四川大学学报（自然科学版）2024，Vol.61Issue(4)：97-103,7.DOI:10.19907/j.0490-6756.2024.041007
周期复合材料二次特征值问题的二阶双尺度分析与计算
Multiscale asymptotic analysis and algorithm for the quadratic eigenvalue problem in periodic composite materials
摘要
Abstract
A second-order two-scale(SOTS)asymptotic analysis and computational method are developed for solving the quadratic eigenvalue problem(QEP)in periodic composited domain.A typical QEP involving the velocity-damping is considered and asymptotic expansions for the eigenfunctions are performed.Then a finite el-ement procedure is proposed and the homogenized QEPs are solved by the linearized method.Numerical ex-amples demonstrate the accuracy and efficiency of the method.It is shown that the method can effectively be ap-plied to such nonlinear eigenvalue problems in which the second-order correctors play an important role for de-scribing the local behavior of eigenfunctions and obtaining better approximation of the eigenvalues at lower cost.关键词
周期复合域/二次特征值问题/二阶双尺度分析Key words
Periodic composite domain/Quadratic eigenvalue problem/Second-order two-scale analysis分类
数学引用本文复制引用
吴玉婷,马强..周期复合材料二次特征值问题的二阶双尺度分析与计算[J].四川大学学报（自然科学版）,2024,61(4):97-103,7.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(2022NSFSCO322) （2022NSFSCO322）
中央高校基本科研业务费专项资金(YJ201811) （YJ201811）
