A discrete total variation calculus with variable time steps is presented for mechanico-electrical systems where there exist non-potential and dissipative forces. By using this discrete variation calculus, the symplec...A discrete total variation calculus with variable time steps is presented for mechanico-electrical systems where there exist non-potential and dissipative forces. By using this discrete variation calculus, the symplectic-energy-first integrators for mechanico-electrical systems are derived. To do this, the time step adaptation is employed. The discrete variational principle and the Euler-Lagrange equation are derived for the systems. By using this discrete algorithm it is shown that mechanico-electrical systems are not symplectic and their energies are not conserved unless they are Lagrange mechanico-electrical systems. A practical example is presented to illustrate these results.展开更多
The reinforcement effect of a reconstruction scheme for a steel factory building was investigated using finite element method and dynamic performance test. The workshop concerned is a portal frame structure with four ...The reinforcement effect of a reconstruction scheme for a steel factory building was investigated using finite element method and dynamic performance test. The workshop concerned is a portal frame structure with four spans and two slope roofs, of which ten columns need cutting for expanding span. The design and reconstruction project of column-cut supported by joist were introduced, which includes column reinforcement, connection rebuilding between brackets and crane beams, and the changing of rigid joint into hinge joint. The construction scheme was put forward in the light of the characteristics of the reinforcement and reconstruction. Spot test of dynamic performance on the workshop and comparison with theoretical analysis results show that the column-cut supported by joist design is effective and the reconstruction project is successful.展开更多
In this paper, we present a new method to obtain the Lie symmetries and conserved quantities of the discrete wave equation with the Ablowitz-Ladik-Lattice equations. Firstly, the wave equation is transformed into a si...In this paper, we present a new method to obtain the Lie symmetries and conserved quantities of the discrete wave equation with the Ablowitz-Ladik-Lattice equations. Firstly, the wave equation is transformed into a simple difference equation with the Ablowitz-Ladik-Lattice method. Secondly, according to the invariance of the discrete wave equation and the Ablowitz-Ladik-Lattice equations under infinitesimal transformation of dependent and independent variables, we derive the discrete determining equation and the discrete restricted equations. Thirdly, a series of the discrete analogs of conserved quantities, the discrete analogs of Lie groups, and the characteristic equations are obtained for the wave equation. Finally, we study a model of a biological macromolecule chain of mechanical behaviors, the Lie symmetry theory of discrete wave equation with the Ablowitz-Ladik-Lattice method is verified.展开更多
This paper focuses on studying Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems. Firstly, the discrete generalized Hamiltonian canonical equations and discrete energy equation of no...This paper focuses on studying Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems. Firstly, the discrete generalized Hamiltonian canonical equations and discrete energy equation of nonholonomic Hamiltonian systems are derived from discrete Hamiltonian action. Secondly, the determining equations and structure equation of Lie symmetry of the system are obtained. Thirdly, the Lie theorems and the conservation quantities are given for the discrete nonholonomic Hamiltonian systems. Finally, an example is discussed to illustrate the application of the results.展开更多
The Noether and Lie symmetries as well as the conserved quantities of Hamiltonian system with fractional derivatives are es-tablished. The definitions and criteria for the fractional symmetrical transformations and qu...The Noether and Lie symmetries as well as the conserved quantities of Hamiltonian system with fractional derivatives are es-tablished. The definitions and criteria for the fractional symmetrical transformations and quasi-symmetrical transformations inthe Noether sense of Hamiltonian system are first discussed. Then, using the invariance of Hamiltonian action under the infini-tesimal transformations with respect to time, generalized coordinates and generalized momentums, the fractional Noethertheorem of the system is obtained. Further, the Lie symmetry and conserved quantity of the system are acquired. Two exam-ples are presented to illustrate the application of the results.展开更多
The theory of velocity-dependent symmetries(or Lie symmetry) and non-Noether conserved quantities are presented corresponding to both the continuous and discrete electromechanical systems.Firstly,based on the invarian...The theory of velocity-dependent symmetries(or Lie symmetry) and non-Noether conserved quantities are presented corresponding to both the continuous and discrete electromechanical systems.Firstly,based on the invariance of Lagrange-Maxwell equations under infinitesimal transformations with respect to generalized coordinates and generalized charge quantities,the definition and the determining equations of velocity-dependent symmetry are obtained for continuous electromechanical systems;the Lie's theorem and the non-Noether conserved quantity of this symmetry are produced associated with continuous electromechanical systems.Secondly,the operators of transformation and the operators of differentiation are introduced in the space of discrete variables;a series of commuting relations of discrete vector operators are defined.Thirdly,based on the invariance of discrete Lagrange-Maxwell equations under infinitesimal transformations with respect to generalized coordinates and generalized charge quantities,the definition and the determining equations of velocity-dependent symmetry are obtained associated with discrete electromechanical systems;the Lie's theorem and the non-Noether conserved quantity are proved for the discrete electromechanical systems.This paper has shown that the discrete analogue of conserved quantity can be directly demonstrated by the commuting relation of discrete vector operators.Finally,an example is discussed to illustrate the results.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10672143 and 60575055)the State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciencesthe Natural Science Foundation of Henan Province Government, China (Grant No 0511022200)
文摘A discrete total variation calculus with variable time steps is presented for mechanico-electrical systems where there exist non-potential and dissipative forces. By using this discrete variation calculus, the symplectic-energy-first integrators for mechanico-electrical systems are derived. To do this, the time step adaptation is employed. The discrete variational principle and the Euler-Lagrange equation are derived for the systems. By using this discrete algorithm it is shown that mechanico-electrical systems are not symplectic and their energies are not conserved unless they are Lagrange mechanico-electrical systems. A practical example is presented to illustrate these results.
