An exact analytical method for free vibration analysis of FG-GPLRC sector cylindrical shells under Levy-type boundary conditions

IF 2.3 3区工程技术 Q2 MECHANICS Acta Mechanica Pub Date : 2024-09-09 DOI:10.1007/s00707-024-04072-0

Ata Alipour Ghassabi, Ali Razgordanisharahi, Gullu Kiziltas Sendur, Yaser Kiani, Christian Hellmich

{"title":"An exact analytical method for free vibration analysis of FG-GPLRC sector cylindrical shells under Levy-type boundary conditions","authors":"Ata Alipour Ghassabi, Ali Razgordanisharahi, Gullu Kiziltas Sendur, Yaser Kiani, Christian Hellmich","doi":"10.1007/s00707-024-04072-0","DOIUrl":null,"url":null,"abstract":"<div><p>In this article, an exact analytical method for the free vibration analysis of functionally graded (FG) graphene platelet (GPL)-reinforced composite (GPLRC) sector cylindrical shells is presented by considering Levy-type boundary conditions for the first time. The analysis relies on the use of the Halpin–Tsai micro-mechanical model for evaluating the material properties of the graded layers of the shell with three different grading patterns. Mathematical modeling of the Levy-type cylindrical shell is based on the Hamilton principle and the Sanders first-order shear deformation theory (FSDT). The governing equations of the composite shell are analytically solved using the state-space method. The validity of the proposed analytical method is demonstrated by the excellent agreement between the obtained results of the exact analytical solution and the results available in the literature. Furthermore, some parametric studies are conducted to reveal the effects of variations in boundary conditions, GPL distribution patterns, GPL weight fraction, and geometrical parameters such as shallowness angle, length-to-radius ratio, and thickness on the free vibration behavior of the shell structure. Natural frequencies and mode switching are reported for different mode numbers.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"235 11","pages":"6849 - 6865"},"PeriodicalIF":2.3000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00707-024-04072-0.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mechanica","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00707-024-04072-0","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

In this article, an exact analytical method for the free vibration analysis of functionally graded (FG) graphene platelet (GPL)-reinforced composite (GPLRC) sector cylindrical shells is presented by considering Levy-type boundary conditions for the first time. The analysis relies on the use of the Halpin–Tsai micro-mechanical model for evaluating the material properties of the graded layers of the shell with three different grading patterns. Mathematical modeling of the Levy-type cylindrical shell is based on the Hamilton principle and the Sanders first-order shear deformation theory (FSDT). The governing equations of the composite shell are analytically solved using the state-space method. The validity of the proposed analytical method is demonstrated by the excellent agreement between the obtained results of the exact analytical solution and the results available in the literature. Furthermore, some parametric studies are conducted to reveal the effects of variations in boundary conditions, GPL distribution patterns, GPL weight fraction, and geometrical parameters such as shallowness angle, length-to-radius ratio, and thickness on the free vibration behavior of the shell structure. Natural frequencies and mode switching are reported for different mode numbers.

Abstract Image

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

列维型边界条件下 FG-GPLRC 扇形圆柱壳自由振动分析的精确分析方法

本文首次考虑了列维型边界条件，提出了对功能分级（FG）石墨烯小板（GPL）增强复合材料（GPLRC）扇形圆柱壳进行自由振动分析的精确分析方法。分析依赖于使用 Halpin-Tsai 微机械模型来评估具有三种不同分级模式的壳体分级层的材料属性。莱维型圆柱形壳体的数学建模基于汉密尔顿原理和桑德斯一阶剪切变形理论（FSDT）。采用状态空间法分析求解了复合材料壳体的控制方程。精确分析求解的结果与文献中的结果非常吻合，这证明了所提出的分析方法的有效性。此外，还进行了一些参数研究，以揭示边界条件、GPL 分布模式、GPL 重量分数以及浅度角、长半径比和厚度等几何参数的变化对壳体结构自由振动行为的影响。报告了不同模态数的固有频率和模态切换。

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分钟内获得全文去求助

来源期刊

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.