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Modeling of nonlinear vibration of graphene sheets using a meshfree method based on nonlocal elasticity theory

机译：基于非局部弹性理论的无网格法建模石墨烯片的非线性振动

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摘要

Due to their valuable and unique properties, graphene sheets (GSs) have attracted increasing attention in recent years. This paper presents the mathematical modeling of the nonlinear vibration behavior of GSs using classic plate theory and nonlocal elasticity theory which accounts for the size effect. The numerical solutions are obtained through the element-free kp-Ritz method. The iteration process is dealt with using the linearized updated mode method. The transformation method is used to impose the boundary conditions. The published results are used to verify the correctness of the present nonlocal element-free kp-Ritz method. The effects of boundary conditions, side length, aspect ratio and nonlocal parameters on the frequency-amplitude response are examined.
机译：由于其宝贵和独特的性能，近年来石墨烯片（GSs）引起了越来越多的关注。本文利用经典板理论和非局部弹性理论，对尺寸效应进行了数学建模。数值解是通过无元素kp-Ritz方法获得的。使用线性化更新模式方法处理迭代过程。变换方法用于施加边界条件。已发布的结果用于验证当前的非局部无kp-Ritz方法的正确性。研究了边界条件，边长，长宽比和非局部参数对频率-幅度响应的影响。

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  • 来源
    《Applied Mathematical Modelling》 |2017年第9期|691-704|共14页
  • 作者

    L.W. Zhang; Yang Zhang; K.M. Liew;

  • 作者单位

    School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;

    Department of Architecture and Civil Engineering City University of Hong Kong, Kowloon, Hong Kong, China,City University of Hong Kong Shenzhen Research Institute, Shenzhen 518057, China;

    Department of Architecture and Civil Engineering City University of Hong Kong, Kowloon, Hong Kong, China,City University of Hong Kong Shenzhen Research Institute, Shenzhen 518057, China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Frequency amplitude response; Nonlocal theory; Nonlinear vibration; Graphene sheets; Meshfree method; Ritz method;

    机译：频率幅度响应;非本地理论;非线性振动;石墨烯片无网格方法;里兹法;

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