{"title":"Integrating finite element modeling with high-order shear deformation theory for nonlinear free vibration of CNT/SiO2 nanocomposite plates","authors":"Raheb Gholami, Reza Ansari, Mohammad Kazem Hassanzadeh-Aghdam, Alireza Moradi, 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.
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.