四川大学学报（自然科学版）2024，Vol.61Issue(4)：80-88,9.DOI:10.19907/j.0490-6756.2024.041005
周期多孔区域压电特征值问题的多尺度渐近算法
Multiscale asymptotic method for the piezoelectric eigenvalue problem in periodically perforated domain
摘要
Abstract
A novel multi-scale asymptotic finite element method based on the Second-Order Two-Scale(SOTS)analysis is proposed for the piezoelectric eigenvalue problem in periodically perforated domain.In this method,the eigen-functions and eigenvalues are expressed in power series of periodicity to the second-order terms and then the homogenized modal equations and effective material coefficients are derived.By the ideal of"corrector equation",the first-and second-order correctors are calculated.A program is established and numerical experiments are carried out on the two-dimensional perforated structures.It is shown that the proposed method is effective to identify the piezoelectric eigenvalues of porous structures as well as the origi-nal eigen-functions for both the displacement and the electric potential can be reproduced by adding the correc-tors to the homogenized solutions.关键词
压电特征值问题/多孔材料/多尺度渐近展开方法/二阶渐近估计Key words
Piezoelectric eigen-problem/Cellular material/Multi-scale asymptotic expansion method/Second-order asymptotic approximation分类
数学引用本文复制引用
陈庭艳,马强..周期多孔区域压电特征值问题的多尺度渐近算法[J].四川大学学报（自然科学版）,2024,61(4):80-88,9.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) （2022NSFSC0322）
中央高校基本科研业务费专项资金(YJ201811) （YJ201811）
