Free vibration analysis of functionally graded rectangular nanoplates considering spatial variation of the nonlocal parameter

IF 1.1 4区工程技术 Q3 MATERIALS SCIENCE, CHARACTERIZATION & TESTING

Archives of Mechanics Pub Date : 2017-11-04 DOI:10.24423/AOM.2414

A. Ghassabi, S. Dag, E. Cigeroglu

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.

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考虑非局部参数空间变化的功能梯度矩形纳米片自由振动分析

我们提出了一种新的基于非局部弹性的功能梯度矩形纳米板自由振动分析方法。引入的方法允许考虑非局部参数的空间变化。运用变分法和汉密尔顿原理导出了控制偏微分方程及其相关的边界条件。位移场以统一的方式表示，以便能够产生与三种不同的板理论有关的数值结果，即Kirchhoff、Mindlin和三阶剪切变形理论。用广义微分求积法对方程组进行了数值求解。数值结果是通过考虑承受自由振动的简支和悬臂纳米板产生的。这些发现证明了无量纲板长、板理论、幂律指数和非局部参数比等因素对振动行为的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Archives of Mechanics 工程技术-材料科学：表征与测试

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

>12 weeks

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.