| Properly understanding the size-dependent behavior of carbon nanotube conveying flow is preliminary to designing and manufacturing related nano equipment.In this thesis,with the related literature reviewed and analyzed,the dynamic behavior of carbon nanotube conveying flow is studied employing continuum mechanics modified by size effect.The main work is as follows.(1)The instable mechanisms of pipe conveying flow with two ends supported and rod bearing compressing load are analyzed and compared,and then a direct solving method of critical velocity,i.e.,equilibrium method,is developed.Meanwhile,the basic model of pipe conveying flow is re-analyzed and discussed.Its governing equation is derived.Two solving methods,including Galerkin method and wave method are compared,discussed and practiced.(2)An improved model of carbon nanotube conveying flow is built,considering the comprehensive size effects of both carbon nanotube and inside flow,which are then,for the first time,detected to be uncoupled.The compatibility condition is extended according to the“weak coupling” principle.And with the comprehensive effects of Knudsen number—including effective viscosity,boundary slip condition and non-uniform flow profile—taken into account and combined with both nonlocal elasticity and Navier-Stokes equation,the governing equation is derived,which is then solved by Galerkin method.By employing equilibrium method,an analytical solution of critical velocity in pinned-pinned boundary condition is also obtained.It can be concluded that the size effect of inside flow shows magnificent influence—the velocity correction factor mainly posed by the slip flow dominates this influence and the contribution of viscosity correction factor is the smallest and thus can be ignored—and that widely distributed nonlocal parameter,unfortunately,impairs the reliability of theoretical prediction.(3)With carbon nanotube conveying flow analyzed using differential Eringen nonlocal model,the inconsistency of nonlocal effects under various boundary conditions is firstly discovered.Two main problems confronting differential Eringen nonlocal model,i.e.,the wide distribution of nonlocal parameter caused by dispute and cantilever paradox,are discussed.Then both Galerkin method and wave method are employed to gain eigenfrequencies of nanobeams under various values of nonlocal parameter,which verifies that both methods can capture the so-called cantilever paradox.And therefore,both are applied to obtain the eigenfrequency of carbon nanotube conveying flow.The results convince us that nonlocal effect can not only enhance the softening effect of inside flow on the structure but also change the stiffness of nanotube,of which,while the former effect is consistent under all four considered boundary conditions,the latter,however,is different under clamped-free boundary condition from those under the other boundary conditions.(4)A local/nonlocal elasticity model is introduced,for the first time,into the model of nanotube conveying flow,to solve the inconsistency of nonlocal effects in various boundary conditions.The derived integro-differential governing equation is transformed into a differential one together with two supplementary boundary conditions.Based on the principle of wave method,the solving format is obtained.And it can be concluded that phase parameters and nonlocal parameter are the two types of parameters that independently determine the nonlocal effect,if phase parameters are out of the neighborhoods of their limit value.Nonlocal effect consistently softens the nanotube and enhances the softening effect of inside flow on the structure under whichever considered boundary condition. |
