石墨烯增强含铰梁结构的非线性模态分析

Nonlinear modal analysis of graphene platelets reinforced hinged beam structure

摘要

将石墨烯增强含铰梁结构视为多自由度连续保守系统，针对悬臂条件下该结构的自由振动进行非线性模态分析。采用修正的Halpin-Tsai模型对结构中石墨烯增强复合材料的等效杨氏模量进行估计。将铰链简化为转角非线性三次函数的无重扭簧。基于有限元方法对结构进行离散，推导出结构发生自由振动的非线性控制方程，利用谐波平衡法求解其非线性频率。在验证算法准确性的基础上，从多个角度画出频能图分析石墨烯相关物性参数以及铰链相关参数对结构非线性模态的影响。数值计算结果表明：石墨烯的质量分数对结构非线性频率影响较大，石墨烯小块的长宽比和长厚比对其非线性模态影响较小；在其他不变的情况下，铰链非线性刚度和铰链个数的增加都会使结构的非线性特性更加明显。

Abstract

The graphene platelets (GPLs) reinforced hinged beam structure is regarded as a multi-degree-of-freedom continuous conservative system, and the nonlinear modal analysis for the free vibration of the structure under cantilever conditions is analyzed. The modified Halpin-Tsai model is used to estimate the equivalent Young's modulus of the GPLs reinforced composite in the structure. The hinge is simplified into a non-gravity torsion spring with a nonlinear cubic function of the angle. The finite element method is employed for the structure separation. The nonlinear governing equation for the free vibration of the structure is derived, and the nonlinear frequency is obtained by harmonic balance method. On the basis of verifying the accuracy of the algorithm, frequency-energy plots are drawn from multiple angles to analyze the effects of GPLs related physical property parameters and hinge related parameters on the structural nonlinear modes. The numerical results show that the mass fraction of GPLs has great influence on the nonlinear frequency of the structure, but the aspect ratio and length-thickness ratio of GPLs have little influence on the nonlinear mode. Under other conditions, the increase of the hinge nonlinear stiffness and the number of hinges will make the nonlinear characteristics of the structure more obvious.

关键词

石墨烯增强复合材料 / 悬臂含铰梁 / 非线性模态 / 频能图 / 谐波平衡方法

Key words

graphene platelets reinforced composite material / cantilever beam / nonlinear mode / frequency-energy plot / harmonic balance method

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基金资助

国家自然科学基金资助项目(12272058)

国家自然科学基金资助项目(11772063)