Dynamics of a non-circular-shaped nanorod with deformable boundaries based on second-order strain gradient theory

IF 2.2 3区 工程技术 Q2 MECHANICS Archive of Applied Mechanics Pub Date : 2024-09-26 DOI:10.1007/s00419-024-02683-6
Ömer Civalek, Murat Akpınar, Büşra Uzun, Mustafa Özgür Yaylı
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Abstract

In this study, a general method is developed for the torsional vibration of non-circular-shaped nanorods with varying boundary conditions using second-order strain gradient theory. In most of the studies in the literature, the cross section of the rods is considered to be circular. The reason for this is that the use of warping function is inevitable when the cross section geometry is not circular. For circular cross sections after torsion, the warping is very small and is considered to be non-existent. For non-circular sections, cross section warping should be taken into account in mathematical calculations. The cross section geometry is different from circular in this study, and the boundary conditions are not rigid, contrary to most studies in the literature. In this paper, the second-order strain gradient theory and the most general solution method are discussed. In some specific cases, it is possible to transform the problem into many studies found in the literature. The correctness of the algorithm is tested by comparing the resulting solutions with closed solutions found in the literature. The influence of some variables on the torsional frequencies is illustrated by a series of graphical figures, and the superiority of the applied method is summarized.

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基于二阶应变梯度理论的具有可变形边界的非圆形纳米棒的动力学特性
本研究利用二阶应变梯度理论,为边界条件变化的非圆形纳米棒的扭转振动开发了一种通用方法。在大多数文献研究中,纳米棒的横截面都被认为是圆形的。原因是当横截面几何形状不是圆形时,使用翘曲函数是不可避免的。对于扭转后的圆形截面,翘曲非常小,被认为不存在。对于非圆形截面,在数学计算中应考虑截面翘曲。本研究的横截面几何形状不同于圆形,边界条件也不是刚性的,这与文献中的大多数研究相反。本文讨论了二阶应变梯度理论和最一般的求解方法。在某些特定情况下,可以将问题转化为文献中的许多研究。通过将得到的解与文献中的封闭解进行比较,检验了算法的正确性。通过一系列图表说明了一些变量对扭转频率的影响,并总结了所应用方法的优越性。
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
CiteScore
4.40
自引率
10.70%
发文量
234
审稿时长
4-8 weeks
期刊介绍: Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.
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