{"title":"Surface and crack effects on longitudinal vibration of thick nanorods with various boundary conditions","authors":"H. Shokrollahi, R. Nazemnezhad","doi":"10.1177/23977914231193632","DOIUrl":null,"url":null,"abstract":"Considering the effect of surface parameters and crack on the longitudinal vibration of nanorods is the aim of this study. The nanorod is assumed to be thick, and it is modeled based on Bishop theory of rods. In thick nanorods, the effects of the inertia of lateral motions and the shear stiffness are considered in the kinetic energy and the strain energy of the nanorod, respectively. In the present study, the crack is modeled as a linear spring in which its stiffness is related to the crack severity. The surface parameters considered are the surface Lamé constants, the surface density, and the surface stress. Considering all surface parameters causes inhomogeneity of governing equations and boundary conditions. After converting inhomogeneous equations to homogeneous ones, the resulted equations are solved numerically. All possible boundary conditions are introduced but only natural frequencies of nanorod with fixed-fixed and fixed-free are reported. In addition to considering the effect of type of boundary conditions on the natural frequencies, the effect of geometrical parameters like radius and length, and mode number is also considered. The results are presented for both thin and thick nanorods to compare the effect of various parameters especially surface parameters on longitudinal frequencies.","PeriodicalId":44789,"journal":{"name":"Proceedings of the Institution of Mechanical Engineers Part N-Journal of Nanomaterials Nanoengineering and Nanosystems","volume":null,"pages":null},"PeriodicalIF":4.2000,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","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/10.1177/23977914231193632","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: 0
Abstract
Considering the effect of surface parameters and crack on the longitudinal vibration of nanorods is the aim of this study. The nanorod is assumed to be thick, and it is modeled based on Bishop theory of rods. In thick nanorods, the effects of the inertia of lateral motions and the shear stiffness are considered in the kinetic energy and the strain energy of the nanorod, respectively. In the present study, the crack is modeled as a linear spring in which its stiffness is related to the crack severity. The surface parameters considered are the surface Lamé constants, the surface density, and the surface stress. Considering all surface parameters causes inhomogeneity of governing equations and boundary conditions. After converting inhomogeneous equations to homogeneous ones, the resulted equations are solved numerically. All possible boundary conditions are introduced but only natural frequencies of nanorod with fixed-fixed and fixed-free are reported. In addition to considering the effect of type of boundary conditions on the natural frequencies, the effect of geometrical parameters like radius and length, and mode number is also considered. The results are presented for both thin and thick nanorods to compare the effect of various parameters especially surface parameters on longitudinal frequencies.
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.