| 张靖华,刘港.石墨烯片增强功能梯度圆柱壳自由振动的解析解[J].计算力学学报,2025,42(2):162~168,204 |
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| 石墨烯片增强功能梯度圆柱壳自由振动的解析解 |
| Analytical solution for free vibration of graphene platelets reinforced functionally graded cylindrical shell |
| 投稿时间：2023-11-06 修订日期：2024-02-11 |
| DOI：10.7511/jslx20231106001 |
| 中文关键词: 石墨烯片增强 功能梯度圆柱壳 自由振动 固有频率 解析解 |
| 英文关键词:graphene platelets reinforcement functionally graded cylindrical shell free vibration natural frequency analytical solution |
| 基金项目:国家自然科学基金(12062010;12362009);甘肃省自然科学基金重点项目(23JRRA775)资助. |
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| 中文摘要: |
| 采用解析法研究石墨烯片(GPL)增强功能梯度圆柱壳的自由振动。首先基于经典壳理论和Hamilton原理推导建立该圆柱壳振动的控制微分方程,其中石墨烯增强复合材料的等效弹性模量由修正的哈尔平-蔡模型计算,等效密度和泊松比根据混合率准则确定。其次,采用Naiver法求解获得固有频率的解析解,并给出解析表达式的数值结果,定量分析石墨烯片的分布模式、含量、尺寸等参数以及圆柱壳的几何参数等对固有频率的影响。研究表明,圆柱壳内外表面填充较多石墨烯片能极大地提高壳的刚度,表面积更大、厚度更薄的石墨烯片增强效果更好,从而使基频增大;并通过调节石墨烯片的各项微观参数能主动改变复合材料壳的自振频率。 |
| 英文摘要: |
| The free vibration of a graphene platelets(GPL)-reinforced functionally graded cylindrical shell is studied analytically.Firstly,the governing differential equations for the vibration of the shell are derived based on the classical shell theory and the Hamilton principle.The equivalent modulus of elastieity of the composites is calculated by the modified Harpin-Tsai model,and the equivalent density and Poisson’s ratio are determined according to the mixing ratio criterion.Then,the analytical expression of the natural frequencies is obtained by using the Naiver method.The numerical results of the analytical expression are also given,and the influences of the distribution scheme,content,size and other parameters of GPL as well as the geometric parameters of the cylindrical shell on the natural frequencies are quantitatively analyzed.The results show that more GPL filled on the inner and outer surfaces of the cylindrical shell can greatly improve the stiffness.And a GPL with a larger surface area and a thinner thickness has a better reinforcement effect,thus increasing the fundamental frequencies.By adjusting the micro parameters of GPL,the natural frequencies of the composite shell can be actively changed. |
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