Nonlinear vibrations and chaotic dynamics of graphene-reinforced titanium-based composite rectangular cantilever plate subjected to transverse excitations

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-03-28 DOI:10.1016/j.cnsns.2025.108801

W. Zhang , Z.H. Nie , Y. Jiang , Y.F. Zhang

{"title":"Nonlinear vibrations and chaotic dynamics of graphene-reinforced titanium-based composite rectangular cantilever plate subjected to transverse excitations","authors":"W. Zhang , Z.H. Nie , Y. Jiang , Y.F. Zhang","doi":"10.1016/j.cnsns.2025.108801","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we investigate the linear vibration behaviors, nonlinear and chaotic dynamics of the functionally graded graphene reinforced titanium-based (FG-GRTB) composite laminated cantilever rectangular plate under the transverse excitation. Based on Halpin-Tsai model, the mechanical properties are calculated for the graphene reinforced titanium-based (GR-TB) composite laminated cantilever rectangular plate. Considering the classical laminated theory, von Karman large deformation theory and Hamilton principle, the partial differential governing equations of motion are derived for the GR-TB composite laminated cantilever rectangular plate subjected to the transverse excitation. The natural vibration behaviors of the system are investigated by Rayleigh-Ritz method. The results are compared with the finite element simulation using COMSOL MUTIPHYSIC software. The ordinary differential equations of the GR-TB composite laminated cantilever rectangular plate are obtained by Galerkin method. The internal and primary resonances of the system are studied by the multi-scale method. The amplitude-frequency and force-amplitude response curves are depicted by the average equations. The chaotic vibrations of the system are studied by using the bifurcation diagram, max Lyapunov exponent, time histories, phase portrait and Poincare map. The results indicate that the graphene volume fraction and graphene distributed type have a significant influence on the natural vibration characteristics of the GR-TB composite laminated cantilever rectangular plate. In addition, the system exhibits the soft spring nonlinear properties in the case of the combination of the internal and primary resonances. Moreover, the system under larger external amplitude or smaller damping triggers the chaotic vibrations easily.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"146 ","pages":"Article 108801"},"PeriodicalIF":3.4000,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570425002126","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

In this paper, we investigate the linear vibration behaviors, nonlinear and chaotic dynamics of the functionally graded graphene reinforced titanium-based (FG-GRTB) composite laminated cantilever rectangular plate under the transverse excitation. Based on Halpin-Tsai model, the mechanical properties are calculated for the graphene reinforced titanium-based (GR-TB) composite laminated cantilever rectangular plate. Considering the classical laminated theory, von Karman large deformation theory and Hamilton principle, the partial differential governing equations of motion are derived for the GR-TB composite laminated cantilever rectangular plate subjected to the transverse excitation. The natural vibration behaviors of the system are investigated by Rayleigh-Ritz method. The results are compared with the finite element simulation using COMSOL MUTIPHYSIC software. The ordinary differential equations of the GR-TB composite laminated cantilever rectangular plate are obtained by Galerkin method. The internal and primary resonances of the system are studied by the multi-scale method. The amplitude-frequency and force-amplitude response curves are depicted by the average equations. The chaotic vibrations of the system are studied by using the bifurcation diagram, max Lyapunov exponent, time histories, phase portrait and Poincare map. The results indicate that the graphene volume fraction and graphene distributed type have a significant influence on the natural vibration characteristics of the GR-TB composite laminated cantilever rectangular plate. In addition, the system exhibits the soft spring nonlinear properties in the case of the combination of the internal and primary resonances. Moreover, the system under larger external amplitude or smaller damping triggers the chaotic vibrations easily.

查看原文本刊更多论文

横向激励下石墨烯增强钛基复合材料矩形悬臂板的非线性振动与混沌动力学

本文研究了梯度石墨烯增强钛基（FG-GRTB）复合材料层合悬臂矩形板在横向激励下的线性振动行为、非线性和混沌动力学。基于Halpin-Tsai模型，计算了石墨烯增强钛基（GR-TB）复合材料层合悬臂矩形板的力学性能。结合经典叠层理论、von Karman大变形理论和Hamilton原理，推导了GR-TB复合材料叠层悬臂矩形板在横向激励下的运动偏微分控制方程。采用瑞利-里兹法研究了系统的自振特性。结果与COMSOL multiphysic有限元模拟结果进行了比较。采用伽辽金法得到了GR-TB复合材料层合悬臂矩形板的常微分方程。用多尺度方法研究了系统的内部共振和主共振。幅频响应曲线和力幅响应曲线用平均方程表示。利用分岔图、max Lyapunov指数、时程图、相像图和庞加莱图研究了系统的混沌振动。结果表明，石墨烯体积分数和石墨烯分布类型对GR-TB复合材料层合悬臂矩形板的自振特性有显著影响。此外，当内共振和主共振同时存在时，系统表现出软弹簧的非线性特性。此外，在较大的外幅值或较小的阻尼条件下，系统容易引发混沌振动。

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

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.