| Graphene sheet?GS?-based mass sensor is one of the important application of the GS.At present,there is no systematic method to solve the governing equations of the GS-based mass sensor via nonlocal theory.This thesis aim to develop a semi-analytical method named the Galerkin strip distributed transfer function method?GSDTFM?.And apply this method to investigate the vibration of the GS-based mass sensor.The main works are as follows:The GSDTFM to analyze the nonlocal Kirchhoff plate is developed based on the classical strip distributed transfer function method by referring to the Galerkin method.And the effects of several parameters'variations on the natural frequencies are studied.The GSDTFM to analyze the single-layered graphene sheet?SLGS?-based mass sensor with an attached mass is established.In GSDTFM,the energy functional of the system is not necessary.And the attached mass can be dealt with better.Using the GSDTFM,the semi-analytical solutions of the SLGS-based mass sensor is given out.And the effects of several parameters'variations on the frequency shift are studied.The results show that the sensitivity of the SLGS-based mass sensor can be at least 1×10-24kg.The GSDTFM to analyze the double-layered graphene sheet?DLGS?-based mass sensor is established on the basis of the SLGS.The DLGS is modeled as two Kirchhoff plate connected by the van der Waals force.At the same time,the attached mass are also considered in the analysis.The effects of several parameters'variations on the frequency shift are investigated.On the basis of the above work,the GSDTFM for the buckling and free vibration of the GS-based mass sensor including the initial in-plane load is established.The critical buckling loads of the GS-based mass sensor are computed.And the differences of the buckling characteristics between the SLGS and DLGS are compared.Taking the SLGS as representation,the effects of several parameters'variations on the frequency shift are discussed.In this thesis,a new method named GSDTFM which can solve the problems whose functional cannot be written out clearly is presented to solve the nonlocal Kirchhoff plate problem.And apply this method to analyze the vibration characteristics of the GS-based mass sensor.The effects of several parameters'variations on the natural frequency are studied.The present work can provide a new way to solve the mathematical problem in physics which cannot write out the functional clearly.And it can also provide a theoretical foundation for designing the GS-based mass sensor. |
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