基于非局部理论的石墨烯纳米质量传感器振动特性研究

The materials at nano scale such as carbon nanotubes(CNT), graphene sheets(GS) can be used as nano-mass sensor to detect the micro-mass such as bacteria, virus or molecule of some gas. Therefore, they are very promising for application in disease therapy, environmental monitoring and so on. The principle of mass detection using the nano-mass sensor from a vibration analysis is in quantifying the change in its resonant frequency due to the added mass. Consequently, the study of the vibration characteristic of the nano-mass sensor is the key technique both in design and practical application. Considering the attached mass effect and size effect, the stress gradient nonlocal continuum mechanics method has been successfully applied in vibration characteristic analysis of CNT based mass sensor. As a 2D nano-structure, there are some defects in the vibration characteristic analysis of GS based mass sensor. The emphasis of the current work is to establish the Kirchhoff plate theoretical model and Galerkin strip transfer function solving method of vibration characteristic analysis for single-layered and double-layered GS based mass sensor via nonlocal theory. Obtained results are helpful to the design and application of GS based resonator as nano-mass sensor. Also, Galerkin strip transfer function method can be used to solve the mathematical physics problem, which is hard to write the explicit functional variational expression.

将碳纳米管、石墨烯等纳米材料用于纳米质量传感器，可探测细菌、病毒、气体分子等原子级质量，在疾病诊疗、环境监测等方面具有重要的应用前景。谐振式质量传感器主要利用附加质量前后传感器固有频率的改变量来识别附加质量，因此，振动特性分析是纳米质量传感器设计和应用中的关键技术。研究纳米质量传感器的振动特性需同时考虑尺度效应和附加质量的影响，应力梯度非局部理论已被成功用于碳纳米管等一维结构质量传感器的振动特性分析。石墨烯质量传感器属二维结构，在分析方法方面还很不成熟。本项目基于非局部理论，开展石墨烯质量传感器振动特性分析方法研究，旨在建立单层和双层石墨烯质量传感器振动特性分析的非局部Kirchhoff板理论模型和Galerkin条形传递函数求解方法，为石墨烯纳米质量传感器的设计和应用提供理论依据，所提Galerkin条形传递函数方法为求解难以直接写出泛函显示表达式的一类数学物理问题提供了一条新的途径。

本项目基于非局部理论，开展石墨烯质量传感器振动特性分析方法研究，旨在建立单层和双层石墨烯质量传感器振动特性分析的非局部Kirchhoff板理论模型和Galerkin条形传递函数求解方法。主要研究内容为：.提出了可用于分析非局部Kirchhoff板振动特性的Galerkin条形传递函数方法。推导了非局部Kirchhoff板动特性分析的理论求解模型，并将结果和有限元结果进行了对比，从而验证所提方法的正确性。.提出了含集中附加质量的单层石墨烯（SLGS）和双层石墨烯(DLGS)质量传感器振动特性分析的Galerkin条形传递函数方法。推导了SLGS和DLGS质量传感器振动特性分析的理论求解模型，分别给出了SLGS和DLGS质量传感器固有频率的Galerkin条形传递函数解。.在前面工作的基础上，提出了考虑预应力的石墨烯（GS）质量传感器屈曲特性和振动特性分析的Galerkin条形传递函数方法。推导了考虑预应力的GS质量传感器的理论求解模型，并给出了GS质量传感器临界荷载与固有频率的Galerkin条形传递函数解。.本课题提出了一种用于求解石墨烯质量传感器的Galerkin条形传递函数方法，并将其应用到石墨烯质量传感器的振动特性分析中。所做工作可为难以写出泛函显示表达式一类数学物理问题提供一条新的求解途径，同时也为石墨烯质量传感器的设计和应用提供了理论支撑。