Dynamic Characteristics Of Carbon Nanotube Mass Sensor

Since carbon nanotubes were first prepared in the laboratory,they have been the focus of attention.As an important member of the classification of nano materials,the excellent properties of carbon nanotubes are being explored and studied.According to the existing data and literature,carbon nanotubes have excellent chemical,electromagnetic and mechanical properties.In addition,as a kind of composite material,carbon nanotubes also show good fatigue resistance,elasticity,strength,strong acid and alkali resistance.Therefore,carbon nanotubes are considered to be a very ideal nanocomponent,which has great potential in nano-mechanical system,transport system,sensor and other aspects.The main methods to study the carbon nanotubes are as follows: Experimental method,molecular dynamics method and continuum mechanics method.Due to the limitation of materials,experimental equipment and observation means,the computational complexity of molecular dynamics simulation is very large,and the computer processing capacity is very high.Therefore,continuum mechanics has become an effective and indispensable method to study the mechanical behavior of carbon nanotubes.Due to the very small size of carbon nanotubes,the nano size effect of material microstructure becomes very important in the process of calculation and analysis.With the development of research,it is found that some laws of classical mechanics are not fully applicable at the nanometer scale.Because the classical mechanical methods ignore the connection between atoms,they can not describe the mechanical properties of microstructure very well.Therefore,for the first time,Lim et.al combined the nonlocal coefficient with the strain gradient coefficient,and established a new theory,the nonlocal strain gradient theory.Because the nonlocal strain gradient theory considers the influence of the internal characteristics of the structure,the results based on this theory are more accurate and credible and make up for the shortcomings of classical mechanics.On the whole,there are many literatures on the nonlocal characteristics of carbon nanotubes,but there are few researches on the strain gradient theory of carbon nanotubes,and there are few reports on the mechanical behavior and vibration stability of carbon nanotubes based on the nonlocal strain gradient theory.The control equation based on this theory is complex and requires a lot of calculation,so it is difficult to find the analytical value.In thispaper,based on the nonlocal strain gradient theory,the differential quadrature method is used to solve different carbon nanotube models.The main research contents and academic contributions of this paper are as follows:(1)The vibration characteristics of carbon nanotube system with heavy end are studied.As an ideal material for quality sensor,carbon nanotubes have high academic value and application value.In this paper,the nano mass sensor is simplified.The vibration equation is established by using Rayleigh beam model and nonlocal theory,and the differential quadrature method is used to solve the vibration equation.The influence of nonlocal coefficient and strain gradient coefficient on the vibration frequency of carbon nanotubes is investigated,and the influence of different inertia and end weight on the system dynamics is compared ? The results show that the nonlocal coefficient has softening effect on the global stiffness,while the strain gradient coefficient has hardening effect on the global stiffness.The moment of inertia and the existence of the end weight can restrain the vibration of CNTs.(2)The vibration characteristics of carbon nanotubes with fluid in the cavity are studied.Using Rayleigh beam model and nonlocal strain gradient theory,the effects of fluid density in carbon nanotubes on vibration frequency,relative frequency shift percentage,nonlocal frequency shift percentage and strain gradient frequency shift percentage are discussed in detail.The results show that the natural frequency decreases with the increase of fluid density.When the analytical solution of the system is difficult to obtain,the differential quadrature method used in this paper provides a relatively simple way to calculate the numerical solution.