基于无网格kp-Ritz法碳纳米增强复合层合板自由振动数值分析
关键词：自由振动；碳纳米管；复合材料；一节剪切变形理论； 无网格法
毕业论文设计说明书外文摘要
Title Numerical aspects of frequency responses for laminated CNT reinforced functionally graded plates
Abstract
This paper mainly presents vibration analysis of thin-to-moderately thick laminated carbon nanotube-reinforced functionally graded composite plate. The laminated plate is composed of perfectly bonded carbon nanotube-reinforced functionally graded layers. Different distributions of single walled carbon nanotubes (SWCNTs) through the thickness of layers are considered; uniform and three kinds of functionally graded distributions of carbon nanotubes along thickness direction of plates. Using the extended rule of mixture, material properties of the laminated nanocomposite plates are estimated. The present formulation is based on the first-order shear deformation theory. The present formulation is coded solve free vibration of laminated carbon nanotube-reinforced functionally graded composite plates, and effects of the volume fractions of carbon nanotubes, plate width-to-thickness ratio, plate aspect ratio, distribution type of carbon nanotubes and boundary conditions on the natural frequencies of the laminated nanocomposite plates. In addition, the effects of number of layers and lamination angle are also examined.
Keywords： Free vibration; Carbon nanotube; Composite; First order shear deformation theory
目 次
1 引言（或绪论）碳纳米管复合材料的兴起和历史概论 1
2 功能梯度复合材料5
2.1 混合扩展规则 5
2.2 Eshelby-Mori-Tanaka法 6
3 理论公式 7
3.1能量函数 7
3.2二文核粒子的形状函数… 8
3.3离散方程… 10
4数值结果… 12
4.1收敛性和比较研究… 12
4.2参数研究… 13
5结论 … 15
致谢 16
参考文献17
附录A 19
1 引言（或绪论）通过研究和实验表明，碳纳米管具有高纵横比低密度高强度和刚度及卓越的机械性能的新型材料，这让人们认识到这种新型材料的潜力。由它增强的高强轻质聚合物有着很强的机械、电气以及热性能，着实让人们兴奋。于是越来越多的人开始关注起来。
碳纳米管具有高纵横比和低密度高强度和刚度的新材料，现在已经引起人们的关注了。许多实验和理论研究表明，碳纳米管具有非常高的刚度重量和强度重量比特性。Treacy等人【1】发现碳纳米管具有非常高的杨氏模量在terapascal(CTPA)范围中。Wong等人【2】发现在原子显微镜下多壁碳纳米管硬度是碳化硅纳米棒的两倍。Salvetat等人【3】报道单壁碳纳米管的弹性模量在1TPa和1GPa之间。基于第一原理的聚类法，在局域密度近似的框架下，周等人【4】研究单壁碳纳米管（SWCNT)的形态，电子结构和力学性能。纳米管的特殊性能的报道让研究人员产生了研究碳纳米管基复合材料的动机。金等人【5】报道了用由X-射线衍射测定取向和取向程度的碳纳米管制备聚合物复合材料的方法。Bower等人【6】通过透射电子显微镜用单轴取向的多壁碳纳米管制备和研究高分子聚合物。用组合使用溶剂浇铸和熔融共混方法，Haggenmacller和同事【7】分散定向单壁碳纳米管在聚（甲基丙烯酸甲酯）（PMMA）。Thosterson和周【8】研究了在强烈的剪切混合可扩展的压延法下，对CVD法生长的多壁碳纳米管实现分散。