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Nonlinear free vibration of graphene platelets reinforced composite corrugated plates

石墨烯片增强复合材料波纹板的非线性自由振动

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Abstract

The nonlinear vibration of graphene platelets reinforced composite corrugated (GPRCC) rectangular plates with shallow trapezoidal corrugations is investigated. Since graphene platelets are prone to agglomeration, a multi-layer distribution is adopted here to match the engineering requirements. Firstly, an equivalent composite plate model is obtained, and then nonlinear equations of motion are derived by the von Kármán nonlinear geometric relationship and Hamilton’s principle. Afterwards, the Galerkin method and harmonic balance method are used to obtain an approximate analytical solution. Results show that the unit cell half period, unit cell inclination angle, unit cell height, graphene platelet dispersion pattern and graphene platelet weight fraction and geometry play important roles in the nonlinear vibration of the GPRCC plates.

摘要

本文研究了石墨烯片增强复合材料波纹(GPRCC)板的非线性自由振动。首先,基于均质化模型建立GPRCC板的等效模型; 其次,利用von-Kármán 非线性几何关系和Hamilton 原理变分推导出非线性运动方程。然后,采用伽辽金法和谐波平衡法得到GPRCC板的近似解析解。结果表明,晶胞半周期长、晶胞倾角、晶胞高度、石墨烯片分布类型、石墨烯片重量分数以及石墨烯片的几何尺寸对GPRCC板非线性振动有重要的影响。

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Authors and Affiliations

  1. State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China

    Yun-fei Liu  (刘云飞), Zhao-ye Qin  (秦朝烨) & Fu-lei Chu  (禇福磊)

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  1. Yun-fei Liu  (刘云飞)
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  2. Zhao-ye Qin  (秦朝烨)
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  3. Fu-lei Chu  (禇福磊)
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Contributions

LIU Yun-fei: Conceptualization, methodology, validation, writing original draft; QIN Zhao-ye: Conceptualization, methodology, writing review & editing, supervision. CHU Fu-lei: Conceptualization, supervision.

Corresponding author

Correspondence to Zhao-ye Qin  (秦朝烨).

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Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Foundation item: Project(11972204) supported by the National Natural Science Foundation of China

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Liu, Yf., Qin, Zy. & Chu, Fl. Nonlinear free vibration of graphene platelets reinforced composite corrugated plates. J. Cent. South Univ. 29, 3054–3064 (2022). https://doi.org/10.1007/s11771-022-5086-6

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