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Nonlinear primary resonance analysis of initially stressed graphene platelet reinforced metal foams doubly curved shells with geometric imperfection

预应力下具有初始几何缺陷的石墨烯增**多孔复合材料双曲率壳结构的非线性主共振分析

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Abstract

This paper studies the nonlinear primary resonance behavior of graphene platelet reinforced metal foams (GPLRMFs) doubly curved shells with initial geometric imperfection and pre-stressing force. On the basis of Reddy’s higher-order shear deformation shell theory and von Karman’s geometric nonlinearity, the nonlinear equations of motion of GPLRMFs doubly curved shells are obtained. By considering simply supported boundary conditions and employing the Galerkin method, the nonlinear ordinary differential equations are derived. The primary resonance of the GPLRMFs doubly curved shells is obtained by solving the nonlinear differential equations with the help of the modified Lindstedt Poincare (MLP) method. In the numerical analyses, the correctness of the present model in this paper is confirmed by comparing with the published literature. In the end, the effects of various parameters including the doubly curved shell types, graphene platelets (GPLs) distribution patterns, porosity distribution forms, initial geometric imperfection, GPLs weight fraction, porosity coefficients, and pre-stressing force on the nonlinear amplitude-frequency response curves are analyzed.

摘要

本文研究了石墨烯增**多孔复合材料(GPLRMFs)双曲率壳结构的非线性主共振行为. 考虑初始几何缺陷和预应力, 并基于Reddy高阶剪切变形壳理论和冯卡门几何非线性, 推导出GPLRMFs双曲率壳的非线性运动方程. 接着, 考虑简支边界条件, 利用伽辽金法进行离散得到了非线性常微分方程, 随后, 利用改进的Lindstedt-Poincare (MLP)法求解, 便可以得到GPLRMFs双曲率壳结构的主共振幅频响应关系. 在数值分析中, 通过与现有文献进行比较, 从而验证了本研究的**确性. 最后, 分析了各个参数(包括壳体类型、石墨烯片(GPLs)分布模式、孔隙率分布类型、初始几何缺陷、GPLs重量分数、孔隙率系数和预应力)对非线性主共振幅频响应曲线的影响.

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Acknowledgements

This work was supported by the Talent Introduction Project of Chongqing University (Grant No. 02090011044159), and the Fundamental Research Funds for the Central Universities (Grant No. 2022CDJXY-005).

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Authors and Affiliations

  1. College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing, 400044, China

    Gui-Lin She  (佘桂林) & Hao-Xuan Ding  (丁浩轩)

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  1. Gui-Lin She  (佘桂林)
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  2. Hao-Xuan Ding  (丁浩轩)
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Correspondence to Gui-Lin She  (佘桂林).

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In this work, Gui-Lin She was responsible for proposing ideas, and formulating or evolving the overall research goals and aims. Besides, he made great contributions to the preparation, creation, and presentation of writing-original manuscript-published works, especially in writing the first draft (including substantive translation). Hao-Xuan Ding was mainly responsible for programming and data processing, designing computer programs to analyze and research data.

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She, GL., Ding, HX. Nonlinear primary resonance analysis of initially stressed graphene platelet reinforced metal foams doubly curved shells with geometric imperfection. Acta Mech. Sin. 39, 522392 (2023). https://doi.org/10.1007/s10409-022-22392-x

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