四川大学学报（自然科学版）2024，Vol.61Issue(4)：89-96,8.DOI:10.19907/j.0490-6756.2024.041006
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
摘要
Abstract
A multiscale asymptotic analysis method based on the Second-Order Two-Scales(SOTS)ap-proach 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 fi-nite 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 ap-proximations 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Key words
Periodic composite structure/Second-order two-scale asymptotic analysis/Quadratic eigenvalue problem/Linearization分类
数学引用本文复制引用
王洪玉,马强..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[J].四川大学学报（自然科学版）,2024,61(4):89-96,8.基金项目
国家自然科学基金(11801387,11971336,11971337) （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) （2022NSFSC0322）
