Nonlocal dynamic response of embedded single-layered graphene sheet via analytical approach

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• 作者：A. Ghorbanpour Arani ; M. H. Jalaei
• 刊名：Journal of Engineering Mathematics
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：98
• 期：1
• 页码：129-144
• 全文大小：849 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Applications of Mathematics
  Analysis
  Mathematical Modeling and IndustrialMathematics
  Numeric Computing
  
• 出版者：Springer Netherlands
• ISSN：1573-2703
• 卷排序：98

文摘

In the present research, static bending and dynamic responses of simply supported single-layered graphene sheet (SLGS) embedded in an elastic medium under uniform and sinusoidal loads are analytically investigated. The surrounding medium is simulated by visco-Pasternak model in which the damping and shearing effects are considered. Third-order shear deformation theory (TDST) is utilized because of its more accuracy relative to other plate theories. In order to consider size effects, nonlocal elasticity theory is employed. Applying Hamilton’s principle, governing equations of the SLGS are obtained and solved using Fourier series–Laplace transforms method. Finally, the detailed parametric study is conducted to scrutinize the influences of small-scale parameter, elastic medium, length-to-thickness ratio and aspect ratio of nanoplate on the static and dynamic behaviours of SLGS. Results indicated that the surrounding medium has a significant effect on the static and dynamic response, so that, increasing shear constant and damping coefficients cause to decrease the deflection of SLGS, considerably. The result of this study can be useful to control and improve the performance of this kind of nano-mechanical systems.KeywordsAnalytical solutionDynamic responseGraphene sheetNonlocal elasticity theoryTSDTVisco-Pasternak foundation