The conditions under which a holonomic mechanical system can be considered as one of the two generalized gradient systems are obtained. The characteristics of the generalized gradient systems can be used to study the stability of the holonomic system. Some examples are given to illustrate the application of the results.展开更多
Lattice constants, total energies, and densities of state of transition metals Co, Rh, and Ir in the VⅢB group with different crystalline structures were calculated via generalized gradient approximation （GGA） of t...Lattice constants, total energies, and densities of state of transition metals Co, Rh, and Ir in the VⅢB group with different crystalline structures were calculated via generalized gradient approximation （GGA） of the total energy plane wave pseudopotential method in first-principles. The lattice stabilities of Rh and Ir are ΔG^ bcc-hcp 〉 Δ G^fcc-hcp 〉 0, agreeing well with those of the projector augmented wave method in first-principles and the CALPHAD method in spite of elemental Co. Analyses of the electronic structures to lattice stability show that crystalline Rh and Ir with fcc structures have the obvious characteristic of a stable phase, agreeing with the results of total energy calculations. Analyses of atomic populations show that the transition rate of electrons from the s state to the p or d state for hcp, fcc, and bcc crystals of Co and Rh increases with the elemental period number to form a stronger cohesion, a higher cohesive energy, or a more stable lattice between atoms in heavier metals.展开更多
The system described by the generalized Birkhoff equations is called a generalized Birkhoffian system. In this paper, the condition under which the generalized Birkhoffian system can be a gradient system is given. The...The system described by the generalized Birkhoff equations is called a generalized Birkhoffian system. In this paper, the condition under which the generalized Birkhoffian system can be a gradient system is given. The stability of equilibrium of the generalized Birkhoffian system is discussed by using the properties of the gradient system. When there is a parameter in the equations, its influences on the stability and the bifurcation problem of the system are considered.展开更多
基金supported by the National Natural Science Foundation of China(No.11972241)the Natural Science Foundation of Jiangsu Province (No.BK20191454)the Scientific Research Foundation of Suzhou University of Science and Technology (No.XKZ2017005)。
文摘The combined gradient representations for generalized Birkhoffian systems in event space are studied.Firstly,the definitions of six kinds of combined gradient systems and corresponding differential equations are given.Secondly,the conditions under which generalized Birkhoffian systems become combined gradient systems are obtained. Finally,the characteristics of combined gradient systems are used to study the stability of generalized Birkhoffian systems in event space. Seven examples are given to illustrate the results.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10772025,10932002 and 10972127)the Natural Science Foundation of Henan Province,China(Grant No.102300410144)the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics,China
文摘Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized BirkhoiYian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.
文摘In this paper, equilibrium stability of generalized Birkhoff's autonomous system is discussed. First, equilibrium equations of generalized Birkhoff's autonomous system are set up, and the n the linear approximate method and direct method of stability in equilibrium st ate are studied. Some results on equilibrium of generalized Birkhoff's autonomou s system are obtained on the basis of Lyapunov's thorem. Last, the applica tion of the results is illustrated with an example.
基金Project supported by the National Natural Science Foundation of China(No.12172169)the Natural Sciences and Engineering Research Council of Canada(No.NSERC RGPIN-2023-03227)。
文摘We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.
基金Project supported by the National Natural Science Foundation of China(Grant No.11272050)
文摘The skew-gradient representation of a generalized Birkhoffian system is studied. A condition under which the generalized Birkhoffian system can be considered as a skew-gradient system is obtained. The properties of the skew-gradient system are used to study the properties, especially the stability, of the generalized Birkhoffian system. Some examples are given to illustrate the application of the result.
基金supported by the National Natural Science Foundation of China(Grant No.11272050)
文摘Two kinds of generalized gradient systems are proposed and the characteristics of the two systems are studied. The conditions under which a holonomic mechanical system can be considered as one of the two generalized gradient systems are obtained. The characteristics of the generalized gradient systems can be used to study the stability of the holonomic system. Some examples are given to illustrate the application of the results.
基金supported by the Doctoral Discipline Foundation of the Ministry of Education of China (No. 20070533118)the National Natural Science Foundation of China (No. 50871124)the Postdoctoral Foundation of Central South University
文摘Lattice constants, total energies, and densities of state of transition metals Co, Rh, and Ir in the VⅢB group with different crystalline structures were calculated via generalized gradient approximation （GGA） of the total energy plane wave pseudopotential method in first-principles. The lattice stabilities of Rh and Ir are ΔG^ bcc-hcp 〉 Δ G^fcc-hcp 〉 0, agreeing well with those of the projector augmented wave method in first-principles and the CALPHAD method in spite of elemental Co. Analyses of the electronic structures to lattice stability show that crystalline Rh and Ir with fcc structures have the obvious characteristic of a stable phase, agreeing with the results of total energy calculations. Analyses of atomic populations show that the transition rate of electrons from the s state to the p or d state for hcp, fcc, and bcc crystals of Co and Rh increases with the elemental period number to form a stronger cohesion, a higher cohesive energy, or a more stable lattice between atoms in heavier metals.
基金supported by the National Natural Science Foundation of China(Grant No.11272050)
文摘The system described by the generalized Birkhoff equations is called a generalized Birkhoffian system. In this paper, the condition under which the generalized Birkhoffian system can be a gradient system is given. The stability of equilibrium of the generalized Birkhoffian system is discussed by using the properties of the gradient system. When there is a parameter in the equations, its influences on the stability and the bifurcation problem of the system are considered.
