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国家自然科学基金(10772147)

作品数:15 被引量:48H指数:4
相关作者:邓子辰胡伟鹏黄永安李文成王艳更多>>
相关机构:西北工业大学大连理工大学华中科技大学更多>>
发文基金:国家自然科学基金工业装备结构分析国家重点实验室开放基金陕西省自然科学基金更多>>
相关领域:理学建筑科学自动化与计算机技术航空宇航科学技术更多>>

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15 条 记 录,以下是 1-10
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Multi-symplectic method for generalized fifth-order KdV equation被引量:6
2008年
This paper considers the multi-symplectic formulations of the generalized fifth-order KdV equation in Hamiltonian space. Recurring to the midpoint rule, it presents an implicit multi-symplectic scheme with discrete multi-symplectic conservation law to solve the partial differential equations which are derived from the generalized fifth-order KdV equation numerically. The results of the numerical experiments show that this multi-symplectic algorithm is good in accuracy and its long-time numerical behaviour is also perfect.
胡伟鹏邓子辰
关键词:MULTI-SYMPLECTIC
Ⅱ类超导体混合态的多辛算法被引量:2
2008年
利用多辛方法研究了两带Ⅱ类超导体混合态的电磁特性.针对描述两带Ⅱ类超导体混合态的依赖于时间的Ginzburg-Landau方程,首先推导出了其满足多个守恒律(多辛守恒律、局部能量守恒律和局部动量守恒律)的一阶多辛偏微分方程组形式;随后构造了其18点多辛隐式格式用以模拟Ginzburg-Landau方程;最后,基于模拟结果,进一步得出了一假想两带Ⅱ类超导体的伏安特性及其在不同外界磁场下的电阻随温度变化关系曲线.算例结果表明两带Ⅱ类超导体混合态的最为突出的特征是:当外加磁场逐渐增强时,超导体的临界温度急剧下降,同时电阻率ρ迅速上升.同时,模拟结果显示出了多辛方法的两大优点:极高的数值精度和良好的长时间数值稳定性.
胡伟鹏邓子辰
关键词:混合态守恒律
The complex multi-symplectic scheme for the generalized sinh-Gordon equation被引量:2
2009年
In this paper,the complex multi-symplectic method and the implementation of the generalized sinhGordon equation are investigated in detail.The multi-symplectic formulations of the generalized sinh-Gordon equation in Hamiltonian space are presented firstly.The complex method is introduced and a complex semi-implicit scheme with several discrete conservation laws(including a multi-symplectic conservation law(CLS),a local energy conservation law(ECL) as well as a local momentum conservation law(MCL)) is constructed to solve the partial differential equations(PDEs) that are derived from the generalized sinh-Gordon equation numerically.The results of the numerical experiments show that the multi-symplectic scheme has excellent long-time numerical behavior and high accuracy.
HU WeiPengDENG ZiChenHAN SongMeiFAN Wei
关键词:GENERALIZEDEQUATIONMULTI-SYMPLECTICCOMPLEXRUNGE-KUTTA
Multi-symplectic method for generalized Boussinesq equation
2008年
The generalized Boussinesq equation that represents a group of important nonlinear equations possesses many interesting properties. Multi-symplectic formulations of the generalized Boussinesq equation in the Hamilton space are introduced in this paper. And then an implicit multi-symplectic scheme equivalent to the multi-symplectic Box scheme is constructed to solve the partial differential equations (PDEs) derived from the generalized Boussinesq equation. Finally, the numerical experiments on the soliton solutions of the generalized Boussinesq equation are reported. The results show that the multi-symplectic method is an efficient algorithm with excellent long-time numerical behaviors for nonlinear partial differential equations.
