{"title":"微结构梁系统与两相非局部梁的关系","authors":"Xiao-Jian Xu, Min-Jie Bu, Chao-Hui Wang","doi":"10.1007/s00419-025-02927-z","DOIUrl":null,"url":null,"abstract":"<div><p>Recent advances in the study of thin beams within the framework of nonlocal elasticity demonstrate a close relationship between micro-structured beam systems and Eringen’s differential-type nonlocal beams. In this paper, we establish relationships between a micro-structured beam system and a two-phase nonlocal beam through the equivalence of natural frequencies under two typical boundary conditions: clamped-free and doubly clamped. The analytical characteristic equations of two-phase nonlocal beams are derived and compared to approximately analytical equations to prevent numerical overflow in cases with small volume fractions of material and nonlocal parameters. This work proposes calibrated procedures that may facilitate the equivalence of material mechanics commonly used in engineering applications.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 10","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Relationships of a micro-structured beam system and a two-phase nonlocal beam\",\"authors\":\"Xiao-Jian Xu, Min-Jie Bu, Chao-Hui Wang\",\"doi\":\"10.1007/s00419-025-02927-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Recent advances in the study of thin beams within the framework of nonlocal elasticity demonstrate a close relationship between micro-structured beam systems and Eringen’s differential-type nonlocal beams. In this paper, we establish relationships between a micro-structured beam system and a two-phase nonlocal beam through the equivalence of natural frequencies under two typical boundary conditions: clamped-free and doubly clamped. The analytical characteristic equations of two-phase nonlocal beams are derived and compared to approximately analytical equations to prevent numerical overflow in cases with small volume fractions of material and nonlocal parameters. This work proposes calibrated procedures that may facilitate the equivalence of material mechanics commonly used in engineering applications.</p></div>\",\"PeriodicalId\":477,\"journal\":{\"name\":\"Archive of Applied Mechanics\",\"volume\":\"95 10\",\"pages\":\"\"},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2025-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archive of Applied Mechanics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00419-025-02927-z\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive of Applied Mechanics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00419-025-02927-z","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
Relationships of a micro-structured beam system and a two-phase nonlocal beam
Recent advances in the study of thin beams within the framework of nonlocal elasticity demonstrate a close relationship between micro-structured beam systems and Eringen’s differential-type nonlocal beams. In this paper, we establish relationships between a micro-structured beam system and a two-phase nonlocal beam through the equivalence of natural frequencies under two typical boundary conditions: clamped-free and doubly clamped. The analytical characteristic equations of two-phase nonlocal beams are derived and compared to approximately analytical equations to prevent numerical overflow in cases with small volume fractions of material and nonlocal parameters. This work proposes calibrated procedures that may facilitate the equivalence of material mechanics commonly used in engineering applications.
期刊介绍：
Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.
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