基于动态刚度矩阵的精确高效方法，用于分析缺陷晶格结构中的波传播

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures Pub Date : 2024-11-18 DOI:10.1016/j.ijsolstr.2024.113147

B.W. Yan, Q. Gao

{"title":"基于动态刚度矩阵的精确高效方法，用于分析缺陷晶格结构中的波传播","authors":"B.W. Yan, Q. Gao","doi":"10.1016/j.ijsolstr.2024.113147","DOIUrl":null,"url":null,"abstract":"<div><div>In this study, we present an efficient and accurate method for analyzing wave propagation in lattice structures with periodic defects, which are composed of three-dimensional (3D) unit cells arranged infinitely in two or three directions, with defects existing periodically along the directions of the arrangement. The unit cell is composed of 3D beams, and the dynamic stiffness formulation of the 3D beam is developed by combining the Timoshenko-Ehrenfest, Rayleigh-Love and torsion theories. Based on the dynamic stiffness matrix, any number or order of natural frequencies of defective lattice structures can be calculated accurately and efficiently using the Wittrick-Williams algorithm. By combining it with the Bloch theorem, the proposed method can be used to calculate the dispersion curves of lattice structures with periodic defects. The accuracy and efficiency of the proposed method are demonstrated through numerical examples. Additionally, the effects of periodic defects in the lattice structures on the bandgap are analyzed.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"308 ","pages":"Article 113147"},"PeriodicalIF":3.4000,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An accurate and efficient method based on the dynamic stiffness matrix for analyzing wave propagation in defective lattice structures\",\"authors\":\"B.W. Yan, Q. Gao\",\"doi\":\"10.1016/j.ijsolstr.2024.113147\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this study, we present an efficient and accurate method for analyzing wave propagation in lattice structures with periodic defects, which are composed of three-dimensional (3D) unit cells arranged infinitely in two or three directions, with defects existing periodically along the directions of the arrangement. The unit cell is composed of 3D beams, and the dynamic stiffness formulation of the 3D beam is developed by combining the Timoshenko-Ehrenfest, Rayleigh-Love and torsion theories. Based on the dynamic stiffness matrix, any number or order of natural frequencies of defective lattice structures can be calculated accurately and efficiently using the Wittrick-Williams algorithm. By combining it with the Bloch theorem, the proposed method can be used to calculate the dispersion curves of lattice structures with periodic defects. The accuracy and efficiency of the proposed method are demonstrated through numerical examples. Additionally, the effects of periodic defects in the lattice structures on the bandgap are analyzed.</div></div>\",\"PeriodicalId\":14311,\"journal\":{\"name\":\"International Journal of Solids and Structures\",\"volume\":\"308 \",\"pages\":\"Article 113147\"},\"PeriodicalIF\":3.4000,\"publicationDate\":\"2024-11-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Solids and Structures\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0020768324005067\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Solids and Structures","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020768324005067","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MECHANICS","Score":null,"Total":0}

引用次数: 0

摘要

在本研究中，我们提出了一种高效、精确的方法，用于分析具有周期性缺陷的晶格结构中的波传播。这种结构由沿两个或三个方向无限排列的三维（3D）单元格组成，缺陷沿排列方向周期性存在。单元格由三维梁组成，通过结合 Timoshenko-Ehrenfest、Rayleigh-Love 和扭转理论，建立了三维梁的动态刚度公式。在动态刚度矩阵的基础上，利用 Wittrick-Williams 算法可以精确高效地计算出缺陷晶格结构的任意数量或顺序的固有频率。通过与布洛赫定理相结合，所提出的方法可用于计算具有周期性缺陷的晶格结构的频散曲线。通过数值示例证明了所提方法的准确性和高效性。此外，还分析了晶格结构中的周期性缺陷对带隙的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

An accurate and efficient method based on the dynamic stiffness matrix for analyzing wave propagation in defective lattice structures

In this study, we present an efficient and accurate method for analyzing wave propagation in lattice structures with periodic defects, which are composed of three-dimensional (3D) unit cells arranged infinitely in two or three directions, with defects existing periodically along the directions of the arrangement. The unit cell is composed of 3D beams, and the dynamic stiffness formulation of the 3D beam is developed by combining the Timoshenko-Ehrenfest, Rayleigh-Love and torsion theories. Based on the dynamic stiffness matrix, any number or order of natural frequencies of defective lattice structures can be calculated accurately and efficiently using the Wittrick-Williams algorithm. By combining it with the Bloch theorem, the proposed method can be used to calculate the dispersion curves of lattice structures with periodic defects. The accuracy and efficiency of the proposed method are demonstrated through numerical examples. Additionally, the effects of periodic defects in the lattice structures on the bandgap are analyzed.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

International Journal of Solids and Structures 物理-力学

CiteScore

6.70

自引率

8.30%

发文量

405

审稿时长

70 days

期刊介绍： The International Journal of Solids and Structures has as its objective the publication and dissemination of original research in Mechanics of Solids and Structures as a field of Applied Science and Engineering. It fosters thus the exchange of ideas among workers in different parts of the world and also among workers who emphasize different aspects of the foundations and applications of the field. Standing as it does at the cross-roads of Materials Science, Life Sciences, Mathematics, Physics and Engineering Design, the Mechanics of Solids and Structures is experiencing considerable growth as a result of recent technological advances. The Journal, by providing an international medium of communication, is encouraging this growth and is encompassing all aspects of the field from the more classical problems of structural analysis to mechanics of solids continually interacting with other media and including fracture, flow, wave propagation, heat transfer, thermal effects in solids, optimum design methods, model analysis, structural topology and numerical techniques. Interest extends to both inorganic and organic solids and structures.