Papers by Keyword: Hamiltonian System

Abstract: Based on many of researches about bend of beam under uniform load in the Hamiltonian system, but few on bend of beam under the force couple with load and the thermal, according to the validity of Hamiltonian method in symplectic space, in this paper, the method is used to solve bending of plane beam under the force couple with load and the thermal, and give out the distribution of displacement under this condition. Numerical simulations show the effect of temperature has great influence on the distribution of displacement of the beam. The results provide a numerical model and reliable reference data for the follow-up study of its analytical solution.

Abstract: A method of port-controlled Hamiltonian (PCH) systems energy-shaping control is presented for the four-quadrant control problem of squirrel cage induction motor (IM) drive system. First, the PCH models of IM drive system are developed. Then, the PCH controllers are designed based on the control theory of closed-loop state error PCH system. The coordinated control of the grid-side and the motor-side are applied in Matlab/simulink, which the motor-side is started after the grid-side is achieved up to stable. The controlled system can be achieved that DC bus voltage controllable, unity power factor, energy bidirectional flow, IM run in the four-quadrant, etc.

Abstract: A novel state error port-controlled Hamiltonian (PCH) system method is presented for speed control the direct current (DC) separately excited motor. The unity power factor regulation of three phase pulse width modulated (PWM) rectifier is also implemented. Then, the state error PCH system control theory, the PCH model of the PWM rectifier and DC motor are proposed. Moreover, the control algorithm of the duty ratio switch function is presented for the PWM rectifier. Theoretical analysis and simulation results show that the controller has good speed tracking and unity power factor control performances.

Abstract: The traditional control technology of doubly fed wind power generator is based on stator flux-oriented control technology but not considering the volatility of wind speed, the non-linear and the robust control of wind generator. This article gives a coordination control technology of DFIG-SMES (Superconducting Magnetic Energy Storage) based on Hamilton function. It derives the stability region of controller parameters and proves the stability condition. It designs and builds control test system of DFIG-SMES controller based on MSP430 chip. It achieves good results through experiments under random wind. The study establishes the foundation for the hardware platform of nonlinear and robust control system of DFIG.

Abstract: The theory of Hamiltonian system is introduced for the problems of laminated transversely isotropic magnetoelectroelastic plates. The partial differential equations of the magnetoelectroelastic solids are derived corresponding to the Lagrange density function and Legendre’s transformation. These equations are a set of the first-order Hamiltonian equations and expressed with displacements, electric potential and magnetic potential, as well as their dual variables--lengthways stress, electric displacement and magnetic induction in the symplectic geometry space. To obtain the solutions of the equations, the schemes of separation of variables and expansion of eigenvector of Hamiltonian operator matrix in the polar direction are implemented. The homogenous solutions of the equations consist of zero eigen-solutions and nonzero eigen-solutions. All the eigen-solutions of zero eigenvalue are obtained in the symmetric deformation. These solutions give the classical Saint-Venant’s solutions because the Hamiltonian matrix is symplectic. The method is rational, analytical method and does not require any trial functions.

Abstract: Hamiltonian system used in dynamics is introduced to formulate the three-dimensional problems of the transversely isotropic magnetoelectroelastic solids. The Hamiltonian dual equations in magnetoelectroelastic solids are developed directly from the modified Hellinger-Reissner variational principle derived from generalized Hellinger-Ressner variational principle with two classes of variables. These variables not only include such origin variables as displaces, electric potential and magnetic potential, but also include such their dual variables as lengthways stress, electric displacement and magnetic induction in the symplectic space. Similar to the Hamiltonian formulation in classic dynamics, the z coordinate is treated analogous to the time coordinate so that the method of separation of variables can be used. The governing equations are a set of first order differential equations in z, and the coefficient matrix of the differential equations is Hamiltonian in (x, y).

Abstract: A new model for elastic constraint wheelset system of rail vehicle is proposed. Assuming the stochastic excitation as Gauss white noise, a stochastic model is built for elastic constraint wheelset system. Here two kinds of stochastic excitations are considered: one is the internal multiplicative excitation inherited in the internal system such as the spring and wheelset/rail contact geometric relationship, the other is the external excitation induced by track random irregularities. The model defined here is considered as a weak damping, weak excitation quasi non-integrable Hamiltonian system. The maximal Lyapunov exponent is calculated by quasi non-integrable Hamiltonian theory and oseledec multiplicative ergodic theory, and the stochastic local stability conditions are obtained. Meanwhile, the stochastic global stability conditions are derived by considering the modality of the singular boundary condition.

Abstract: An acoustic wave propagation simulating method based on semi-symplectic theory is developed. The acoustic wave equations with n degree of freedom in space domain of Lagrange System which are obtained in FEM are converted to equations with 2n degree of freedom in Hamiltonian System with the Legendre’s Transformation. These equations are then integrated with the Precision Integration algorithm in time domain. The algorithm is employed to simulate the acoustical wave propagation in two dimensional medium. We demonstrate the remarkable stability of the presented algorithm by comparison of the results of the FEM and that of the Semi-Sympectic Theory under different time steps. The results presented in this paper show that the proposed algorithm is effective, accurate, and not sensitive to time step.

Abstract: The end effects of symplectic direct solution to Stokes flow in a rectangular cavity are considered. Based on establishing the dual equations for Stokes flow in Hamilton system, the non-zero eigenvalues and their eigensolutions for an anti-symmetric problem were obtained. Expanding the solutions of dual equations by non-zero eigensolutions and determining the expansion coefficients by the end boundary conditions, the decay tendency and interaction mechanism of end effects were discussed and the end boundary errors were investigated. The resultant velocity caused by tangentially driving lid is gradually decayed along the longitudinal direction of cavity. The more number of the expansion items are superposed, the more accurate the solutions are. The smaller the depth-to-width ratios are, the stronger the interference between the end velocities is. The error of ends moving in the same directions is bigger than that in opposite directions.

Abstract: Beam reinforcement is reduced to mechanics behavior of structures of multilayer materials in this paper. An analytical method is presented based on Hamiltonian system. In the system, displacements and stresses are pairs of dual variables. The state vectors of the system describe directly connective conditions on the interfaces of two materials and structures so that the rule of normal and shear stresses on the interface can be revealed. Based on the criterion of lamination crack, the interface strength is determined. Results show that the lamination crack correlates highly with the ratios of material constants and geometrical parameters of structures. The result and conclusion provide a design criterion for structure reinforcement.