Highl'/> Exact modes for post-buckling characteristics of nonlocal nanobeams in a longitudinal magnetic field
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Exact modes for post-buckling characteristics of nonlocal nanobeams in a longitudinal magnetic field

机译：纵向磁场中非局部纳米束屈曲后特性的精确模式

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摘要

Highlights•Exact mode solution is utilized to analyze postbuckling dynamics of the nanobeam in a longitudinal magnetic field.•The introduced magnetic field can increase the critical buckling load to enhance the stability of the nanobeam.•The nonlocal impact results in a decrease in the critical buckling load.•The nonlocal effect can speed up the activation of the internal resonance between the first two modes.•A significant difference is obtained for the first frequency when considering classical and exact mode solutions.AbstractAn exact mode solution that investigates the prebuckling and postbuckling characteristics of nonlocal nanobeams with fixed–fixed, hinged–hinged, and fixed–hinged boundary conditions in a longitudinal magnetic field is determined. The geometric nonlinearity arising from mid-plane stretching is considered to obtain the nonlinear governing equation of motion by virtue of Hamilton's principle. The influences of the nonlocal and magnetic parameters on the prebuckling and postbuckling dynamics of nanobeams with various boundary conditions are evaluated, indicating that the critical buckling force can be decreased with the increase of the nonlocal parameter while can be increased with increasing the magnetic parameter. It is demonstrated that the first natural frequency of the nanobeam with fixed–fixed and fixed–hinged conditions in postbuckling configuration is increased from zero to a constant value for higher values of the nonlocal parameter with increasing the axial force. The second natural frequency of the buckled nanobeam is always decreased with an increase of the nonlocal parameter. The results show that the internal resonance between the first and second modes of the postbuckling nanobeams can be quickly and easily activated by increasing the nonlocal parameters, especially for fixed–fixed and hinged–hinged boundary conditions. In addition, the results obtained by exact mode solution are compared those obtained by classical mode solution. It is found that the classical mode is valid only for nonlocal nanobeams with the hinged–hinged boundary conditions.
机译： 突出显示 • 精确模式解决方案用于分析纳米束在纵向磁场中的屈曲后动力学。 • 引入的磁场会增加临界屈曲载荷，从而增强纳米束的稳定性。 • 非本地影响导致临界屈曲载荷的减少。 • 非局部效应可以加快前两种模式之间的内部共振的激活。 • 摘要 一种精确模式解决方案，用于研究具有固定-固定，铰接-铰接和固定状态的非局部纳米光束的预屈曲和后屈曲特性确定了纵向磁场中的铰接边界条件。借助汉密尔顿原理，考虑了由中平面拉伸产生的几何非线性，从而获得了运动的非线性控制方程。评估了非局部和磁参数对具有各种边界条件的纳米束的预屈曲和后屈曲动力学的影响，表明临界屈曲力可以随非局部参数的增加而减小，而随屈曲强度随磁参数的增加而增大。结果表明，随着轴向力的增加，在非局部参数较高的情况下，后屈曲状态下具有固定-固定和固定-铰接条件的纳米束的第一固有频率从零增加到恒定值。弯曲的纳米束的第二固有频率总是随着非局部参数的增加而降低。结果表明，通过增加非局部参数，可以快速，轻松地激活屈曲后纳米束的第一和第二模式之间的内部共振，特别是对于固定-固定和铰接-铰接的边界条件。另外，将通过精确模式解获得的结果与通过经典模式解获得的结果进行比较。发现经典模式仅对具有铰接铰接边界条件的非局部纳米光束有效。

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  • 来源
    《Applied Mathematical Modelling》 |2018年第3期|758-775|共18页
  • 作者

    H.L. Dai; S. Ceballes; A. Abdelkefi; Y.Z. Hong; L. Wang;

  • 作者单位

    Department of Mechanics, Huazhong University of Science and Technology,Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment;

    Department of Mechanical and Aerospace Engineering, New Mexico State University;

    Department of Mechanical and Aerospace Engineering, New Mexico State University;

    Department of Mechanics, Huazhong University of Science and Technology,Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment;

    Department of Mechanics, Huazhong University of Science and Technology,Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment;

  • 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

    Nonlocal nanobeam; Postbuckling; Exact mode solution; Boundary conditions; Longitudinal magnetic field; Internal resonance;

    机译：非局域纳米束;后屈曲;精确模式解;边界条件;纵向磁场;内部共振;

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