{"title":"Elastic wave propagation in periodic stress-driven nonlocal Timoshenko beams","authors":"","doi":"10.1016/j.ijsolstr.2024.113103","DOIUrl":null,"url":null,"abstract":"<div><div>Nonlocal theories are well established to model statics and dynamics of small-size structures. Recent studies investigated elastic wave propagation in nonlocal beams and attention focused on periodic nonlocal beams, either endowed with resonators or resting on supports, for relevant applications at small scale. In this context, this work proposes a stress-driven nonlocal Timoshenko beam formulation and develops an original and comprehensive analytical/computational framework for wave propagation analysis in bare and periodic beams.</div><div>The framework addresses infinite and finite beams. First, exact analytical expressions are derived for the dispersion curves of the bare beam, which provide full insight into the effects of nonlocality. Second, an exact Plane Wave Expansion method is devised for periodic beams, either equipped with mass-spring resonators or resting on elastic supports; both <span><math><mrow><mi>ω</mi><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>q</mi><mrow><mo>(</mo><mi>ω</mi><mo>)</mo></mrow></mrow></math></span> dispersion curves are derived in this work, where <span><math><mi>ω</mi></math></span> is the frequency and <span><math><mi>q</mi></math></span> is the wave number. Third, an approximate homogenization approach is formulated to estimate opening frequencies and sizes of band gaps induced by mass-spring resonators. Finally, a two-field finite element method is proposed to calculate the transmittance of finite periodic beams.</div><div>Numerical applications investigate the dispersion diagram of bare and periodic beams for different internal lengths of the stress-driven nonlocal model. Remarkably, results for finite periodic beams validate the predictions from wave propagation analysis of corresponding infinite ones. Moreover, parametric analyses show the capability of the stress-driven nonlocal model in capturing typical small-size effects.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":null,"pages":null},"PeriodicalIF":3.4000,"publicationDate":"2024-10-10","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/S0020768324004621","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
Abstract
Nonlocal theories are well established to model statics and dynamics of small-size structures. Recent studies investigated elastic wave propagation in nonlocal beams and attention focused on periodic nonlocal beams, either endowed with resonators or resting on supports, for relevant applications at small scale. In this context, this work proposes a stress-driven nonlocal Timoshenko beam formulation and develops an original and comprehensive analytical/computational framework for wave propagation analysis in bare and periodic beams.
The framework addresses infinite and finite beams. First, exact analytical expressions are derived for the dispersion curves of the bare beam, which provide full insight into the effects of nonlocality. Second, an exact Plane Wave Expansion method is devised for periodic beams, either equipped with mass-spring resonators or resting on elastic supports; both and dispersion curves are derived in this work, where is the frequency and is the wave number. Third, an approximate homogenization approach is formulated to estimate opening frequencies and sizes of band gaps induced by mass-spring resonators. Finally, a two-field finite element method is proposed to calculate the transmittance of finite periodic beams.
Numerical applications investigate the dispersion diagram of bare and periodic beams for different internal lengths of the stress-driven nonlocal model. Remarkably, results for finite periodic beams validate the predictions from wave propagation analysis of corresponding infinite ones. Moreover, parametric analyses show the capability of the stress-driven nonlocal model in capturing typical small-size effects.
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.