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A quasi-dynamic model and a symplectic algorithm of super slender Kirchhoff rod

International Journal of Modeling, Simulation, and Scientific Computing 2017年第3期8卷 285-295页

作者： Dandan Yang Jianfei Huang Weijia Zhao School of Mathematical Science Huaiyin Normal University Jiangsu Huaian 223300 P.R.China College of Mathematical Sciences Yangzhou University Yangzhou 225002P.R.China College of Mathematics Qingdao University Qingdao 266071P.R.China

Recently the Kirchhoff rod and the methods of dynamical analogue have been widely used in modeling *** features of a DNA such as its super slender and super large deformation raise new challenges in modeling and numerical simulations of a Kirchhoff *** this paper,Euler parameters are introduced to set up the quasi-Hamilton system of an elastic rod,then a symplectic algorithm is applied in its numerical ***,a simplified surface model of the rod is given based on the hypothesis of rigid cross-section.

关键词： Kirchhoff rod euler parameters quasi-hamilton system symplectic algorithm surface equation

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Plasma photonic crystals numerical and filter characteristics analysis based on symplectic algorithm

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OPTIK 2014年第17期125卷 4762-4765页

作者： Yang, Hong Wei Yang, Ze kun Liu, Han Bin Wang, Guang Nanjing Agr Univ Dept Phys Nanjing 210095 Jiangsu Peoples R China Xidian Univ Sch Comp Sci & Technol Xian 710071 Peoples R China Univ Elect Sci & Technol China Dept Comp Chengdu 611731 Peoples R China Southeast Univ State Key Lab Millimeter Waves Nanjing 210096 Jiangsu Peoples R China

From the Maxwell equation, the method of symplectic finite-difference time-domain is applied in analyzing one-dimensional plasma photonic crystal. The propagation process of electromagnetic pulse in one-dimensional vacuum plasma photonic crystal structure is simulated by symplectic algorithm discrete in 2nd order time 2nd order space (T2S2), and 2nd order time 4th order space (T2S4) respectively. Then, from the perspective of frequency domain, the reflection coefficient of the plasma vacuum photonic crystals is analyzed. The results show that the symplectic finite-difference time-domain method is accuracy and correctness. In the end, the filter characteristics of the plasma photonic crystals (PPCs) are analyzed in different thickness of plasma. (C) 2014 Elsevier GmbH. All rights reserved.

关键词： Plasma Photonic crystals symplectic algorithm Hamilton system Reflection coefficient

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A symplectic homotopy perturbation method for random structural dynamics response analysis based on Birkhoffian systems

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STRUCTURES 2023年 47卷 1668-1679页

作者： Qiu, Zhiping Zhu, Bo Beihang Univ Inst Solid Mech Sch Aeronaut Sci & Engn Beijing 100083 Peoples R China

With the enhancement of the engineering structure complexity, numerical computation plays a prominent role in structural dynamics analysis. In theory, general mechanical systems can be transformed into Birkhoffian forms, whose matching symplectic numerical algorithms perform well in accuracy and stability. Besides, the influence of uncertainty cannot be ignored in practical engineering, but the research on uncertainty symplectic algorithms of Birkhoffian systems is still weak. This paper proposes a symplectic homotopy perturbation method (SHPM) for general Birkhoffian equations with random uncertainties. Different from the traditional perturbation method, the proposed method does not depend on small parameters. Based on the homotopy perturbation method, embedded parameters are introduced to establish the matrix and parameter perturbation equations of random Birkhoffian equations, respectively. Then the formulas for calculating the mean value and standard deviation of the response are derived with probability theory. Combined with Birkhoffian symplectic preserving algorithms, a symplectic homotopy perturbation method for the numerical solution of random Birkhoffian equations is proposed. Finally, numerical examples are given to verify the applicability and effectiveness of the proposed method and its su-periority compared with the traditional non-symplectic method.

关键词： Structural dynamics Birkhoffian system Random uncertainty Homotopy perturbation symplectic algorithm

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A symplectic conservative perturbation series expansion method for nonlinear Hamiltonian equations with perturbation terms

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STRUCTURES 2023年 52卷 312-319页

作者： Zheng, Yuning Sci & Technol Space Phys Lab Beijing 100076 Peoples R China

A novel numerical method is proposed to solve the nonlinear Hamiltonian equation with consideration of perturbation terms in this study. Firstly, the original nonlinear Hamiltonian equation is formulated in the formal way and the corresponding conservation law is introduced. Considering the constant perturbation terms in the original nonlinear Hamiltonian equation, the perturbation series expansion method is proposed to obtain the response of the nonlinear Hamiltonian equation. Within the method, the solution to the original equation can be transformed into a perturbation series by introducing said small parameters. Based on the Taylor series expansion method, a series of modified nonlinear Hamiltonian equations for predicting the responses are derived. Moreover, the time history and phase diagram of the nonlinear Hamiltonian equation can be obtained based on the symplectic conservative algorithm. Additionally, the conservative law for the modified Hamiltonian equation is given. The performance of the proposed perturbation series expansion method is evaluated by using three numerical examples. Numerical examples indicate that the proposed method is effective and feasible for calculating the response of nonlinear Hamiltonian equation taking into account perturbation terms.

