周期复合结构上的弹性二次特征值问题的多尺度渐近分析方法  

A multi-scale asymptotic analysis method for the elastic quadratic eigenvalue problems in periodically composite structure

作　　者：王洪玉 马强 WANG Hong-Yu;MA Qiang(School of Mathematics,Sichuan University,Chengdu 610064,China)

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2024年第4期89-96,共8页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11801387,11971336,11971337);四川省自然科学基金(2022NSFSC0322);中央高校基本科研业务费专项资金(YJ201811)。

摘　　要：针对周期复合结构上的弹性二次特征值问题,本文提出了一种基于二阶双尺度(Second-Order Two-Scale, SOTS)方法的多尺度分析方法 .该方法考虑速度阻尼效应的二次特征值问题,给出了特征值、特征函数的二阶渐近展开,以及特征值的误差估计.本文给出了方法的有限元实现,并通过近似值和参考解之间的定性和定量比较验证了方法的有效性.数值算例结果表明,特征值与特征函数中的二阶校正项对于重构单胞内特征函数的局部信息发挥着重要作用.A multiscale asymptotic analysis method based on the Second-Order Two-Scales(SOTS)approach is proposed for the elastic quadratic eigenvalue problems in periodic composite structure.In this method,the typical quadratic eigenvalue problems with velocity damping effect are considered and the second order asymptotic expansions of eigenvalues and eigen-functions are given by the SOTS approach.Then the finite element procedures are established and the error of eigenvalues are performed.Effectiveness of the method is demonstrated by both the qualitative and quantitative comparisons between the computed SOTS approximations and the reference solutions.It is indicated that the second-order correctors are of importance to reconstruct the detailed information of the original eigenfunctions within the micro cells.

关 键 词：周期复合结构 二阶双尺度渐近分析 二次特征值问题 线性化 

分 类 号：O241.82[理学—计算数学]