压电功能梯度碳纳米管增强复合材料结构的非线性动力学研究

Nowadays, the rapid development of aerospace, railway, marine, and high-rise buildings in China has imposed great challenges. The advancement of smart materials plays a pivotal role in responding to such challenges. In reality, smart material structures subject to complicated environment will cause nonlinear vibration and structural instabilities. This leads to the reduction of safety and reliability of engineering structures. Hence, intensive studies on the dynamical response of smart materials are of paramount importance. The present project aims to analyse the nonlinear dynamical response of piezoelectric functionally graded carbon nanotube-reinforced composite plates. The investigation of such smart material structures is currently one of the frontier topics in mechanics. Making use of the higher order shear deformation theory, large deformation theory and nonlinear dynamical theory, the mathematical model of piezoelectric functionally graded carbon nanotube-reinforced composite plates can be constructed. Based on the mathematical model, the research on dynamical behaviour of these composite plate structures under various loading effects will be considered. Besides, theoretical analysis and numerical simulation will be carried out for studying the nonlinear dynamical behaviour of piezoelectric functionally graded carbon nanotube-reinforced composite plates, including bifurcation and chaotic motion. Furthermore, this project will extend to perform experimental studies that will be used to compare and verify the theoretical results. The success of this project will not only become the basis of further research and design considerations for engineering structures, but also will provide scientific knowledge and information for the practical use of piezoelectric functionally graded carbon nanotube-reinforced composite material structures.

伴随着中国在航天、铁路、船舶和建筑等多方面的高速发展，加强对新型智能复合材料的基础研究日趋重要，亦是国家大力提倡发展的重要目标。在实际应用中，由于智能材料所处的工程环境复杂，往往会产生非线性振动和稳定性问题，降低结构使用的安全性和可靠性。因此，研究智能复合材料结构的非线性动力行为及其稳定性具有重要的理论意义和广阔的应用前景。本项目将针对压电材料与功能梯度碳纳米管增强材料结构及其关键科学问题展开研究，综合利用高阶剪切变形理论、板结构大变形理论和非线性动力学理论来研究压电功能梯度碳纳米管增强复合板在不同载荷作用下的非线性振动反应。对该类结构的分岔、混沌等非线性行为进行理论研究和数值仿真。开展这种复合材料结构的非线性动态特性实验研究，并与理论分析结果进行对比。期望研究成果能对压电功能梯度碳纳米管增强复合材料结构的设计提供理论依据及在实际工程中获得应用。

石墨烯在纳米机电系统中有广泛的应用前景。本项目用原子连续体多尺度法研究了单层石墨烯的非线性动力学行为，所得的结果与用半解析法求得的线性振动分析的结果吻合较好。针对石墨烯复合材料，本项目研究了由石墨烯蒙皮和交叉铺层压电纤维复合材料构成的矩形复合材料板的非线性动力行为，为此类复合材料结构在实际工程中应用提供了重要的指导。本项目还对非线性动力学领域的相关问题进行了研究。首先，研究了非局域动力学行为的纳米结构依赖性。通过对纳米结构的轴向振动、纳米梁的横向振动以及纳米板的自由振动的动态分析来确定非局域尺度参数的上限。为非局部理论的发展及其在纳米力学中的潜在应用提供了有益的指导。基于菲涅耳波法线方程，提出了一种确定碳纳米管阵列薄膜有效折射率的理论，该理论模型揭示了碳纳米管阵列薄膜的光学行为。此外，针对具有弱周期扰动的非光滑振子，提出了一些简单易行的抑制同宿混沌的新方法。数值模拟验证了Melnikov方法对非光滑振子抑制混沌的有效性。最后，研究了MEMS微梁的非线性自由振动和强迫振动响应。基于牛顿谐波平衡法推导对应的低阶解析近似解，得到简单而精确的解析表达式。低阶解析近似结果与标准龙格-库塔(Runge-Kutta)方法得到的结果在整个动力学范围都非常吻合。期望本项目研究成果能对压电功能梯度碳纳米管增强复合材料结构的设计提供理论依据及在实际工程中获得应用。