Wave propagation responses of porous bi-directional functionally graded magneto-electro-elastic nanoshells via nonlocal strain gradient theory

IF 4.5 2区工程技术 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Mechanics-English Edition Pub Date : 2023-09-30 DOI:10.1007/s10483-023-3043-7

Xinte Wang, Juan Liu, Biao Hu, Bo Zhang, Huoming Shen

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Abstract

This study examines the wave propagation characteristics for a bi-directional functional grading of barium titanate (BaTiO₃) and cobalt ferrite (CoFe₂O₄) porous nanoshells, the porosity distribution of which is simulated by the honeycomb-shaped symmetrical and asymmetrical distribution functions. The nonlocal strain gradient theory (NSGT) and first-order shear deformation theory are used to determine the size effect and shear deformation, respectively. Nonlocal governing equations are derived for the nanoshells by Hamilton’s principle. The resulting dimensionless differential equations are solved by means of an analytical solution of the combined exponential function after dimensionless treatment. Finally, extensive parametric surveys are conducted to investigate the influence of diverse parameters, such as dimensionless scale parameters, radius-to-thickness ratios, bi-directional functionally graded (FG) indices, porosity coefficients, and dimensionless electromagnetic potentials on the wave propagation characteristics. Based on the analysis results, the effect of the dimensionless scale parameters on the dispersion relationship is found to be related to the ratio of the scale parameters. The wave propagation characteristics of nanoshells in the presence of a magnetoelectric field depend on the bi-directional FG indices.

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基于非局部应变梯度理论的多孔双向功能梯度磁电弹性纳米壳的波传播响应

本研究考察了钛酸钡（BaTiO3）和钴铁氧体（CoFe2O4）多孔纳米壳的双向功能分级的波传播特性，其孔隙率分布通过蜂窝状对称和非对称分布函数模拟。采用非局部应变梯度理论（NSGT）和一阶剪切变形理论分别确定了尺寸效应和剪切变形。利用汉密尔顿原理导出了纳米壳的非局部控制方程。所得到的无量纲微分方程是通过无量纲处理后的组合指数函数的解析解来求解的。最后，进行了广泛的参数调查，以研究不同参数对波传播特性的影响，如无量纲尺度参数、径厚比、双向功能梯度（FG）指数、孔隙率系数和无量纲电磁势。基于分析结果，发现无量纲尺度参数对色散关系的影响与尺度参数的比值有关。在存在磁电场的情况下，纳米壳的波传播特性取决于双向FG指数。

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

Applied Mathematics and Mechanics-English Edition 数学-力学

CiteScore

6.70

自引率

9.10%

发文量

106

审稿时长

2.0 months

期刊介绍： Applied Mathematics and Mechanics is the English version of a journal on applied mathematics and mechanics published in the People''s Republic of China. Our Editorial Committee, headed by Professor Chien Weizang, Ph.D., President of Shanghai University, consists of scientists in the fields of applied mathematics and mechanics from all over China. Founded by Professor Chien Weizang in 1980, Applied Mathematics and Mechanics became a bimonthly in 1981 and then a monthly in 1985. It is a comprehensive journal presenting original research papers on mechanics, mathematical methods and modeling in mechanics as well as applied mathematics relevant to neoteric mechanics.