{"title":"Free vibration analysis of functionally graded rectangular nanoplates considering spatial variation of the nonlocal parameter","authors":"A. Ghassabi, S. Dag, E. Cigeroglu","doi":"10.24423/AOM.2414","DOIUrl":null,"url":null,"abstract":"We present a new nonlocal elasticity-based analysis method for free vibrations of functionally graded rectangular nanoplates. The introduced method allows taking into account spatial variation of the nonlocal parameter. Governing partial differential equations and associated boundary conditions are derived by employing the variational approach and applying Hamilton’s principle. Displacement field is expressed in a unified way to be able to produce numerical results pertaining to three different plate theories, namely Kirchhoff, Mindlin, and third-order shear deformation theories. The equations are solved numerically by means of the generalized differentia quadrature method. Numerical results are generated by considering simply-supported and cantilever nanoplates undergoing free vibrations. These findings demonstrate the influences of factors such as dimensionless plate length, plate theory, power-law index, and nonlocal parameter ratio upon vibration behavior.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2017-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archives of Mechanics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.24423/AOM.2414","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATERIALS SCIENCE, CHARACTERIZATION & TESTING","Score":null,"Total":0}
引用次数: 7
Abstract
We present a new nonlocal elasticity-based analysis method for free vibrations of functionally graded rectangular nanoplates. The introduced method allows taking into account spatial variation of the nonlocal parameter. Governing partial differential equations and associated boundary conditions are derived by employing the variational approach and applying Hamilton’s principle. Displacement field is expressed in a unified way to be able to produce numerical results pertaining to three different plate theories, namely Kirchhoff, Mindlin, and third-order shear deformation theories. The equations are solved numerically by means of the generalized differentia quadrature method. Numerical results are generated by considering simply-supported and cantilever nanoplates undergoing free vibrations. These findings demonstrate the influences of factors such as dimensionless plate length, plate theory, power-law index, and nonlocal parameter ratio upon vibration behavior.
期刊介绍：
Archives of Mechanics provides a forum for original research on mechanics of solids, fluids and discrete systems, including the development of mathematical methods for solving mechanical problems. The journal encompasses all aspects of the field, with the emphasis placed on:
-mechanics of materials: elasticity, plasticity, time-dependent phenomena, phase transformation, damage, fracture; physical and experimental foundations, micromechanics, thermodynamics, instabilities;
-methods and problems in continuum mechanics: general theory and novel applications, thermomechanics, structural analysis, porous media, contact problems;
-dynamics of material systems;
-fluid flows and interactions with solids.
Papers published in the Archives should contain original contributions dealing with theoretical, experimental, or numerical aspects of mechanical problems listed above.
The journal publishes also current announcements and information about important scientific events of possible interest to its readers, like conferences, congresses, symposia, work-shops, courses, etc.
Occasionally, special issues of the journal may be devoted to publication of all or selected papers presented at international conferences or other scientific meetings. However, all papers intended for such an issue are subjected to the usual reviewing and acceptance procedure.
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