Surface and crack effects on longitudinal vibration of thick nanorods with various boundary conditions

H. Shokrollahi, R. Nazemnezhad
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Abstract

Considering the effect of surface parameters and crack on the longitudinal vibration of nanorods is the aim of this study. The nanorod is assumed to be thick, and it is modeled based on Bishop theory of rods. In thick nanorods, the effects of the inertia of lateral motions and the shear stiffness are considered in the kinetic energy and the strain energy of the nanorod, respectively. In the present study, the crack is modeled as a linear spring in which its stiffness is related to the crack severity. The surface parameters considered are the surface Lamé constants, the surface density, and the surface stress. Considering all surface parameters causes inhomogeneity of governing equations and boundary conditions. After converting inhomogeneous equations to homogeneous ones, the resulted equations are solved numerically. All possible boundary conditions are introduced but only natural frequencies of nanorod with fixed-fixed and fixed-free are reported. In addition to considering the effect of type of boundary conditions on the natural frequencies, the effect of geometrical parameters like radius and length, and mode number is also considered. The results are presented for both thin and thick nanorods to compare the effect of various parameters especially surface parameters on longitudinal frequencies.
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不同边界条件下,表面和裂纹对粗纳米棒纵向振动的影响
考虑表面参数和裂纹对纳米棒纵向振动的影响是本研究的目的。假设纳米棒很粗,并基于Bishop棒理论对其进行建模。在厚纳米棒中,横向运动惯量和剪切刚度的影响分别考虑在纳米棒的动能和应变能中。在本研究中,将裂纹建模为线性弹簧,其刚度与裂纹严重程度相关。所考虑的表面参数是表面lam常数、表面密度和表面应力。考虑所有表面参数导致控制方程和边界条件的不均匀性。将非齐次方程转化为齐次方程,对所得方程进行数值求解。引入了所有可能的边界条件,但只报道了固定-固定和自由-固定纳米棒的固有频率。除了考虑边界条件类型对固有频率的影响外,还考虑了半径、长度、模态数等几何参数对固有频率的影响。本文给出了薄纳米棒和厚纳米棒的实验结果,比较了各种参数特别是表面参数对纵向频率的影响。
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来源期刊
CiteScore
6.00
自引率
1.70%
发文量
24
期刊介绍: Proceedings of the Institution of Mechanical Engineers Part N-Journal of Nanomaterials Nanoengineering and Nanosystems is a peer-reviewed scientific journal published since 2004 by SAGE Publications on behalf of the Institution of Mechanical Engineers. The journal focuses on research in the field of nanoengineering, nanoscience and nanotechnology and aims to publish high quality academic papers in this field. In addition, the journal is indexed in several reputable academic databases and abstracting services, including Scopus, Compendex, and CSA's Advanced Polymers Abstracts, Composites Industry Abstracts, and Earthquake Engineering Abstracts.
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