Soroush Sepehri, M. Mosavi Mashhadi, Mir Masoud Seyyed Fakhrabadi
{"title":"Wave propagation and directionality in two-dimensional periodic lattices considering shear deformations","authors":"Soroush Sepehri, M. Mosavi Mashhadi, Mir Masoud Seyyed Fakhrabadi","doi":"10.1177/23977914211069474","DOIUrl":null,"url":null,"abstract":"The effects of shear deformation on analysis of the wave propagation in periodic lattices are often assumed negligible. However, this assumption is not always true, especially for the lattices made of beams with smaller aspect ratios. Therefore, in the present paper, the effect of shear deformation on wave propagation in periodic lattices with different topologies is studied and their wave attenuation and directionality performances are compared. Current experimental limitations make the researchers focus more on the wave propagation in the direction perpendicular to the plane of periodicity in micro/nanoscale lattice materials while for their macro/mesoscale counterparts, in-plane modes can also be analyzed as well as the out-of-plane ones. Four well-known topologies of hexagonal, triangular, square, and Kagomé are considered in the current paper and their wave propagation is investigated both in the plane of periodicity and in the out-of-plane direction. The finite element method is used to formulate the governing equations and Bloch’s theorem is used to solve the dispersion relations. To investigate the effect of shear deformation, both the Timoshenko and Euler-Bernoulli beam theories are implemented. The results indicate that including shear deformation in wave propagation has a softening effect on the band diagrams of wave propagation and moves the dispersion branches to lower frequencies. It can also reveal some bandgaps that are not predicted without considering the shear deformation.","PeriodicalId":44789,"journal":{"name":"Proceedings of the Institution of Mechanical Engineers Part N-Journal of Nanomaterials Nanoengineering and Nanosystems","volume":"122 1","pages":"101 - 116"},"PeriodicalIF":4.2000,"publicationDate":"2022-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Institution of Mechanical Engineers Part N-Journal of Nanomaterials Nanoengineering and Nanosystems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1177/23977914211069474","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"NANOSCIENCE & NANOTECHNOLOGY","Score":null,"Total":0}
引用次数: 1
Abstract
The effects of shear deformation on analysis of the wave propagation in periodic lattices are often assumed negligible. However, this assumption is not always true, especially for the lattices made of beams with smaller aspect ratios. Therefore, in the present paper, the effect of shear deformation on wave propagation in periodic lattices with different topologies is studied and their wave attenuation and directionality performances are compared. Current experimental limitations make the researchers focus more on the wave propagation in the direction perpendicular to the plane of periodicity in micro/nanoscale lattice materials while for their macro/mesoscale counterparts, in-plane modes can also be analyzed as well as the out-of-plane ones. Four well-known topologies of hexagonal, triangular, square, and Kagomé are considered in the current paper and their wave propagation is investigated both in the plane of periodicity and in the out-of-plane direction. The finite element method is used to formulate the governing equations and Bloch’s theorem is used to solve the dispersion relations. To investigate the effect of shear deformation, both the Timoshenko and Euler-Bernoulli beam theories are implemented. The results indicate that including shear deformation in wave propagation has a softening effect on the band diagrams of wave propagation and moves the dispersion branches to lower frequencies. It can also reveal some bandgaps that are not predicted without considering the shear deformation.
期刊介绍:
Proceedings of the Institution of Mechanical Engineers Part N-Journal of Nanomaterials Nanoengineering and Nanosystems is a peer-reviewed scientific journal published since 2004 by SAGE Publications on behalf of the Institution of Mechanical Engineers. The journal focuses on research in the field of nanoengineering, nanoscience and nanotechnology and aims to publish high quality academic papers in this field. In addition, the journal is indexed in several reputable academic databases and abstracting services, including Scopus, Compendex, and CSA's Advanced Polymers Abstracts, Composites Industry Abstracts, and Earthquake Engineering Abstracts.