关键词： Hamiltonian equation Nonlinear Perturbation series Conservative law symplectic algorithm

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A symplectic homotopy perturbation method for stochastic and interval Hamiltonian systems and its applications in structural dynamic systems

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COMPUTATIONAL & APPLIED MATHEMATICS 2022年第8期41卷 1-30页

作者： Qiu, Zhiping Jiang, Nan Beihang Univ Sch Aeronaut Sci & Engn Inst Solid Mech Beijing 100083 Peoples R China

This paper presents a symplectic homotopy perturbation method for Hamiltonian systems with uncertainties. The effects of uncertainties cannot be ignored, but the research on symplectic algorithms of Hamiltonian systems with uncertainties is still weak. Besides, the nonlinear dynamic systems with uncertainties are far more complicated than deterministic linear systems. In this paper, taking two kinds of uncertainties into consideration, the dynamic responses of stochastic and interval Hamiltonian systems, especially uncertain nonlinear Hamiltonian systems, are investigated based on the homotopy perturbation method, respectively. By introducing an embedding parameter, a series of homotopy perturbation equations are deduced, and the uncertain mathematical characteristics of the dynamic responses of stochastic and interval Hamiltonian systems can be obtained by the symplectic algorithms, respectively. Then, the comparative study of calculation results by the symplectic homotopy perturbation method of stochastic and interval Hamiltonian systems is carried out and their compatible relationship is discussed. Eventually, three numerical examples are used to demonstrate the validity and engineering applicability in structural dynamic systems of the proposed method. The numerical results show the superiority of the proposed method in accuracy, stability and symplectic conservative compared with the non-symplectic Runge-Kutta method.

关键词： Hamiltonian systems Homotopy perturbation method Uncertainty symplectic algorithm Nonlinearity Dynamic response

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Chaotic dynamics analysis of double inverted pendulum with large swing angle based on Hamiltonian function

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NONLINEAR DYNAMICS 2022年第4期108卷 4373-4384页

作者： He, Jingxiu Cui, Li Sun, Jingru Huang, Pan Huang, Yuan Hunan Univ Sci & Technol Xiangtan 411201 Hunan Peoples R China Hunan Univ Coll Comp Sci & Elect Engineer Changsha 410082 Peoples R China

In this paper, the chaotic dynamics of double inverted pendulum with big swing angle is studied based on the Hamiltonian canonical equation. At the same time, since Hamiltonian system has the property of symplectic geometry, the basic tools of symplectic geometry are used to deal with the Jacobian matrix in the system. So far, there are few outcomes from this method in the study of chaotic dynamics of double inverted pendulum, so the present work fills the blank in this field. In this paper, analytical mechanics is used to establish the Lagrange function for double inverted pendulum at first, then the corresponding Hamiltonian function is obtained through Legendre transformation, and finally the Hamilton canonical equation is obtained. Then, the Hamiltonian canonical equation of the inverted pendulum with big swing angle is analyzed by methods such as Lyapunov exponent, bifurcation diagram and Poincare section. In the course of analysis, because of the symplectic property of Hamiltonian system, the Jacobian matrix obtained also has the symplectic property. symplectic algorithm maintains the structure of symplectic transformation in numerical calculation, so it has high stability and is most suitable for classical mechanical systems. In analyzing the equilibrium points of the system, it is found that the system has an infinite number of equilibrium points, so as long as the swing angle of one of the swing arms is 0 degree, the inverted pendulum can maintain a state of equilibrium. The study can provide new ideas and theoretical basis for analysis of chaotic dynamics in fields of aerospace, electronic technology and biological manufacturing.

