Study On Fluid-solid Coupling Of Fluid-filled Single-walled Carbon Nanotubes Based On Non-local Strain Gradient Beam And Shell Model

Since it was discovered in the 1990 s,Carbon nanotubes have attracted the attention of many researchers.The study on the mechanical properties of carbon nanotubes is also of great significance.However,the theory of macroscopic pipeline cannot accurately describe the flow and fluctuation characteristics of pipeline in the microscopic environment,so the influence of microscale effect should be considered in the nanoscale.Currently,there are some studies based on the mechanics of non-local continuum,but this theory is essentially a method for applying the classical mechanics model of macroscopic equilibrium and boundary conditions to nanomaterials.This method has some shortcomings and even contradicts the results of molecular dynamics method.Similar to the nonlocal theory which considers nanoscale effects in the stress tensor,the strain gradient theory considers the scale effects in the strain tensor and quantitatively describes the effects of the scale effects on the carbon nanotubes through the gradient analytic formula.These two theories fully consider the discreteness of structures and the effect of nanoscale on the constitutive properties of materials,but both of them are inadequate.Because the scale effect affects both stress and strain,not just one of the tensors.In contrast,Lim combined non-local theory with strain gradient theory to explain the scale effect more comprehensively.In this paper,based on the Hamiltonian method and the variational principle,the non-local strain gradient constitutive relation of carbon nanotubes is obtained.On this basis,the influence of the fluid scale effect on the system is innovatively incorporated,and the free vibrating shell model and the forced vibrating euler beam model of the single-walled carbon nanotubes are established.By solving the control equation of the system,the effects of different scale effects on the vibration and wave characteristics of the system are analyzed.It is found that the first-order wave conduction based on the shell model is promoted by the strain gradient effect and damped by the non-local effect,while the fluid-scale effect has no effect on the first-order wave conduction.For the second-order mode of the system,the strain gradient effect has no effect,the non-local effect plays a promoting role,and the non-local fluid scale effect promotes the low-speed flow.When the velocity reaches a critical value,the fluid scale effect hinders the flow.Based on the classical euler beam model,theresults of the forced vibration of fluid-filled carbon nanotubes show that the strain gradient effect can promote the amplitude of the steady-state response deflection,while the non-local effect can damp the amplitude of the steady-state response deflection.The fluid scale effect hinders the flow,the low speed flow enhances the amplitude of the forced vibration deflection,and the high velocity attenuation,and the critical velocity of the vibration system increases with the increase of the external simple harmonic excitation frequency.The above research conclusions clarify the influence law of different scale effects on the dynamic characteristics of fluid-solid coupling system of micro-nano pipeline,and provide theoretical support for the design of micro-nano electromechanical system for different USES.