Papers by Keyword: Hamiltonian System

Abstract: Hamiltonian system used in dynamics is introduced to formulate the transversely isotropic magnetoelectroelastic solids plane problem in rectangular domain and symplectic dual equation is derived corresponding to the generalized variational principle of the magnetoelectroelastic solids. The equation is expressed with displacements, electric potential and magnetic potential, as well as their duality variables--lengthways stress, electric displacement and magnetic induction in the symplectic geometry space. Since the x-coordinate is treated as time variable so that z becomes the independent coordinate in the Hamiltonian matrix operator. The symplectic dual approach enables the separation of variables to work and all the Saint Venant solutions in the symmetric deformation are obtained directly via the zero eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian operator matrix and the boundary condition. An example is presented to illustrate the proposed approach.

Abstract: In this paper, precise integration in a symplectic system is used to analyze the stop-band characteristic of the dielectric layer PBG structure in a waveguide. The transverse section is made discrete by using edge elements. The stiff matrices of a dielectric layer and an air layer can be calculated by precision integration based on Riccati equations in a Hamiltonian system. The export stiff matrices of a period can be obtained by a combination of substructures, and then the whole structure can be solved. The stop-band characteristic of a dielectric layer PBG structure in a waveguide is obtained and the effects of the size of period and the number of periods are discussed. The examples presented show that this method is precise and efficient.

Abstract: A precise integration algorithm for solving the restricted three body problem was put forward based on precise integration method, which divided a large integration time into small intervals and only small value matrix participates in the iterative process during the computation of the exponent matrix. And another symplectic algorithm for solving non-separable Hamiltonian system constructed by flow complex was also introduced, which only had periodic variational energy. The results of both algorithms were compared with fourth Runge-Kutta algorithm and their performances and advantages were analyzed, showing the validities of these two algorithms.

Abstract: This paper proposes a Hamiltonian perturbation approach for analyzing the dynamic characteristics of the damaged structure. Firstly, structural vibration governing equation is transformed to the general expression of state variables composed of displacement and momentum. On the basis of the conjugate symplectic orthogonal relation, the first-, and second- order perturbation expression of the damaged structural eigensolution are obtained. Finally, the numerical simulation and cantilever experiment prove the effectiveness of this approach.