Integrating finite element modeling with high-order shear deformation theory for nonlinear free vibration of CNT/SiO2 nanocomposite plates

IF 2.9 3区 工程技术 Q2 MECHANICS
Raheb Gholami, Reza Ansari, Mohammad Kazem Hassanzadeh-Aghdam, Alireza Moradi, Saeid Sahmani
{"title":"Integrating finite element modeling with high-order shear deformation theory for nonlinear free vibration of CNT/SiO2 nanocomposite plates","authors":"Raheb Gholami,&nbsp;Reza Ansari,&nbsp;Mohammad Kazem Hassanzadeh-Aghdam,&nbsp;Alireza Moradi,&nbsp;Saeid Sahmani","doi":"10.1007/s00707-025-04406-6","DOIUrl":null,"url":null,"abstract":"<div><p>This study establishes a unified framework to investigate the mechanical properties and geometrically nonlinear free vibration of polymer nanocomposite rectangular plates containing carbon nanotubes (CNTs) and silica nanoparticles (SiO<sub>2</sub>). A micromechanics-based finite element approach is employed to predict the effective mechanical properties of the hybrid nanocomposite, accounting for factors such as volume fraction, nanofiller geometries, interphase characteristics, and clustering effects. The geometrically nonlinear governing equations are derived using Reddy’s third-order shear deformation plate theory, von Kármán-type nonlinear strain–displacement relations, and Hamilton’s principle. In order to solve the governing equations, a multistep numerical methodology is applied, incorporating the generalized differential quadrature scheme, Galerkin approach, time-periodic differential scheme, pseudo-arc-length continuation algorithm, and modified Newton–Raphson method. A comprehensive assessment of nonlinear frequency response curves is performed with consideration of microstructure-level parameters and boundary condition variations. It is concluded that increasing nanofiller content, leveraging elongated CNTs and fine SiO<sub>2</sub>, and optimizing nanofiller dispersion patterns significantly enhance both linear and nonlinear frequencies, with fully clamped boundary conditions exhibiting the highest frequencies. When the length (width)-to-thickness ratio of a 1 vol.% CNT/5 vol.% SiO<sub>2</sub>/polymer nanocomposite plate is 12, the non-dimensional linear frequencies incorporating aligned, randomly oriented, and agglomerated nanofillers are 0.6765, 0.5814, and 0.5237, respectively, under simply supported edges, and 1.187, 1.0196, and 0.9179, respectively, under fully clamped edges.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 8","pages":"4699 - 4725"},"PeriodicalIF":2.9000,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mechanica","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00707-025-04406-6","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0

Abstract

This study establishes a unified framework to investigate the mechanical properties and geometrically nonlinear free vibration of polymer nanocomposite rectangular plates containing carbon nanotubes (CNTs) and silica nanoparticles (SiO2). A micromechanics-based finite element approach is employed to predict the effective mechanical properties of the hybrid nanocomposite, accounting for factors such as volume fraction, nanofiller geometries, interphase characteristics, and clustering effects. The geometrically nonlinear governing equations are derived using Reddy’s third-order shear deformation plate theory, von Kármán-type nonlinear strain–displacement relations, and Hamilton’s principle. In order to solve the governing equations, a multistep numerical methodology is applied, incorporating the generalized differential quadrature scheme, Galerkin approach, time-periodic differential scheme, pseudo-arc-length continuation algorithm, and modified Newton–Raphson method. A comprehensive assessment of nonlinear frequency response curves is performed with consideration of microstructure-level parameters and boundary condition variations. It is concluded that increasing nanofiller content, leveraging elongated CNTs and fine SiO2, and optimizing nanofiller dispersion patterns significantly enhance both linear and nonlinear frequencies, with fully clamped boundary conditions exhibiting the highest frequencies. When the length (width)-to-thickness ratio of a 1 vol.% CNT/5 vol.% SiO2/polymer nanocomposite plate is 12, the non-dimensional linear frequencies incorporating aligned, randomly oriented, and agglomerated nanofillers are 0.6765, 0.5814, and 0.5237, respectively, under simply supported edges, and 1.187, 1.0196, and 0.9179, respectively, under fully clamped edges.

Abstract Image

基于高阶剪切变形理论的CNT/SiO2纳米复合材料板非线性自由振动有限元建模
本研究建立了一个统一的框架来研究含碳纳米管(CNTs)和二氧化硅纳米颗粒(SiO2)的聚合物纳米复合材料矩形板的力学性能和几何非线性自由振动。采用基于微力学的有限元方法,考虑了体积分数、纳米填料几何形状、界面特征和聚类效应等因素,预测了混合纳米复合材料的有效力学性能。利用Reddy的三阶剪切变形板理论、von Kármán-type非线性应变-位移关系和Hamilton原理推导出几何非线性控制方程。为了求解控制方程,采用了多步数值方法,包括广义微分正交格式、Galerkin方法、时间周期微分格式、伪弧长延拓算法和改进的Newton-Raphson方法。考虑微观结构参数和边界条件变化,对非线性频响曲线进行了综合评价。结果表明,增加纳米填料含量、利用细长型碳纳米管和细SiO2以及优化纳米填料色散模式可显著提高线性和非线性频率,其中完全箝位边界条件下的频率最高。当1 vol.% CNT/5 vol.% SiO2/聚合物纳米复合材料板的长(宽)厚比为12时,包含排列、随机取向和团聚纳米填料的无维线性频率在简支边下分别为0.6765、0.5814和0.5237,在完全夹紧边下分别为1.187、1.0196和0.9179。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Acta Mechanica
Acta Mechanica 物理-力学
CiteScore
4.30
自引率
14.80%
发文量
292
审稿时长
6.9 months
期刊介绍: Since 1965, the international journal Acta Mechanica has been among the leading journals in the field of theoretical and applied mechanics. In addition to the classical fields such as elasticity, plasticity, vibrations, rigid body dynamics, hydrodynamics, and gasdynamics, it also gives special attention to recently developed areas such as non-Newtonian fluid dynamics, micro/nano mechanics, smart materials and structures, and issues at the interface of mechanics and materials. The journal further publishes papers in such related fields as rheology, thermodynamics, and electromagnetic interactions with fluids and solids. In addition, articles in applied mathematics dealing with significant mechanics problems are also welcome.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信