A Hardening Nonlocal Elasticity Approach to Axial Vibration Analysis of an Arbitrarily Supported FG Nanorod

IF 1.8 4区材料科学 Q2 MATERIALS SCIENCE, CHARACTERIZATION & TESTING

Physical Mesomechanics Pub Date : 2023-06-30 DOI:10.1134/S1029959923030050

B. Uzun, Ö. Civalek, M. Ö. Yayli

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Abstract

The present work is aimed at analyzing free longitudinal vibrations of nanorods composed of a functionally graded (FG) material with deformable boundaries within a hardening nonlocal elasticity approach. For this purpose, a FG nanorod composed of the ceramic and metal constituents is considered to be elastically supported by means of axial springs at both ends. Then the analytical method based on the association of the Fourier sine series and the Stokes transformation is developed to solve the free axial vibration problem of a FG nanorod with both deformable and nondeformable boundaries. Free axial vibration of a restrained FG nanorod is first studied within hardening nonlocal elasticity. To show the validity and profitability of the proposed analytical method, the presented Fourier series method with the Stokes transformation is used for the analysis of axial vibration of a rigidly supported homogeneous nanorod by setting the appropriate spring stiffness values. The main superiority of this new approach is in its power of dealing with numerous boundary conditions to determine longitudinal vibration frequencies of FG nanorods. Using the present solution method, various numerical applications are given for different small-scale parameters, gradient index, and nanorod length.

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任意支承FG纳米棒轴向振动分析的硬化非局部弹性方法

目前的工作旨在分析由具有可变形边界的功能梯度(FG)材料组成的纳米棒在硬化非局部弹性方法中的自由纵向振动。为此，一个由陶瓷和金属成分组成的FG纳米棒被认为是通过两端的轴向弹簧进行弹性支撑的。在此基础上，提出了基于傅立叶正弦级数和Stokes变换关联的解析方法，用于求解具有变形边界和非变形边界的FG纳米棒的自由轴向振动问题。在非局部弹性硬化条件下，首次研究了受约束FG纳米棒的自由轴向振动。为了验证所提分析方法的有效性和可操作性，通过设置适当的弹簧刚度值，采用Stokes变换的傅里叶级数方法对刚性支承均匀纳米棒的轴向振动进行了分析。该方法的主要优点在于它能够处理大量的边界条件来确定FG纳米棒的纵向振动频率。利用该方法，给出了不同小尺度参数、梯度指数和纳米棒长度的数值应用。

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来源期刊

Physical Mesomechanics Materials Science-General Materials Science

CiteScore

3.50

自引率

18.80%

发文量

期刊介绍： The journal provides an international medium for the publication of theoretical and experimental studies and reviews related in the physical mesomechanics and also solid-state physics, mechanics, materials science, geodynamics, non-destructive testing and in a large number of other fields where the physical mesomechanics may be used extensively. Papers dealing with the processing, characterization, structure and physical properties and computational aspects of the mesomechanics of heterogeneous media, fracture mesomechanics, physical mesomechanics of materials, mesomechanics applications for geodynamics and tectonics, mesomechanics of smart materials and materials for electronics, non-destructive testing are viewed as suitable for publication.