关键词： Double inverted pendulum with large swing angle Hamiltonian system symplectic algorithm N-S bifurcation Chaos

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Explicit structure-preserving geometric particle-in-cell algorithm in curvilinear orthogonal coordinate systems and its applications to whole-device 6D kinetic simulations of tokamak physics

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Plasma Science and Technology 2021年第5期23卷 18-41页

作者： Jianyuan XIAO Hong QIN School of Nuclear Science and Technology University of Science and Technology of ChinaHefei 230026People's Republic of China Plasma Physics Laboratory Princeton UniversityPrincetonNJ 08543United States of America

Explicit structure-preserving geometric particle-in-cell(PIC)algorithm in curvilinear orthogonal coordinate systems is *** work reported represents a further development of the structure-preserving geometric PIC algorithm achieving the goal of practical applications in magnetic fusion *** algorithm is constructed by discretizing the field theory for the system of charged particles and electromagnetic field using Whitney forms,discrete exterior calculus,and explicit non-canonical symplectic *** addition to the truncated infinitely dimensional symplectic structure,the algorithm preserves exactly many important physical symmetries and conservation laws,such as local energy conservation,gauge symmetry and the corresponding local charge *** a result,the algorithm possesses the long-term accuracy and fidelity required for first-principles-based simulations of the multiscale tokamak *** algorithm has been implemented in the Sym PIC code,which is designed for highefficiency massively-parallel PIC simulations in modern *** code has been applied to carry out whole-device 6 D kinetic simulation studies of tokamak physics.A self-consistent kinetic steady state for fusion plasma in the tokamak geometry is numerically found with a predominately diagonal and anisotropic pressure *** state also admits a steady-state subsonic ion flow in the range of 10 km s-1,agreeing with experimental observations and analytical calculations Kinetic ballooning instability in the self-consistent kinetic steady state is *** is shown that high-n ballooning modes have larger growth rates than low-n global modes,and in the nonlinear phase the modes saturate approximately in 5 ion transit times at the 2%level by the E×B flow generated by the *** results are consistent with early and recent electromagnetic gyrokinetic simulations.

关键词： curvilinear orthogonal mesh charge-conservative particle-in-cell symplectic algorithm whole-device plasma simulation

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Large Deformation Dynamic Analysis of a Cable System by a New Hamiltonian Finite Element Method

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INTERNATIONAL JOURNAL OF APPLIED MECHANICS 2021年第6期13卷

作者： Ding, Huaiping Yin, Xiaochun Wang, Qiao Zhu, Zheng H. Nanjing Univ Sci & Technol Dept Mech & Engn Sci 200 Xiaolingwei St Nanjing 210094 Peoples R China Inner Mongolia North Heavy Ind Grp Co Ltd Inst Equipment Res 3 Binggong Rd Baotou 014030 Inner Mongolia Peoples R China York Univ Dept Mech Engn Toronto ON M3J 1P3 Canada

This paper develops a new Hamiltonian nodal position finite element method for dynamic analysis of spatial flexible cable systems with large deformation. The dynamic governing equation is derived from finite elasticity theory. Logarithmic strain is applied to construct large deformation Hamiltonian canonical equations. An efficient second-order symplectic difference algorithm is built to solve the canonical equations numerically. A large strain conical pendulum system is analyzed numerically by the proposed method, and the numerical results are compared with those retracted from the existing Hamiltonian methods and Livermore Software Technology Corporation: dynamics (LS-DYNA). The proposed method is further verified by two tethered dynamic experiments involving large displacement motion and large deformation. The comparisons and verifications demonstrate that the proposed method is of symplectic conservation, has high accuracy and has stability for calculating flexible cable system dynamics with large deformation.

关键词： Cable systems dynamics large deformation nodal position finite element method Hamiltonian symplectic algorithm

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symplectic Radial Basis Approximation of Multi-variate Hamiltonian PDEs

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IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE 2019年第A4期43卷 1789-1797页

作者： Zhang, Shengliang Nanjing Forestry Univ Coll Econ & Management Nanjing Jiangsu Peoples R China

A meshless symplectic algorithm for multi-dimensional linear Hamiltonian partial differential equations with radial basis interpolation has been suggested when the solving domain is Rd. In this study, for sake of application, the energy error estimate of the proposed symplectic scheme is made when the targeted domain is bounded. The paper also extends the algorithm to solve the nonlinear two-dimensional Klein-Gordon equation. As numerical experiments shown, the algorithm preserves the discretization energy, and it is efficient to deal with the nonlinear case.

关键词： Meshless method Radial basis functions Energy error estimate symplectic algorithm Klein-Gordon equation

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Maslov Asymptotic Theory and symplectic algorithm

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Chinese Journal of Geophysics 2013年第4期43卷 556-567页

作者： MengZhao QIN JinxBo CHEN

In order to overcome the caustic problem in seismic tomography, we systematically study the Maslov asymptotic theory and symplectic algorithm. A numerical method for evaluating Maslov wave field, which is based on symplectic algorithm, is presented. In addition, we perform numerical simulation in ray tracing with symplectic algorithm and nonsymplectic algorithm. The result shows that the precision of both is almost the same, however, the symplectic algorithm is faster. Furthermore, in keeping Hamitonlian quantities for a long time, the symplectic algorithm has an incomparable superiority over nonsymplectic algorithm.

关键词： Maslov theory Asymptotic Caustics symplectic algorithm

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