基于一阶剪切变形理论的CNTRC板的自由振动分析

基于Reissner-Mindlin一阶剪切变形假设（First-order shear deformation theory，FSDT），考虑碳纳米管（Carbon nanotube，CNT）功能梯度材料的不均匀性，建立CNT梯度增强复合薄板结构的自由振动分析模型，模型中考虑了CNT增强体的分布形式、体积率、边界条件及结构的边厚比等因素对该复合薄板结构自由振动响应的影响。克服了经典板理论中不考虑剪切应力的缺陷，通过四边简支（Simply supported，SSSS）板的振动响应特征验证模型的准确性，利用所建模型对CNT梯度增强薄板结构进行了自由振动分析及模态分析。研究表明：CNT增强复合薄板结构的自振频率随着CNT体积率的增加发生几乎线性化的增长；不同的CNT分布形式对振动频率的影响：X型分布的功能梯度板的自振频率最大，O型分布的功能梯度板的自振频率最小，均一及V型分布的固有频率大小介于两者之间。边界条件对板振动形态的影响：由于四边固支（Clamped，CCCC）的边界条件比SSSS约束性更强，其对于边厚比的变化更灵敏，并且随着宽厚比值的增大，边界条件产生的影响越来越大。CNT增强体分布形式、体积率、结构边厚比及边界条件对复合薄板结构自由振动的频率及振动模态有显著的影响。

Free Vibration Analysis of CNTRC Plates Based on First-Order Shear Deformation Theory

Based on the Reissner-Mindlin hypothesis, a free vibration analysis of CNTRC (carbon nanotube reinforced composite) plate is investigated with consideration of the nonhomogeneous of CNT. The effects of the distribution form, volume ratio of the CNT reinforcement, boundary conditions and geometric parameters of the plates on the frequency response of the composite structure are verified, respectively. The accuracy of the model is verified by the experiment of simply supported plate. The free vibration analysis of CNT-reinforced functionally graded plate is carried out using the model. The research shows that the effect of 1CNT volume fracture is nearly linear on the vibration of fundamental frequency parameters. Among different distribution forms:the nature frequency of X-shaped functionally graded plate is the largest, followed by V-shaped CNT plate and that of O-shaped distributed form is the lowest. Since the constrains are much stronger in CCCC boundary conditions than in SSSS conditions, CCCC CNTRC plates became more sensitive to width-to-thickness ratio, and the influence of boundary conditions becomes bigger as the width-to-thickness ratio increases. To sum up, the distribution form, volume ratio, width-to-thickness ratio and boundary condition of CNT have a significant effect on the frequency and vibration mode of plate structures.