线性阻尼杆振动问题基于变量变换的多辛算法  

Multi-symplectic Algorithm for Vibration Analysis of the Rods with Linear Damping

作　　者：鲍四元[1] 邓子辰[2] BAO Si-yuan;DENG Zi-chen(School of Civil Engineering, University of Science and Technology of Suzhou, Suzhou 215011, Jiangsu China;Department of Engineering Mechanics, Northwestern Polytechnic University, Xi’an 710072, China)

机构地区：[1]苏州科技大学土木工程学院,江苏苏州215011 [2]西北工业大学工程力学系,西安710072

出　　处：《噪声与振动控制》2017年第1期16-19,共4页Noise and Vibration Control

基　　金：国家自然科学基金资助项目(11202146)

摘　　要：提出线性阻尼杆振动问题基于变量变换的多辛离散算法。首先通过变量变换把耗散系统化为保守系统。其次以变换变量组成状态向量并采用中点离散方法构造中点Box多辛离散格式,然后,基于空间层的状态变量建立矩阵形式的递推关系,最后结合空间边界条件和初始条件建立线性方程组求解。研究结果表明,构造的多辛算法不仅能够保持系统守恒型几何性质,通过状态变量合理表示了边界条件,而且能够较准确地体现系统的耗散效应。The discrete multi- symplectic alogrithim for vibration problem analysis of the rods with linear damping is proposed. First of all, the dissipation system is transformed into a conservative system by variable transformation. Then, the state vector is formed by the transformed variables, and the midpoint box multi-symplectic form is generated based on themidpoint discrete method. Finally, the matrix-type recurrence formula is established based on the state vector and the linear equation set including the boundary condition and the initial condition is formed and solved. The numerical results show that the proposed multi- symplectic algorithm can reserve the conservative geometrical properties of the system, reasonably express the boundary condition by the state variables, and accurately reflect the dissipation effect of the system.

关 键 词：振动与波 变量变换 多辛 保结构 耗散 

分 类 号：O326[理学—一般力学与力学基础] O422.6[理学—力学]