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911.
Fractional differential equations of motion in terms of combined Riemann—Liouville derivatives 下载免费PDF全文
In this paper,we focus on studying the fractional variational principle and the differential equations of motion for a fractional mechanical system.A combined Riemann-Liouville fractional derivative operator is defined,and a fractional Hamilton principle under this definition is established.The fractional Lagrange equations and the fractional Hamilton canonical equations are derived from the fractional Hamilton principle.A number of special cases are given,showing the universality of our conclusions.At the end of the paper,an example is given to illustrate the application of the results. 相似文献
912.
The Pauli principle is included in a multisubband deterministic solver for two-dimensional devices without approximations.The nonlinear Boltzmann equations are treated properly without compromising on accuracy,convergence,or CPU time.The simulation results indicate the significant impact of the Pauli principle on the transport properties of the quasi-2D electron gas,especially for the on state. 相似文献
913.
914.
刘东生 《应用数学和力学(英文版)》2009,30(9):1169-1176
In this paper, we describe the nonlinear models of a rod in three-dimensional space based on the Cosserat theory. Using the pseudo-rigid body method and variational principle, we obtain the motion equations of a Cosserat rod including shear deformations. 相似文献
915.
Base force element method of complementary energy principle for large rotation problems 总被引:1,自引:0,他引:1
Using the concept of the base forces, a new finite element method (base force element method, BFEM) based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM. 相似文献
916.
917.
Strain-gradient plasticity theories are reviewed in which some measure of the plastic strain rate is treated as an independent kinematic variable. Dislocation arguments are invoked in order to provide a physical basis for the hardening at interfaces. A phenomenological, flow theory version of gradient plasticity is constructed in which stress measures, work-conjugate to plastic strain and its gradient, satisfy a yield condition. Plastic work is also done at internal interfaces and a yield surface is postulated for the work-conjugate stress quantities at the interface. Thereby, the theory has the potential to account for grain size effects in polycrystals. Both the bulk and interfacial stresses are taken to be dissipative in nature and due attention is paid to ensure that positive plastic work is done. It is shown that the mathematical structure of the elasto-plastic strain-gradient theory has similarities to conventional rigid-plasticity theory. Uniqueness and extremum principles are constructed for the solution of boundary value problems. 相似文献
918.
The dynamical behavior of the Φ6-Van der Pol system subjected to both external and parametric excitation is investigated. The effect of parametric excitation
amplitude on the routes to chaos is studied by numerical analysis. It is found that the probability of chaos happening increases
along with the parametric excitation amplitude increases while the external excitation amplitude fixed. Based on the invariance
principle of differential equations, the system is lead to desirable periodic orbit or chaotic state (synchronization) with
different control techniques. Numerical simulations are provided to validate the proposed method. 相似文献
919.
After introducing some of the basic definitions and results
from the theory of groupoid and Lie algebroid, we investigate the
discrete Lagrangian mechanics from the viewpoint of groupoid theory
and give the connection between groupoids variation and the methods
of the first and second discrete variational principles. 相似文献
920.
Wenxian SHEN 《Frontiers of Mathematics in China》2009,4(3):523-562
The current paper deals with spatial spreading and front propagating dynamics for spatially discrete KPP (Kolmogorov, Petrovsky
and Paskunov) models in time recurrent environments, which include time periodic and almost periodic environments as special
cases. The notions of spreading speed interval, generalized propagating speed interval, and traveling wave solutions are first
introduced, which are proper modifications of those introduced for spatially continuous KPP models in time almost periodic
environments. Among others, it is then shown that the spreading speed interval in a given direction is the minimal generalized
propagating speed interval in that direction. Some important upper and lower bounds for the spreading and generalized propagating
speed intervals are provided. When the environment is unique ergodic and the so called linear determinacy condition is satisfied,
it is shown that the spreading speed interval in any direction is a singleton (called the spreading speed), which equals the
classical spreading speed if the environment is actually periodic. Moreover, in such a case, a variational principle for the
spreading speed is established and it is shown that there is a front of speed c in a given direction if and only if c is greater than or equal to the spreading speed in that direction.
相似文献