A diffraction problem for the biharmonic wave equation in one-dimensional periodic structures

被引：4
|
作者：
Yue, Junhong [1 ]
Li, Peijun [2 ]
Yuan, Xiaokai [3 ]
Zhu, Xiaopeng [4 ,5 ]
机构：
[1] Taiyuan Univ Technol, Coll Data Sci, Taiyuan 030024, Shanxi, Peoples R China
[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA
[3] Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China
[4] Chinese Acad Sci, Acad Math & Syst Sci, LSEC, NCMIS,ICMSEC, Beijing 100190, Peoples R China
[5] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
来源：
RESULTS IN APPLIED MATHEMATICS | 2023年 / 17卷
基金：
美国国家科学基金会;
关键词：
Biharmonic wave equation; Periodic structures; Adaptive finite element method; A posteriori error estimate; FINITE-ELEMENT-METHOD; MATCHED ABSORBING LAYERS; GRATING PROBLEM; SCATTERING;
D O I：
10.1016/j.rinam.2022.100350
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This work concerns the propagation of flexural waves through one-dimensional periodic structures embedded in thin elastic plates. We show that the out-of-plane displacement of the plate only contains the Helmholtz wave component and the modified Helmholtz wave component is not supported when the Navier boundary condition is imposed. An adaptive finite element method with transparent boundary condition is developed for solving the associated boundary value problem. Numerical results show that the method is effective to solve the diffraction grating problem of the biharmonic wave equation. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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页数：11
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