基金Supported by Program for New Century Excellent Talents in University (No. NCET-06-0228)
文摘The reinforcement effect of a reconstruction scheme for a steel factory building was investigated using finite element method and dynamic performance test. The workshop concerned is a portal frame structure with four spans and two slope roofs, of which ten columns need cutting for expanding span. The design and reconstruction project of column-cut supported by joist were introduced, which includes column reinforcement, connection rebuilding between brackets and crane beams, and the changing of rigid joint into hinge joint. The construction scheme was put forward in the light of the characteristics of the reinforcement and reconstruction. Spot test of dynamic performance on the workshop and comparison with theoretical analysis results show that the column-cut supported by joist design is effective and the reconstruction project is successful.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11072218 and 11272287)
文摘In this paper, we present a new method to obtain the Lie symmetries and conserved quantities of the discrete wave equation with the Ablowitz-Ladik-Lattice equations. Firstly, the wave equation is transformed into a simple difference equation with the Ablowitz-Ladik-Lattice method. Secondly, according to the invariance of the discrete wave equation and the Ablowitz-Ladik-Lattice equations under infinitesimal transformation of dependent and independent variables, we derive the discrete determining equation and the discrete restricted equations. Thirdly, a series of the discrete analogs of conserved quantities, the discrete analogs of Lie groups, and the characteristic equations are obtained for the wave equation. Finally, we study a model of a biological macromolecule chain of mechanical behaviors, the Lie symmetry theory of discrete wave equation with the Ablowitz-Ladik-Lattice method is verified.
基金supported by the National Natural Science Foundations of China (Grant No. 11072218)the Natural Science Foundation of Zhejiang Province of China (Grant No. Y6110314)
文摘This paper focuses on studying Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems. Firstly, the discrete generalized Hamiltonian canonical equations and discrete energy equation of nonholonomic Hamiltonian systems are derived from discrete Hamiltonian action. Secondly, the determining equations and structure equation of Lie symmetry of the system are obtained. Thirdly, the Lie theorems and the conservation quantities are given for the discrete nonholonomic Hamiltonian systems. Finally, an example is discussed to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (Grant No. 11072218)
文摘The Noether and Lie symmetries as well as the conserved quantities of Hamiltonian system with fractional derivatives are es-tablished. The definitions and criteria for the fractional symmetrical transformations and quasi-symmetrical transformations inthe Noether sense of Hamiltonian system are first discussed. Then, using the invariance of Hamiltonian action under the infini-tesimal transformations with respect to time, generalized coordinates and generalized momentums, the fractional Noethertheorem of the system is obtained. Further, the Lie symmetry and conserved quantity of the system are acquired. Two exam-ples are presented to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (Grant Nos.10672143 and 11072218)
文摘The theory of velocity-dependent symmetries(or Lie symmetry) and non-Noether conserved quantities are presented corresponding to both the continuous and discrete electromechanical systems.Firstly,based on the invariance of Lagrange-Maxwell equations under infinitesimal transformations with respect to generalized coordinates and generalized charge quantities,the definition and the determining equations of velocity-dependent symmetry are obtained for continuous electromechanical systems;the Lie's theorem and the non-Noether conserved quantity of this symmetry are produced associated with continuous electromechanical systems.Secondly,the operators of transformation and the operators of differentiation are introduced in the space of discrete variables;a series of commuting relations of discrete vector operators are defined.Thirdly,based on the invariance of discrete Lagrange-Maxwell equations under infinitesimal transformations with respect to generalized coordinates and generalized charge quantities,the definition and the determining equations of velocity-dependent symmetry are obtained associated with discrete electromechanical systems;the Lie's theorem and the non-Noether conserved quantity are proved for the discrete electromechanical systems.This paper has shown that the discrete analogue of conserved quantity can be directly demonstrated by the commuting relation of discrete vector operators.Finally,an example is discussed to illustrate the results.