胡伟鹏邓子辰
旋转刚-柔耦合系统动力学及热冲击响应分析被引量:2
2008年
利用FOAC模型理论,给出了大范围运动的大变形变截面柔性梁的位移描述,继而得到系统的机械能的高阶表述,然后基于广义Hamilton原理得到系统的动力学模型。系统模型考虑了柔性梁在不同方向的相互耦合影响,使得系统能够对较高速度的旋转刚柔耦合结构进行动力学仿真,避免了传统ZOAC模型对高速旋转柔性系统仿真结果发散的不足,从本质上分析了动力刚化作用。在此基础上,考虑热冲击对系统的动力学响应,包括梁两侧同等热冲击和不等温热冲击,为航天结构和热场环境救援机器人的动力学行为提供仿真模型。
魏麟欢黄永安邓子辰
关键词:多体动力学HAMILTON原理有限元
广义Benjamin-Bona-Mahoney方程的多辛算法
2008年
文章基于Bridges意义下的多辛理论构造了广义Benjamin-Bona-Mahoney方程的多辛偏微分方程组,利用变分原理得到了多种守恒律,构造了一种等价于Preissmann格式的隐式多辛格式。钟状孤波解的数值模拟结果表明该多辛格式具有较好的长时间数值稳定性。
胡伟鹏邓子辰
关键词:数值模拟多辛算法
Symplectic analysis for elastic wave propagation in two-dimensional cellular structures被引量:5
2010年
On the basis of the finite element analysis, the elastic wave propagation in cellular structures is investigated using the symplectic algorithm. The variation principle is first applied to obtain the dual variables and the wave propagation problem is then transformed into two-dimensional (2D) symplectic eigenvalue problems, where the extended Wittrick-Williams algorithm is used to ensure that no phase propagation eigenvalues are missed during computation. Three typical cellular structures, square, triangle and hexagon, are introduced to illustrate the unique feature of the symplectic algorithm in higher-frequency calculation, which is due to the conserved properties of the structure-preserving symplectic algorithm. On the basis of the dispersion relations and phase constant surface analysis, the band structure is shown to be insensitive to the material type at lower frequencies, however, much more related at higher frequencies. This paper also demonstrates how the boundary conditions adopted in the finite element modeling process and the structures' configurations affect the band structures. The hexagonal cells are demonstrated to be more efficient for sound insulation at higher frequencies, while the triangular cells are preferred at lower frequencies. No complete band gaps are observed for the square cells with fixed-end boundary conditions. The analysis of phase constant surfaces guides the design of 2D cellular structures where waves at certain frequencies do not propagate in specified directions. The findings from the present study will provide invaluable guidelines for the future application of cellular structures in sound insulation.
Xiu-Hui HouZi-Chen DengJia-Xi ZhouTie-Quan Liu
结构动力方程的增维分块精细积分法被引量:11
2008年
在增维精细积分法的基础上,对矩阵进行分块计算。考虑非齐次项的特点,减小了矩阵的维数,实现简化计算,提高了计算效率,同时算法仍然具有增维精细积分法的原有优点。数值算例表明本方法在保持精度的同时提高了计算效率,在处理大型问题时将有着很大的优势。
张继锋邓子辰
关键词:精细积分
Symplectic analysis for wave propagation in one-dimensional nonlinear periodic structures被引量:1
2010年
The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear dynamic equation is linearized using the small parameter perturbation method. Eigen-solutions of the symplectic matrix are used to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain, arising from the nonlinear spring stiffness effect, has profound effects on the overall transmission of the chain. The wave propagation characteristics are altered due to nonlinearity, and related to the incident wave intensity, which is a genuine nonlinear effect not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to closing of transmitting gaps. Comparison with the normal recursive approach shows effectiveness and superiority of the symplectic method for the wave propagation problem in nonlinear periodic structures.
侯秀慧邓子辰周加喜
Multi-symplectic method to analyze the mixed state of Ⅱ-superconductors被引量:4
2008年
The mixed state of two-band II-superconductor is analyzed by the multi-symplectic method. As to the Ginzburg-Landau equation depending on time that describes the mixed state of two-band II-superconductor, the multi-symplectic formulations with several conservation laws: a multi-symplectic conservation law, an energy con- servation law, as well as a momentum conservation law, are presented firstly; then an eighteen points scheme is constructed to simulate the multi-symplectic partial differential equations (PDEs) that are derived from the Ginzburg-Landau equation; finally, based on the simulation results, the volt-ampere characteristic curves are obtained, as well as the relationships between the temperature and resistivity of a suppositional two-band II-superconductor model under different magnetic intensi- ties. From the results of the numerical experiments, it is concluded that the notable property of the mixed state of the two-band II-superconductor is that: The trans- formation temperature decreases and the resistivity ρ increases rapidly with the increase of the magnetic intensity B. In addition, the simulation results show that the multi-symplectic method has two remarkable advantages: high accuracy and excellent long-time numerical behavior.
HU WeiPeng1↑ & DENG ZiChen1,2 1 School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710072, China
关键词:GINZBURG-LANDAUMULTI-SYMPLECTICCONSERVATIONLAW
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