摘要
本文基于Bridges教授建立的多辛算法理论及其Hamilton变分原理,采用广义多辛算法研究了大阻尼杆的阻尼振动特性.引入正交动量后,首先将描述大阻尼杆振动的控制方程降阶为一阶Hamilton近似对称形式,即广义多辛形式;随后采用中点离散方法构造形式广义多辛形式的中点Box广义多辛离散格式;最后通过计算机模拟研究大阻尼杆振动过程中的耗散效应.研究结果表明,本文构造的广义多辛算法不仅能够保持系统守恒型几何性质,同时能够再现系统的耗散效应.
This paper studies the damping vibration properties of the big damping bar by the generalized multi symplectic method based on the Bridges’s multi symplectic method and the Hamilton variation principle. Introducing orthogonal momenta, a first order approximate symplectic form, named generalized multi symplectic form is derived from the control equation of the big damping bar vibration firstly. And then a midpoint Box generalized multi symplectic scheme is constructed by the midpoint method; Finally, the dissipation effect of the big damping bar vibration is studied. From the results of the numerical experiment, the good properties of the generalized multi symplectic method are verified: satisfying the conservative properties of the system and reproducing the dissipation effect of the system.
出处
《动力学与控制学报》
2013年第1期1-4,共4页
Journal of Dynamics and Control
基金
国家自然科学基金(10972182
11002115
11172239)
111引智计划(B07050)
航空科学基金(2010ZB53021)
中国博士后科学基金特别资助(201003682)
西北工业大学基础研究基金(JC20110259)
高校博士点基金(20106102110019)
机械系统与振动国家重点实验室开放课题(MSV-2011-21)
大连理工大学工业装备结构分析国家重点实验室开放基金(GZ0802)资助项目~~
关键词
广义多辛
保结构
耗散
哈密顿
generalized multi-symplectic, structure-preserving, dissipation, Hamilto generalized