大阻尼杆振动的广义多辛算法

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 multisymplectic 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.